text
stringlengths 4
2.77k
| input_ids
sequencelengths 3
510
| attention_mask
sequencelengths 3
510
| labels
sequencelengths 3
510
| ner_tags
sequencelengths 3
510
| tokens
sequencelengths 3
510
| paper_name
stringclasses 80
values | __index_level_0__
int64 0
2.08k
|
---|---|---|---|---|---|---|---|
aviors [22]β[26]. In addition, Sharples and
Domingue proposed a blockchain-based permanent distributed
record of intellectual effort which instantiates and democra-
tises educational reputation beyond the academic communi-
ty [27]. In [28], authors proposed a new blockchain-based fair
payment to study the cyber physical system (CPS), in which
reputation system is applied such that a subscriber evaluate
the published event and mark the publisher based on the
reputation.
In this paper, we propose a new rep | [
10828,
10209,
113,
3969,
17355,
1403,
119,
127,
114,
119,
1135,
1110,
1145,
2602,
1115,
1103,
12478,
1785,
1104,
1103,
5244,
10296,
11934,
1383,
1118,
1103,
4528,
2618,
13974,
1103,
2905,
7143,
1104,
5463,
13546,
119,
1109,
1167,
9483,
1103,
5244,
2469,
26440,
1110,
117,
1103,
2299,
1103,
7143,
7881,
119,
159,
119,
18732,
15517,
2162,
13329,
24805,
1708,
1109,
5244,
14235,
2011,
1107,
1142,
2526,
1110,
170,
3843,
2109,
6978,
117,
1134,
1169,
6187,
10205,
14248,
3209,
19450,
1120,
1103,
2674,
1105,
3843,
19450,
1121,
4577,
1103,
5463,
4528,
119,
1109,
5244,
23896,
5822,
10255,
1110,
170,
11432,
6978,
1106,
4959,
2480,
1103,
13418,
1107,
1103,
5463,
4528,
1138,
10478,
18764,
1204,
170,
9705,
4894,
118,
27466,
2707,
4658,
119,
1650,
11892,
1103,
5244,
118,
1359,
6978,
1195,
2011,
117,
13418,
6613,
1106,
7345,
5463,
1111,
2299,
15664,
6245,
1105,
4444,
5515,
170,
10923,
1113,
6111,
1352,
119,
1130,
1142,
2526,
117,
1195,
17794,
170,
5244,
118,
1359,
6978,
1115,
17233,
12478,
13418,
1106,
2317,
12051,
119,
4737,
1160,
10540,
1104,
5244,
1114,
14235,
12890,
21517,
1105,
23896,
5822,
1358,
118,
1120,
1988,
10099,
117,
1103,
9228,
1104,
1103,
4193,
1104,
10478,
18764,
1204,
13418,
1110,
11519,
2788,
119,
1792,
1106,
1103,
5244,
118,
1359,
6978,
1195,
3000,
117,
1103,
4528,
2618,
10802,
8247,
1116,
1344,
118,
3068,
13418,
117,
1134,
1110,
1304,
16250,
1106,
1103,
1718,
1104,
1103,
2113,
2528,
1394,
1449,
119,
155,
14663,
9637,
11680,
10954,
1708,
164,
122,
166,
156,
119,
11896,
1968,
12610,
117,
107,
27400,
2528,
1394,
131,
138,
8536,
118,
1106,
118,
8536,
4828,
5948,
1449,
117,
107,
2061,
11594,
117,
1369,
119,
18630,
131,
120,
120,
2113,
2528,
1394,
119,
8916,
120,
2113,
2528,
1394,
119,
185,
1181,
2087,
164,
123,
166,
157,
119,
150,
1665,
1658,
7637,
5084,
1183,
117,
3084,
2393,
119,
117,
107,
2562,
7147,
1394,
2137,
2064,
131,
170,
188,
7867,
1895,
3510,
7147,
1394,
8539,
117,
107,
1446,
119,
18630,
131,
120,
120,
7001,
119,
1992,
7147,
24704,
1830,
119,
3254,
120,
1653,
26311,
120,
1992,
7147,
24704,
1830,
118,
1653,
26311,
119,
185,
1181,
2087,
164,
124,
166,
162,
119,
13049,
117,
1105,
143,
119,
7014,
117,
107,
8093,
7147,
1394,
131,
1109,
1352,
1104,
1103,
1893,
1105,
2174,
14652,
117,
107,
2173,
1161,
24842,
1161,
14009,
4578,
113,
1922,
114,
117,
10857,
119,
3565,
117,
1185,
119,
125,
117,
4329,
119,
3615,
1475,
118,
3927,
1527,
117,
1446,
119,
164,
125,
166,
153,
119,
15324,
117,
156,
119,
5329,
117,
162,
119,
27901,
4553,
117,
1105,
147,
119,
1670,
117,
107,
12120,
2050,
2064,
6726,
25264,
131,
170,
4901,
3510,
7147,
4935,
118,
1359,
5343,
19416,
2249,
4220,
1111,
146,
1186,
1942,
6379,
117,
107,
16206,
3291,
6262,
3488,
119,
7085,
1403,
119,
117,
10857,
3731,
117,
1185,
119,
130,
117,
4329,
119,
5603,
118,
4859,
117,
1504,
119,
164,
126,
166,
162,
119,
9132,
117,
155,
119,
14760,
1403,
117,
147,
119,
23274,
117,
148,
119,
8772,
117,
1105,
141,
119,
23673,
117,
107,
157,
25370,
2036,
131,
3496,
13849,
2501,
12565,
3403
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
14,
14,
0,
0,
1,
2,
2,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
14,
14,
0,
0,
1,
2,
2,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"upward",
"trend",
"(",
"See",
"Fi",
"##g",
".",
"6",
")",
".",
"It",
"is",
"also",
"shown",
"that",
"the",
"rational",
"##ity",
"of",
"the",
"reputation",
"admission",
"parameters",
"set",
"by",
"the",
"pool",
"manager",
"affects",
"the",
"overall",
"revenue",
"of",
"mining",
"pools",
".",
"The",
"more",
"reasonable",
"the",
"reputation",
"access",
"criterion",
"is",
",",
"the",
"higher",
"the",
"revenue",
"receives",
".",
"V",
".",
"CO",
"##NC",
"##L",
"##US",
"##ION",
"##S",
"The",
"reputation",
"interval",
"designed",
"in",
"this",
"paper",
"is",
"a",
"prevent",
"##ive",
"mechanism",
",",
"which",
"can",
"disc",
"##rim",
"##inate",
"potential",
"attackers",
"at",
"the",
"source",
"and",
"prevent",
"attackers",
"from",
"joining",
"the",
"mining",
"pool",
".",
"The",
"reputation",
"flu",
"##ct",
"##uation",
"is",
"a",
"detection",
"mechanism",
"to",
"determine",
"whether",
"the",
"miners",
"in",
"the",
"mining",
"pool",
"have",
"dish",
"##ones",
"##t",
"a",
"##gg",
"##res",
"-",
"si",
"##ve",
"behavior",
".",
"By",
"applying",
"the",
"reputation",
"-",
"based",
"mechanism",
"we",
"designed",
",",
"miners",
"tend",
"to",
"honest",
"mining",
"for",
"higher",
"accumulated",
"benefits",
"and",
"ultimately",
"achieve",
"a",
"consensus",
"on",
"stable",
"state",
".",
"In",
"this",
"paper",
",",
"we",
"propose",
"a",
"reputation",
"-",
"based",
"mechanism",
"that",
"encourages",
"rational",
"miners",
"to",
"mine",
"honestly",
".",
"Through",
"two",
"evaluation",
"of",
"reputation",
"with",
"interval",
"est",
"##imation",
"and",
"flu",
"##ct",
"##u",
"-",
"at",
"##ion",
"measuring",
",",
"the",
"judgment",
"of",
"the",
"identity",
"of",
"dish",
"##ones",
"##t",
"miners",
"is",
"basically",
"realized",
".",
"According",
"to",
"the",
"reputation",
"-",
"based",
"mechanism",
"we",
"proposed",
",",
"the",
"pool",
"manager",
"strictly",
"select",
"##s",
"high",
"-",
"quality",
"miners",
",",
"which",
"is",
"very",
"beneficial",
"to",
"the",
"development",
"of",
"the",
"bit",
"##co",
"##in",
"system",
".",
"R",
"##EF",
"##ER",
"##EN",
"##CE",
"##S",
"[",
"1",
"]",
"S",
".",
"Na",
"##ka",
"##moto",
",",
"\"",
"Bit",
"##co",
"##in",
":",
"A",
"peer",
"-",
"to",
"-",
"peer",
"electronic",
"cash",
"system",
",",
"\"",
"White",
"Paper",
",",
"2008",
".",
"https",
":",
"/",
"/",
"bit",
"##co",
"##in",
".",
"org",
"/",
"bit",
"##co",
"##in",
".",
"p",
"##d",
"##f",
"[",
"2",
"]",
"T",
".",
"M",
"##c",
"##C",
"##ona",
"##gh",
"##y",
",",
"et",
"al",
".",
",",
"\"",
"Big",
"##cha",
"##in",
"##D",
"##B",
":",
"a",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"database",
",",
"\"",
"2016",
".",
"https",
":",
"/",
"/",
"www",
".",
"big",
"##cha",
"##ind",
"##b",
".",
"com",
"/",
"white",
"##paper",
"/",
"big",
"##cha",
"##ind",
"##b",
"-",
"white",
"##paper",
".",
"p",
"##d",
"##f",
"[",
"3",
"]",
"Y",
".",
"Yuan",
",",
"and",
"F",
".",
"Wang",
",",
"\"",
"Block",
"##cha",
"##in",
":",
"The",
"state",
"of",
"the",
"art",
"and",
"future",
"trends",
",",
"\"",
"Act",
"##a",
"Automatic",
"##a",
"Sin",
"##ica",
"(",
"Chinese",
")",
",",
"vol",
".",
"42",
",",
"no",
".",
"4",
",",
"pp",
".",
"48",
"##1",
"-",
"49",
"##4",
",",
"2016",
".",
"[",
"4",
"]",
"P",
".",
"Sharma",
",",
"S",
".",
"Singh",
",",
"Y",
".",
"Je",
"##ong",
",",
"and",
"J",
".",
"Park",
",",
"\"",
"Di",
"##st",
"##B",
"##lock",
"##Net",
":",
"a",
"distributed",
"block",
"##cha",
"##ins",
"-",
"based",
"secure",
"SD",
"##N",
"architecture",
"for",
"I",
"##o",
"##T",
"networks",
",",
"\"",
"IEEE",
"Co",
"##mm",
"##un",
".",
"Ma",
"##g",
".",
",",
"vol",
"55",
",",
"no",
".",
"9",
",",
"pp",
".",
"78",
"-",
"85",
",",
"2017",
".",
"[",
"5",
"]",
"Y",
".",
"Zhang",
",",
"R",
".",
"Den",
"##g",
",",
"J",
".",
"Shu",
",",
"K",
".",
"Yang",
",",
"and",
"D",
".",
"Zheng",
",",
"\"",
"T",
"##KS",
"##E",
":",
"trust",
"##worthy",
"key",
"##word",
"search"
] | Incentivizing Honest Mining in Blockchain Networks A Reputation Approach | 100 |
utation-based mecha-
nism to incentivize miners to conduct honest mining, thereby
promote the efficient of bitcoin system. Specifically, we first
describe the system model in term of PoW-based blockchain
network, where miners present some malicious behaviors
during the mining process. We then design a reputation mech-
1549-7747 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.htm | [
1166,
4035,
1665,
1616,
15514,
2233,
1114,
1160,
118,
1334,
1396,
2047,
18771,
5474,
2258,
3510,
7147,
1394,
117,
107,
16206,
11737,
117,
10857,
119,
127,
117,
4329,
119,
18333,
1559,
1559,
118,
18333,
1604,
1559,
117,
1857,
119,
164,
127,
166,
138,
119,
3180,
1182,
117,
145,
119,
140,
5082,
18917,
3822,
1377,
117,
162,
119,
13872,
117,
153,
119,
1249,
1358,
4426,
11848,
117,
140,
119,
6291,
25925,
152,
2571,
1324,
117,
1105,
163,
119,
3477,
117,
107,
8093,
7147,
1394,
118,
1359,
9652,
2501,
2635,
1111,
1119,
25710,
27054,
2285,
9998,
6312,
2344,
117,
107,
16206,
4639,
7149,
147,
119,
117,
10857,
119,
125,
117,
1185,
119,
127,
117,
4329,
119,
10022,
118,
9869,
117,
1504,
119,
164,
128,
166,
162,
119,
16749,
117,
162,
119,
5255,
117,
154,
119,
19569,
117,
139,
119,
8772,
117,
1105,
162,
119,
10684,
117,
107,
22087,
22712,
11030,
118,
4841,
131,
3510,
7147,
1394,
118,
1359,
4652,
7727,
1114,
5244,
1111,
10682,
172,
1183,
3169,
2952,
2344,
117,
107,
16206,
11737,
117,
10857,
119,
127,
117,
4329,
119,
13381,
1580,
1571,
118,
13414,
1568,
1495,
117,
1857,
119,
164,
129,
166,
163,
119,
23673,
117,
156,
119,
20802,
1162,
117,
145,
119,
23084,
117,
161,
119,
8742,
117,
1105,
145,
119,
7014,
117,
107,
1760,
24431,
1104,
3510,
7147,
1394,
2815,
131,
4220,
117,
10923,
117,
1105,
2174,
14652,
117,
107,
1107,
1504,
16206,
1130,
1204,
119,
16752,
1403,
1197,
119,
2562,
7154,
117,
17652,
117,
145,
2240,
117,
3066,
117,
4329,
119,
3731,
1559,
118,
4376,
1527,
117,
12865,
119,
1512,
118,
1476,
117,
1504,
119,
164,
130,
166,
143,
119,
157,
9022,
3864,
1732,
1105,
139,
119,
20452,
4638,
10232,
4119,
117,
107,
27400,
2528,
1394,
1105,
2894,
131,
170,
4301,
5980,
1113,
11858,
4412,
2200,
3539,
16408,
11604,
9885,
117,
107,
16206,
3291,
6262,
3488,
119,
8157,
1116,
17037,
2145,
119,
117,
10857,
119,
1407,
117,
1185,
119,
124,
117,
4329,
119,
19980,
1527,
118,
19538,
1495,
117,
1446,
119,
164,
1275,
166,
140,
119,
10215,
117,
163,
119,
8772,
117,
163,
119,
23673,
117,
163,
119,
8742,
117,
1105,
161,
119,
5255,
117,
107,
12504,
1105,
25161,
1104,
1342,
4267,
23397,
1107,
18959,
2924,
10923,
9932,
117,
107,
2173,
1161,
24842,
1161,
14009,
4578,
113,
1922,
114,
117,
10857,
119,
3887,
117,
1185,
119,
130,
117,
4329,
119,
15722,
1568,
118,
17777,
1475,
117,
1504,
119,
164,
1429,
166,
146,
119,
3096,
25918,
117,
140,
119,
2499,
117,
138,
119,
12107,
1584,
10659,
1182,
117,
1105,
150,
119,
24580,
7355,
117,
107,
5096,
10008,
1104,
3246,
131,
4252,
118,
6613,
1158,
27400,
2528,
1394,
112,
188,
6777,
1104,
1250,
2258,
6777,
1104,
8219,
117,
107,
9690,
2107,
156,
23413,
14424,
23313,
9741,
1708,
117,
10857,
119,
3565,
117,
1185,
119,
124,
117,
4329,
119,
3236,
118,
3413,
117,
1387,
119,
164,
1367,
166,
162,
119,
148,
16732,
117,
141,
119,
4246,
117,
162,
119,
6913,
117,
142,
119,
159,
11192,
14170,
117,
1105,
162,
119,
4246,
117,
107,
4108,
15589,
1105,
3644,
4267,
23397,
1116,
131
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"over",
"en",
"##c",
"##ry",
"##pted",
"data",
"with",
"two",
"-",
"side",
"ve",
"##ri",
"##fia",
"##bility",
"via",
"block",
"##cha",
"##in",
",",
"\"",
"IEEE",
"Access",
",",
"vol",
".",
"6",
",",
"pp",
".",
"310",
"##7",
"##7",
"-",
"310",
"##8",
"##7",
",",
"2018",
".",
"[",
"6",
"]",
"A",
".",
"Le",
"##i",
",",
"H",
".",
"C",
"##ru",
"##icks",
"##han",
"##k",
",",
"Y",
".",
"Cao",
",",
"P",
".",
"As",
"##u",
"##q",
"##uo",
",",
"C",
".",
"Any",
"##igor",
"O",
"##ga",
"##h",
",",
"and",
"Z",
".",
"Sun",
",",
"\"",
"Block",
"##cha",
"##in",
"-",
"based",
"dynamic",
"key",
"management",
"for",
"he",
"##tero",
"##gene",
"##ous",
"intelligent",
"transportation",
"systems",
",",
"\"",
"IEEE",
"Internet",
"Things",
"J",
".",
",",
"vol",
".",
"4",
",",
"no",
".",
"6",
",",
"pp",
".",
"1832",
"-",
"1843",
",",
"2017",
".",
"[",
"7",
"]",
"Y",
".",
"Zhao",
",",
"Y",
".",
"Li",
",",
"Q",
".",
"Mu",
",",
"B",
".",
"Yang",
",",
"and",
"Y",
".",
"Yu",
",",
"\"",
"Se",
"##cure",
"pub",
"-",
"sub",
":",
"block",
"##cha",
"##in",
"-",
"based",
"fair",
"payment",
"with",
"reputation",
"for",
"reliable",
"c",
"##y",
"##ber",
"physical",
"systems",
",",
"\"",
"IEEE",
"Access",
",",
"vol",
".",
"6",
",",
"pp",
".",
"122",
"##9",
"##5",
"-",
"123",
"##0",
"##3",
",",
"2018",
".",
"[",
"8",
"]",
"Z",
".",
"Zheng",
",",
"S",
".",
"Xi",
"##e",
",",
"H",
".",
"Dai",
",",
"X",
".",
"Chen",
",",
"and",
"H",
".",
"Wang",
",",
"\"",
"An",
"overview",
"of",
"block",
"##cha",
"##in",
"technology",
":",
"architecture",
",",
"consensus",
",",
"and",
"future",
"trends",
",",
"\"",
"in",
"2017",
"IEEE",
"In",
"##t",
".",
"Con",
"##g",
"##r",
".",
"Big",
"Data",
",",
"Honolulu",
",",
"H",
"##I",
",",
"USA",
",",
"pp",
".",
"55",
"##7",
"-",
"56",
"##4",
",",
"Jun",
".",
"25",
"-",
"30",
",",
"2017",
".",
"[",
"9",
"]",
"F",
".",
"T",
"##sch",
"##ors",
"##ch",
"and",
"B",
".",
"Sc",
"##he",
"##uer",
"##mann",
",",
"\"",
"Bit",
"##co",
"##in",
"and",
"beyond",
":",
"a",
"technical",
"survey",
"on",
"decent",
"##ral",
"##ized",
"digital",
"cu",
"##rre",
"##ncies",
",",
"\"",
"IEEE",
"Co",
"##mm",
"##un",
".",
"Survey",
"##s",
"Tu",
"##ts",
".",
",",
"vol",
".",
"18",
",",
"no",
".",
"3",
",",
"pp",
".",
"208",
"##4",
"-",
"212",
"##3",
",",
"2016",
".",
"[",
"10",
"]",
"C",
".",
"Tang",
",",
"Z",
".",
"Yang",
",",
"Z",
".",
"Zheng",
",",
"Z",
".",
"Chen",
",",
"and",
"X",
".",
"Li",
",",
"\"",
"Analysis",
"and",
"optimization",
"of",
"game",
"di",
"##lemma",
"in",
"Po",
"##W",
"consensus",
"algorithm",
",",
"\"",
"Act",
"##a",
"Automatic",
"##a",
"Sin",
"##ica",
"(",
"Chinese",
")",
",",
"vol",
".",
"43",
",",
"no",
".",
"9",
",",
"pp",
".",
"152",
"##0",
"-",
"153",
"##1",
",",
"2017",
".",
"[",
"11",
"]",
"I",
".",
"Ben",
"##tov",
",",
"C",
".",
"Lee",
",",
"A",
".",
"Mi",
"##z",
"##rah",
"##i",
",",
"and",
"M",
".",
"Rosen",
"##feld",
",",
"\"",
"Pro",
"##of",
"of",
"activity",
":",
"ex",
"-",
"tend",
"##ing",
"Bit",
"##co",
"##in",
"'",
"s",
"proof",
"of",
"work",
"via",
"proof",
"of",
"stake",
",",
"\"",
"AC",
"##M",
"S",
"##IG",
"##ME",
"##TR",
"##IC",
"##S",
",",
"vol",
".",
"42",
",",
"no",
".",
"3",
",",
"pp",
".",
"34",
"-",
"37",
",",
"2014",
".",
"[",
"12",
"]",
"Y",
".",
"K",
"##won",
",",
"D",
".",
"Kim",
",",
"Y",
".",
"Son",
",",
"E",
".",
"V",
"##ass",
"##erman",
",",
"and",
"Y",
".",
"Kim",
",",
"\"",
"Be",
"selfish",
"and",
"avoid",
"di",
"##lemma",
"##s",
":"
] | Incentivizing Honest Mining in Blockchain Networks A Reputation Approach | 101 |
l for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCSII.2019.2901746, IEEE
Transactions on Circuits and Systems II: Express Briefs
2
anism based on the interval estimation and the fluctuation of
reputation to incentive the honest mining for miners, in which
the reputation depends on the historical evaluation. We find
that the pool manage | [
13097,
1170,
1114,
20139,
113,
6820,
2924,
114,
3690,
1113,
2113,
2528,
1394,
117,
107,
1107,
5096,
1665,
119,
1504,
9690,
2107,
156,
23413,
8055,
1658,
16752,
2087,
119,
6701,
1105,
6345,
4354,
117,
5043,
117,
2245,
117,
3066,
117,
4329,
119,
18500,
118,
21040,
117,
14125,
119,
1476,
118,
14152,
119,
124,
117,
1504,
119,
164,
1492,
166,
148,
119,
11896,
2315,
1377,
117,
156,
119,
9392,
117,
138,
119,
3902,
117,
1105,
142,
119,
14104,
117,
107,
1457,
10354,
7107,
5463,
131,
5565,
1197,
118,
2393,
4404,
15589,
5463,
1105,
12459,
1114,
1126,
22623,
2035,
117,
107,
1107,
1446,
16206,
1735,
156,
17162,
1643,
119,
4354,
1105,
153,
2047,
2497,
3457,
117,
17784,
1813,
27824,
1424,
117,
1860,
117,
4329,
119,
22289,
118,
14116,
117,
9751,
119,
1626,
118,
1572,
117,
1446,
119,
164,
1489,
166,
162,
119,
20802,
1161,
1105,
141,
119,
2404,
117,
107,
13704,
20727,
1104,
2703,
4909,
6379,
117,
107,
16206,
13809,
119,
7887,
1116,
156,
6834,
1204,
119,
117,
1563,
117,
16409,
1643,
119,
139,
24683,
1116,
117,
10857,
119,
3731,
117,
1185,
119,
122,
117,
4329,
119,
2625,
118,
5691,
117,
1369,
119,
164,
1405,
166,
146,
119,
142,
18543,
117,
107,
1109,
2317,
1197,
112,
188,
4267,
23397,
117,
107,
1107,
5096,
1665,
119,
1410,
16206,
156,
17162,
1643,
119,
4354,
1105,
153,
2047,
2497,
3457,
117,
1727,
7438,
117,
8784,
117,
3066,
117,
4329,
119,
5840,
118,
9550,
117,
1318,
1542,
118,
1626,
117,
1410,
119,
164,
1479,
166,
156,
119,
18757,
1403,
117,
156,
119,
155,
1358,
3361,
117,
1105,
148,
119,
26364,
1182,
117,
107,
27400,
2528,
1394,
3510,
1114,
20139,
2035,
131,
3622,
1105,
26410,
13499,
2116,
117,
107,
16206,
13809,
119,
1130,
2087,
119,
1370,
5026,
4724,
4354,
117,
10857,
119,
1367,
117,
1185,
119,
129,
117,
4329,
119,
2573,
118,
2406,
117,
1504,
119,
164,
1542,
166,
141,
148,
119,
1706,
2737,
117,
3084,
2393,
119,
117,
107,
4354,
14755,
1104,
3510,
7147,
1394,
7180,
1114,
3622,
1104,
3510,
1114,
20139,
2035,
117,
107,
1107,
5096,
1665,
119,
4815,
16206,
120,
9690,
2107,
1130,
1204,
119,
156,
17162,
1643,
119,
140,
23225,
117,
11804,
1105,
144,
10132,
20463,
117,
6331,
117,
2722,
117,
4329,
119,
2532,
1604,
118,
3993,
1559,
117,
1318,
1489,
118,
1542,
117,
1504,
119,
164,
1407,
166,
150,
119,
157,
119,
2750,
10886,
117,
107,
21902,
10522,
9044,
14975,
1106,
11552,
18661,
1107,
1263,
118,
1858,
8866,
3254,
19675,
1116,
117,
107,
15840,
1197,
119,
3291,
8223,
3818,
119,
20452,
1182,
119,
117,
10857,
119,
1969,
1604,
117,
1185,
119,
113,
123,
118,
124,
114,
117,
4329,
119,
22690,
118,
21606,
117,
1369,
119,
164,
1627,
166,
147,
119,
138,
119,
148,
10747,
117,
146,
119,
140,
119,
22618,
117,
1105,
142,
119,
160,
119,
11907,
26929,
117,
107,
1109,
8142,
1104,
27400,
2528,
1394,
5463,
1137,
117,
27400,
2528,
1394,
1107,
1103,
2915,
1104,
8050,
10704,
5927,
117,
107,
1109,
157,
7921,
9654,
1582,
16350,
1113,
1103,
7525,
1104,
4219,
4354,
113,
160,
27514,
1708,
1381,
114,
117,
1994,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"fork",
"after",
"with",
"##holding",
"(",
"FA",
"##W",
")",
"attacks",
"on",
"bit",
"##co",
"##in",
",",
"\"",
"in",
"Pro",
"##c",
".",
"2017",
"AC",
"##M",
"S",
"##IG",
"##SA",
"##C",
"Con",
"##f",
".",
"Computer",
"and",
"Communications",
"Security",
",",
"Dallas",
",",
"Texas",
",",
"USA",
",",
"pp",
".",
"195",
"-",
"209",
",",
"Oct",
".",
"30",
"-",
"Nov",
".",
"3",
",",
"2017",
".",
"[",
"13",
"]",
"K",
".",
"Na",
"##ya",
"##k",
",",
"S",
".",
"Kumar",
",",
"A",
".",
"Miller",
",",
"and",
"E",
".",
"Shi",
",",
"\"",
"St",
"##ub",
"##born",
"mining",
":",
"gene",
"##r",
"-",
"al",
"##izing",
"selfish",
"mining",
"and",
"combining",
"with",
"an",
"eclipse",
"attack",
",",
"\"",
"in",
"2016",
"IEEE",
"European",
"S",
"##ym",
"##p",
".",
"Security",
"and",
"P",
"##ri",
"##va",
"##cy",
",",
"Sa",
"##ar",
"##bruck",
"##en",
",",
"Germany",
",",
"pp",
".",
"305",
"-",
"320",
",",
"Mar",
".",
"21",
"-",
"24",
",",
"2016",
".",
"[",
"14",
"]",
"Y",
".",
"Xi",
"##a",
"and",
"D",
".",
"Hill",
",",
"\"",
"Attack",
"vulnerability",
"of",
"complex",
"communication",
"networks",
",",
"\"",
"IEEE",
"Trans",
".",
"Circuit",
"##s",
"S",
"##ys",
"##t",
".",
",",
"II",
",",
"Ex",
"##p",
".",
"B",
"##rief",
"##s",
",",
"vol",
".",
"55",
",",
"no",
".",
"1",
",",
"pp",
".",
"65",
"-",
"69",
",",
"2008",
".",
"[",
"15",
"]",
"I",
".",
"E",
"##yal",
",",
"\"",
"The",
"mine",
"##r",
"'",
"s",
"di",
"##lemma",
",",
"\"",
"in",
"Pro",
"##c",
".",
"2015",
"IEEE",
"S",
"##ym",
"##p",
".",
"Security",
"and",
"P",
"##ri",
"##va",
"##cy",
",",
"San",
"Jose",
",",
"CA",
",",
"USA",
",",
"pp",
".",
"89",
"-",
"103",
",",
"May",
"17",
"-",
"21",
",",
"2015",
".",
"[",
"16",
"]",
"S",
".",
"Ba",
"##g",
",",
"S",
".",
"R",
"##u",
"##j",
",",
"and",
"K",
".",
"Sakura",
"##i",
",",
"\"",
"Bit",
"##co",
"##in",
"block",
"with",
"##holding",
"attack",
":",
"analysis",
"and",
"mit",
"##iga",
"##tion",
",",
"\"",
"IEEE",
"Trans",
".",
"In",
"##f",
".",
"For",
"##ens",
"##ics",
"Security",
",",
"vol",
".",
"12",
",",
"no",
".",
"8",
",",
"pp",
".",
"1967",
"-",
"1978",
",",
"2017",
".",
"[",
"17",
"]",
"D",
"K",
".",
"To",
"##sh",
",",
"et",
"al",
".",
",",
"\"",
"Security",
"implications",
"of",
"block",
"##cha",
"##in",
"cloud",
"with",
"analysis",
"of",
"block",
"with",
"##holding",
"attack",
",",
"\"",
"in",
"Pro",
"##c",
".",
"17th",
"IEEE",
"/",
"AC",
"##M",
"In",
"##t",
".",
"S",
"##ym",
"##p",
".",
"C",
"##luster",
",",
"Cloud",
"and",
"G",
"##rid",
"Computing",
",",
"Madrid",
",",
"Spain",
",",
"pp",
".",
"45",
"##8",
"-",
"46",
"##7",
",",
"May",
"14",
"-",
"17",
",",
"2017",
".",
"[",
"18",
"]",
"M",
".",
"T",
".",
"Good",
"##rich",
",",
"\"",
"Pi",
"##pel",
"##ined",
"algorithms",
"to",
"detect",
"cheating",
"in",
"long",
"-",
"term",
"grid",
"com",
"##putation",
"##s",
",",
"\"",
"Theo",
"##r",
".",
"Co",
"##mp",
"##ut",
".",
"Sc",
"##i",
".",
",",
"vol",
".",
"40",
"##8",
",",
"no",
".",
"(",
"2",
"-",
"3",
")",
",",
"pp",
".",
"199",
"-",
"207",
",",
"2008",
".",
"[",
"19",
"]",
"J",
".",
"A",
".",
"K",
"##roll",
",",
"I",
".",
"C",
".",
"Davey",
",",
"and",
"E",
".",
"W",
".",
"Fe",
"##lten",
",",
"\"",
"The",
"economics",
"of",
"Bit",
"##co",
"##in",
"mining",
"or",
",",
"Bit",
"##co",
"##in",
"in",
"the",
"presence",
"of",
"ad",
"##vers",
"##aries",
",",
"\"",
"The",
"T",
"##we",
"##lf",
"##th",
"Workshop",
"on",
"the",
"Economics",
"of",
"Information",
"Security",
"(",
"W",
"##EI",
"##S",
"2013",
")",
",",
"Washington",
","
] | Incentivizing Honest Mining in Blockchain Networks A Reputation Approach | 102 |
r strictly selects high-quality miners based
on the reputation mechanism we proposed, which contributes
understanding for PoW consensus algorithm and provides a
new method to explore the bitcoin system.
II. SYSTEM MODEL AND REPUTATION MECHANISM
A. System Model
Consider a PoW-based blockchain network with J individ-
ual miners, which organize themselves into I mining pools
in solving a crypto-puzzle competition to win the reward.
According to the Nakamoto Consensus protocol [1], only the
pool which acco | [
5227,
117,
12865,
119,
1429,
118,
1367,
117,
1381,
119,
18630,
131,
120,
120,
7001,
119,
174,
7235,
1394,
14467,
2217,
1665,
119,
8916,
120,
12406,
120,
1195,
1548,
10973,
17668,
120,
4580,
120,
148,
10747,
2137,
8308,
1183,
2271,
1883,
5208,
2924,
27514,
1708,
10973,
17668,
119,
185,
1181,
2087,
164,
1406,
166,
146,
119,
142,
18543,
1105,
142,
119,
2203,
1200,
117,
107,
23670,
1110,
1136,
1536,
131,
27400,
2528,
1394,
5463,
1110,
8018,
117,
107,
3291,
6262,
3488,
119,
9690,
2107,
117,
10857,
119,
5391,
117,
1185,
119,
128,
117,
4329,
119,
4573,
118,
9081,
117,
1857,
119,
164,
1626,
166,
139,
119,
2921,
117,
138,
119,
5976,
1584,
1968,
117,
147,
119,
15161,
27752,
5700,
117,
150,
119,
159,
6530,
1377,
1105,
157,
119,
4673,
117,
107,
3497,
118,
1103,
4474,
2941,
3622,
1104,
23232,
1186,
1708,
3690,
1222,
2113,
2528,
1394,
5463,
13546,
117,
107,
1130,
131,
155,
119,
139,
19593,
18208,
1162,
117,
150,
119,
139,
5123,
2511,
117,
157,
119,
4673,
117,
150,
119,
2159,
113,
14625,
119,
114,
117,
7748,
15586,
6451,
9543,
1105,
7154,
4354,
117,
4329,
119,
5117,
118,
5942,
117,
3206,
117,
17880,
131,
18919,
117,
1387,
119,
164,
1659,
166,
163,
119,
7014,
117,
149,
119,
7014,
117,
163,
119,
162,
119,
23845,
1105,
140,
119,
162,
119,
20802,
1161,
117,
107,
1130,
6732,
3384,
5244,
14710,
1103,
7243,
1104,
7395,
1107,
15442,
1934,
4267,
23397,
1638,
117,
107,
153,
2162,
1186,
1708,
1141,
117,
10857,
119,
128,
117,
1185,
119,
128,
117,
1893,
119,
1185,
119,
131,
174,
12882,
18202,
1604,
117,
1368,
119,
164,
1695,
166,
162,
119,
20802,
1161,
1105,
141,
119,
2404,
117,
107,
138,
9652,
12418,
5800,
112,
188,
18311,
15942,
1107,
2703,
3254,
13601,
118,
11437,
14520,
6379,
117,
107,
16206,
13809,
119,
7887,
1116,
156,
6834,
1204,
119,
1563,
117,
16409,
1643,
119,
139,
24683,
1116,
117,
10857,
119,
2539,
117,
1185,
119,
124,
117,
4329,
119,
19639,
118,
20039,
117,
1381,
119,
164,
1572,
166,
145,
119,
20164,
117,
160,
119,
10684,
117,
144,
119,
23158,
117,
154,
119,
17584,
1389,
117,
1105,
147,
119,
13872,
117,
107,
6750,
22184,
1372,
10923,
1104,
4321,
118,
3677,
2344,
1107,
1103,
7395,
118,
2208,
2443,
117,
107,
16206,
13809,
119,
7887,
1116,
156,
6834,
1204,
119,
146,
117,
23287,
119,
19023,
117,
10857,
119,
5519,
117,
1185,
119,
1429,
117,
4329,
119,
20022,
1545,
118,
21355,
1559,
117,
1446,
119,
164,
1512,
166,
144,
119,
23880,
7702,
1105,
140,
119,
27368,
23107,
117,
107,
146,
26318,
18415,
1104,
3496,
1105,
5244,
2635,
1111,
1714,
118,
187,
27303,
5093,
3677,
2699,
117,
107,
16206,
156,
6834,
1204,
119,
147,
119,
117,
10857,
119,
130,
117,
1185,
119,
123,
117,
4329,
119,
3731,
1545,
118,
4376,
1545,
117,
1410,
119,
164,
1744,
166,
145,
119,
26197,
117,
162,
119,
12221,
117,
148,
119,
17784,
20488,
117,
1105,
163,
119,
5255,
117,
107,
13832,
3822,
4869,
1884,
24960,
1988,
1231,
5053,
7174,
3633,
1107,
5244,
2344,
117,
107,
16206,
13809,
119,
23994,
4838,
1233,
12120
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"DC",
",",
"Jun",
".",
"11",
"-",
"12",
",",
"2013",
".",
"https",
":",
"/",
"/",
"www",
".",
"e",
"##con",
"##in",
"##fo",
"##se",
"##c",
".",
"org",
"/",
"archive",
"/",
"we",
"##is",
"##20",
"##13",
"/",
"papers",
"/",
"K",
"##roll",
"##D",
"##ave",
"##y",
"##F",
"##el",
"##ten",
"##W",
"##EI",
"##S",
"##20",
"##13",
".",
"p",
"##d",
"##f",
"[",
"20",
"]",
"I",
".",
"E",
"##yal",
"and",
"E",
".",
"Sir",
"##er",
",",
"\"",
"Majority",
"is",
"not",
"enough",
":",
"Bit",
"##co",
"##in",
"mining",
"is",
"vulnerable",
",",
"\"",
"Co",
"##mm",
"##un",
".",
"AC",
"##M",
",",
"vol",
".",
"61",
",",
"no",
".",
"7",
",",
"pp",
".",
"95",
"-",
"102",
",",
"2018",
".",
"[",
"21",
"]",
"B",
".",
"Johnson",
",",
"A",
".",
"Las",
"##z",
"##ka",
",",
"J",
".",
"Gross",
"##kla",
"##gs",
",",
"M",
".",
"V",
"##ase",
"##k",
"and",
"T",
".",
"Moore",
",",
"\"",
"Game",
"-",
"the",
"##ore",
"##tic",
"analysis",
"of",
"DD",
"##o",
"##S",
"attacks",
"against",
"bit",
"##co",
"##in",
"mining",
"pools",
",",
"\"",
"In",
":",
"R",
".",
"B",
"##ΓΆ",
"##hm",
"##e",
",",
"M",
".",
"B",
"##ren",
"##ner",
",",
"T",
".",
"Moore",
",",
"M",
".",
"Smith",
"(",
"eds",
".",
")",
",",
"Financial",
"Cry",
"##pt",
"##ography",
"and",
"Data",
"Security",
",",
"pp",
".",
"72",
"-",
"86",
",",
"Berlin",
",",
"Heidelberg",
":",
"Springer",
",",
"2014",
".",
"[",
"22",
"]",
"Z",
".",
"Wang",
",",
"L",
".",
"Wang",
",",
"Z",
".",
"Y",
".",
"Yin",
"and",
"C",
".",
"Y",
".",
"Xi",
"##a",
",",
"\"",
"In",
"##fer",
"##ring",
"reputation",
"promotes",
"the",
"evolution",
"of",
"cooperation",
"in",
"spatial",
"social",
"di",
"##lemma",
"games",
",",
"\"",
"P",
"##L",
"##o",
"##S",
"one",
",",
"vol",
".",
"7",
",",
"no",
".",
"7",
",",
"art",
".",
"no",
".",
":",
"e",
"##40",
"##21",
"##8",
",",
"2012",
".",
"[",
"23",
"]",
"Y",
".",
"Xi",
"##a",
"and",
"D",
".",
"Hill",
",",
"\"",
"A",
"dynamic",
"bra",
"##ess",
"'",
"s",
"para",
"##dox",
"in",
"complex",
"com",
"##mu",
"-",
"ni",
"##cation",
"networks",
",",
"\"",
"IEEE",
"Trans",
".",
"Circuit",
"##s",
"S",
"##ys",
"##t",
".",
"II",
",",
"Ex",
"##p",
".",
"B",
"##rief",
"##s",
",",
"vol",
".",
"60",
",",
"no",
".",
"3",
",",
"pp",
".",
"172",
"-",
"176",
",",
"2013",
".",
"[",
"24",
"]",
"H",
".",
"Hu",
",",
"W",
".",
"Yu",
",",
"G",
".",
"Wen",
",",
"Q",
".",
"Xu",
"##an",
",",
"and",
"J",
".",
"Cao",
",",
"\"",
"Rev",
"##erse",
"group",
"consensus",
"of",
"multi",
"-",
"agent",
"systems",
"in",
"the",
"cooperation",
"-",
"competition",
"network",
",",
"\"",
"IEEE",
"Trans",
".",
"Circuit",
"##s",
"S",
"##ys",
"##t",
".",
"I",
",",
"Reg",
".",
"Papers",
",",
"vol",
".",
"63",
",",
"no",
".",
"11",
",",
"pp",
".",
"203",
"##6",
"-",
"204",
"##7",
",",
"2016",
".",
"[",
"25",
"]",
"G",
".",
"Gee",
"##tha",
"and",
"C",
".",
"Jaya",
"##kumar",
",",
"\"",
"I",
"##mple",
"##mentation",
"of",
"trust",
"and",
"reputation",
"management",
"for",
"free",
"-",
"r",
"##oaming",
"mobile",
"agent",
"security",
",",
"\"",
"IEEE",
"S",
"##ys",
"##t",
".",
"J",
".",
",",
"vol",
".",
"9",
",",
"no",
".",
"2",
",",
"pp",
".",
"55",
"##6",
"-",
"56",
"##6",
",",
"2015",
".",
"[",
"26",
"]",
"H",
".",
"Shen",
",",
"Y",
".",
"Lin",
",",
"K",
".",
"Sa",
"##pra",
",",
"and",
"Z",
".",
"Li",
",",
"\"",
"En",
"##han",
"##cing",
"co",
"##llus",
"##ion",
"re",
"##si",
"##lie",
"##nce",
"in",
"reputation",
"systems",
",",
"\"",
"IEEE",
"Trans",
".",
"Para",
"##lle",
"##l",
"Di"
] | Incentivizing Honest Mining in Blockchain Networks A Reputation Approach | 103 |
mplishes the PoW firstly will be rewarded.
Therefore, we pay our attention to the payoff of miners in the
target pool. Define the strategy set of miners as S = | [
2050,
2047,
1830,
119,
156,
6834,
1204,
119,
117,
10857,
119,
1765,
117,
1185,
119,
129,
117,
4329,
119,
23689,
1527,
118,
24618,
1559,
117,
1446,
119,
164,
1765,
166,
150,
119,
13319,
2897,
1105,
147,
119,
16727,
1158,
4175,
117,
107,
1109,
3510,
7147,
1394,
1105,
180,
18109,
1116,
131,
138,
4901,
1449,
1111,
4339,
1647,
117,
5244,
1105,
10703,
117,
107,
1130,
131,
159,
1200,
7488,
148,
119,
117,
13319,
2897,
150,
119,
117,
148,
2858,
7925,
18308,
1813,
157,
119,
113,
14625,
119,
114,
117,
19222,
6451,
2109,
1105,
19222,
21919,
2165,
9681,
117,
24705,
1306,
117,
4507,
131,
18919,
119,
164,
1743,
166,
162,
119,
16749,
117,
3084,
2393,
119,
117,
107,
22087,
22712,
11030,
118,
4841,
131,
8093,
7147,
1394,
118,
1359,
4652,
7727,
1114,
5244,
1111,
10682,
172,
1183,
3169,
2952,
2344,
117,
107,
16206,
11737,
117,
10857,
119,
127,
117,
4329,
119,
13381,
1580,
1571,
118,
13414,
1568,
1495,
117,
1857,
119
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
7,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
7,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##st",
"##ri",
"##b",
".",
"S",
"##ys",
"##t",
".",
",",
"vol",
".",
"27",
",",
"no",
".",
"8",
",",
"pp",
".",
"227",
"##4",
"-",
"228",
"##7",
",",
"2016",
".",
"[",
"27",
"]",
"M",
".",
"Sharp",
"##les",
"and",
"J",
".",
"Dom",
"##ing",
"##ue",
",",
"\"",
"The",
"block",
"##cha",
"##in",
"and",
"k",
"##udo",
"##s",
":",
"A",
"distributed",
"system",
"for",
"educational",
"record",
",",
"reputation",
"and",
"reward",
",",
"\"",
"In",
":",
"V",
"##er",
"##bert",
"K",
".",
",",
"Sharp",
"##les",
"M",
".",
",",
"K",
"##lo",
"##bu",
"##Δ",
"##ar",
"T",
".",
"(",
"eds",
".",
")",
",",
"Ada",
"##pt",
"##ive",
"and",
"Ada",
"##pta",
"##ble",
"Learning",
",",
"Cha",
"##m",
",",
"Switzerland",
":",
"Springer",
".",
"[",
"28",
"]",
"Y",
".",
"Zhao",
",",
"et",
"al",
".",
",",
"\"",
"Se",
"##cure",
"pub",
"-",
"sub",
":",
"Block",
"##cha",
"##in",
"-",
"based",
"fair",
"payment",
"with",
"reputation",
"for",
"reliable",
"c",
"##y",
"##ber",
"physical",
"systems",
",",
"\"",
"IEEE",
"Access",
",",
"vol",
".",
"6",
",",
"pp",
".",
"122",
"##9",
"##5",
"-",
"123",
"##0",
"##3",
",",
"2018",
"."
] | Incentivizing Honest Mining in Blockchain Networks A Reputation Approach | 104 |
State of the Art and Challenges Facing Consensus
Protocols on Blockchain
Nutthakorn Chalaemwongwan
Information Science and Technology
Mahanakorn University of Technology
Bangkok, Thailand
[email protected]
Werasak Kurutach
Information Science and Technology
Mahanakorn University of Technology
Bangkok, Thailand
[email protected]
AbstractβNowadays, the blockchain is a favorite platform,
for instance, for use with cryptocurrency, smart contracts, IoT,
and | [
1426,
1104,
1103,
2051,
1105,
6571,
1116,
143,
18715,
16752,
3792,
14410,
17580,
1116,
1113,
8093,
7147,
1394,
151,
25131,
21893,
8456,
24705,
1742,
5521,
16732,
1403,
5491,
4219,
2444,
1105,
3529,
7085,
17013,
26989,
1179,
1239,
1104,
3529,
12829,
117,
5872,
22664,
7702,
26989,
1179,
119,
172,
137,
7121,
7235,
21032,
119,
1884,
119,
24438,
1284,
7297,
3715,
23209,
5082,
1777,
1732,
4219,
2444,
1105,
3529,
7085,
17013,
26989,
1179,
1239,
1104,
3529,
12829,
117,
5872,
1195,
7297,
3715,
137,
182,
3818,
119,
170,
1665,
119,
24438,
138,
4832,
15017,
783,
25883,
117,
1103,
3510,
7147,
1394,
1110,
170,
5095,
3482,
117,
1111,
5374,
117,
1111,
1329,
1114,
5354,
6451,
13335,
2149,
5123,
3457,
117,
6866,
8216,
117,
146,
1186,
1942,
117,
1105,
1177,
5275,
119,
8093,
7147,
4935,
1132,
4901,
21340,
1733,
1115,
9396,
3512,
1150,
1202,
1136,
3496,
1296,
1168,
1106,
4731,
2231,
119,
1109,
3512,
5340,
1113,
1103,
3796,
117,
4718,
117,
1105,
19160,
1104,
1103,
2231,
119,
1109,
3510,
7147,
1394,
12175,
1103,
10923,
11309,
1106,
23073,
1103,
3510,
1134,
1110,
23099,
1103,
2443,
14372,
119,
16752,
3792,
14410,
1144,
1242,
5660,
1216,
1112,
117,
1111,
1859,
117,
8377,
1704,
2463,
117,
5096,
10008,
1104,
1250,
117,
1105,
5096,
10008,
1104,
8219,
119,
1438,
117,
1175,
1138,
1136,
1151,
2567,
4580,
1115,
1138,
10510,
3622,
1114,
7328,
1106,
1672,
5402,
117,
1105,
1134,
1138,
4572,
1103,
10156,
14940,
1112,
5806,
1106,
1103,
4048,
119,
1130,
1142,
2526,
117,
1195,
1138,
2136,
170,
4301,
1396,
12231,
3189,
1114,
7328,
1106,
1103,
10923,
9932,
1678,
1121,
2166,
1844,
119,
1109,
3703,
1209,
3531,
170,
10923,
11309,
117,
1105,
1103,
9932,
3417,
19774,
1116,
1103,
4048,
1106,
1801,
1134,
3482,
1110,
5806,
1118,
10761,
1103,
14372,
4193,
117,
2308,
7740,
1105,
1103,
21073,
1181,
1540,
1104,
1103,
8050,
10704,
3113,
117,
1103,
2233,
2235,
117,
1846,
117,
7581,
117,
4048,
117,
1105,
5136,
119,
4428,
117,
1195,
3146,
1118,
11124,
1317,
1844,
7768,
1114,
7328,
1106,
1103,
10923,
11309,
119,
7443,
15573,
131,
3510,
7147,
1394,
132,
10923,
132,
4901,
21340,
1197,
132,
4901,
10923,
132,
10923,
14975,
146,
119,
15969,
23313,
15609,
21986,
21669,
11414,
138,
21340,
1197,
1110,
170,
4148,
8297,
1134,
2075,
1126,
2802,
1647,
1104,
14409,
119,
1370,
5374,
117,
170,
21340,
1197,
1209,
1647,
14409,
1206,
1317,
2595,
5482,
117,
1137,
4817,
10476,
1114,
1227,
3512,
119,
1760,
7631,
1104,
3510,
7147,
4935,
1110,
1115,
1103,
21340,
1197,
1110,
16498,
1906,
3665,
1113,
1593,
1155,
1103,
15029,
119,
9841,
117,
14409,
1132,
8968,
1154,
5511,
117,
1173,
25953,
1106,
1141,
1330,
119,
6589,
117,
1103,
4901,
21340,
1197,
1110,
170,
16498,
1906,
25337,
1178,
2233,
8297,
119,
138,
3510,
7147,
1394,
3471,
1114,
1103,
3288,
2231,
117,
1229,
1103,
21340,
1197,
3002,
1155,
1103,
1607,
1104,
1103,
16547,
7791,
119,
138,
5531,
11653,
4901,
21340,
1733,
1180,
1705,
6120,
1172,
1107,
2538,
1104,
1210,
5402,
119,
113,
138,
14566,
8355,
117,
1249,
9388,
117,
1105,
3291,
1394,
114,
119,
7245,
117,
1103,
4048,
1687,
1113,
1103,
1499,
1104,
1103,
21340,
1197,
23497,
1103
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"State",
"of",
"the",
"Art",
"and",
"Challenge",
"##s",
"F",
"##acing",
"Con",
"##sen",
"##sus",
"Protocol",
"##s",
"on",
"Block",
"##cha",
"##in",
"N",
"##utt",
"##hak",
"##orn",
"Cha",
"##la",
"##em",
"##won",
"##g",
"##wan",
"Information",
"Science",
"and",
"Technology",
"Ma",
"##hana",
"##kor",
"##n",
"University",
"of",
"Technology",
"Bangkok",
",",
"Thailand",
"nut",
"##tha",
"##kor",
"##n",
".",
"c",
"@",
"monster",
"##con",
"##nect",
".",
"co",
".",
"th",
"We",
"##ras",
"##ak",
"Ku",
"##ru",
"##ta",
"##ch",
"Information",
"Science",
"and",
"Technology",
"Ma",
"##hana",
"##kor",
"##n",
"University",
"of",
"Technology",
"Bangkok",
",",
"Thailand",
"we",
"##ras",
"##ak",
"@",
"m",
"##ut",
".",
"a",
"##c",
".",
"th",
"A",
"##bs",
"##tract",
"β",
"Nowadays",
",",
"the",
"block",
"##cha",
"##in",
"is",
"a",
"favorite",
"platform",
",",
"for",
"instance",
",",
"for",
"use",
"with",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
",",
"smart",
"contracts",
",",
"I",
"##o",
"##T",
",",
"and",
"so",
"forth",
".",
"Block",
"##cha",
"##ins",
"are",
"distributed",
"ledge",
"##rs",
"that",
"enable",
"parties",
"who",
"do",
"not",
"trust",
"each",
"other",
"to",
"maintain",
"states",
".",
"The",
"parties",
"agree",
"on",
"the",
"existence",
",",
"values",
",",
"and",
"histories",
"of",
"the",
"states",
".",
"The",
"block",
"##cha",
"##in",
"applies",
"the",
"consensus",
"protocol",
"to",
"verify",
"the",
"block",
"which",
"is",
"distributing",
"the",
"network",
"node",
".",
"Con",
"##sen",
"##sus",
"has",
"many",
"practices",
"such",
"as",
",",
"for",
"example",
",",
"Byzantine",
"general",
"problem",
",",
"Pro",
"##of",
"of",
"work",
",",
"and",
"Pro",
"##of",
"of",
"stake",
".",
"However",
",",
"there",
"have",
"not",
"been",
"numerous",
"papers",
"that",
"have",
"undertaken",
"analysis",
"with",
"regard",
"to",
"various",
"aspects",
",",
"and",
"which",
"have",
"incorporated",
"the",
"adoption",
"summary",
"as",
"appropriate",
"to",
"the",
"application",
".",
"In",
"this",
"paper",
",",
"we",
"have",
"provided",
"a",
"technical",
"ve",
"##rification",
"review",
"with",
"regard",
"to",
"the",
"consensus",
"algorithm",
"taken",
"from",
"previous",
"research",
".",
"The",
"audience",
"will",
"receive",
"a",
"consensus",
"protocol",
",",
"and",
"the",
"algorithm",
"typically",
"analyze",
"##s",
"the",
"application",
"to",
"match",
"which",
"platform",
"is",
"appropriate",
"by",
"viewing",
"the",
"node",
"identity",
",",
"energy",
"saving",
"and",
"the",
"tolerate",
"##d",
"power",
"of",
"the",
"ad",
"##vers",
"##ary",
",",
"the",
"data",
"model",
",",
"language",
",",
"execution",
",",
"application",
",",
"and",
"examples",
".",
"Finally",
",",
"we",
"finish",
"by",
"presenting",
"several",
"research",
"directions",
"with",
"regard",
"to",
"the",
"consensus",
"protocol",
".",
"Key",
"##words",
":",
"block",
"##cha",
"##in",
";",
"consensus",
";",
"distributed",
"ledge",
"##r",
";",
"distributed",
"consensus",
";",
"consensus",
"algorithms",
"I",
".",
"IN",
"##TR",
"##OD",
"##UC",
"##TI",
"##ON",
"A",
"ledge",
"##r",
"is",
"a",
"documentary",
"framework",
"which",
"includes",
"an",
"ordered",
"record",
"of",
"transactions",
".",
"For",
"instance",
",",
"a",
"ledge",
"##r",
"will",
"record",
"transactions",
"between",
"several",
"commercial",
"banks",
",",
"or",
"goods",
"exchanged",
"with",
"known",
"parties",
".",
"An",
"aspect",
"of",
"block",
"##cha",
"##ins",
"is",
"that",
"the",
"ledge",
"##r",
"is",
"replica",
"##ted",
"entirely",
"on",
"almost",
"all",
"the",
"nodes",
".",
"Moreover",
",",
"transactions",
"are",
"assembled",
"into",
"blocks",
",",
"then",
"chained",
"to",
"one",
"another",
".",
"Therefore",
",",
"the",
"distributed",
"ledge",
"##r",
"is",
"a",
"replica",
"##ted",
"attach",
"only",
"data",
"framework",
".",
"A",
"block",
"##cha",
"##in",
"begins",
"with",
"the",
"initial",
"states",
",",
"while",
"the",
"ledge",
"##r",
"records",
"all",
"the",
"history",
"of",
"the",
"revision",
"procedure",
".",
"A",
"technique",
"encouraging",
"distributed",
"ledge",
"##rs",
"could",
"class",
"##ify",
"them",
"in",
"terms",
"of",
"three",
"aspects",
".",
"(",
"A",
"##cco",
"##unt",
",",
"As",
"##set",
",",
"and",
"Co",
"##in",
")",
".",
"Initially",
",",
"the",
"application",
"created",
"on",
"the",
"top",
"of",
"the",
"ledge",
"##r",
"establishes",
"the"
] | State of the art and challenges facing consensus p | 105 |
State of the Art and Challenges Facing Consensus
Protocols on Blockchain
Nutthakorn Chalaemwongwan
Information Science and Technology
Mahanakorn University of Technology
Bangkok, Thailand
[email protected]
Werasak Kurutach
Information Science and Technology
Mahanakorn University of Technology
Bangkok, Thailand
[email protected]
AbstractβNowadays, the blockchain is a favorite platform,
for instance, for use with cryptocurrency, smart contracts, IoT,
and | [
1426,
1104,
1103,
2051,
1105,
6571,
1116,
143,
18715,
16752,
3792,
14410,
17580,
1116,
1113,
8093,
7147,
1394,
151,
25131,
21893,
8456,
24705,
1742,
5521,
16732,
1403,
5491,
4219,
2444,
1105,
3529,
7085,
17013,
26989,
1179,
1239,
1104,
3529,
12829,
117,
5872,
22664,
7702,
26989,
1179,
119,
172,
137,
7121,
7235,
21032,
119,
1884,
119,
24438,
1284,
7297,
3715,
23209,
5082,
1777,
1732,
4219,
2444,
1105,
3529,
7085,
17013,
26989,
1179,
1239,
1104,
3529,
12829,
117,
5872,
1195,
7297,
3715,
137,
182,
3818,
119,
170,
1665,
119,
24438,
138,
4832,
15017,
783,
25883,
117,
1103,
3510,
7147,
1394,
1110,
170,
5095,
3482,
117,
1111,
5374,
117,
1111,
1329,
1114,
5354,
6451,
13335,
2149,
5123,
3457,
117,
6866,
8216,
117,
146,
1186,
1942,
117,
1105,
1177,
5275,
119,
8093,
7147,
4935,
1132,
4901,
21340,
1733,
1115,
9396,
3512,
1150,
1202,
1136,
3496,
1296,
1168,
1106,
4731,
2231,
119,
1109,
3512,
5340,
1113,
1103,
3796,
117,
4718,
117,
1105,
19160,
1104,
1103,
2231,
119,
1109,
3510,
7147,
1394,
12175,
1103,
10923,
11309,
1106,
23073,
1103,
3510,
1134,
1110,
23099,
1103,
2443,
14372,
119,
16752,
3792,
14410,
1144,
1242,
5660,
1216,
1112,
117,
1111,
1859,
117,
8377,
1704,
2463,
117,
5096,
10008,
1104,
1250,
117,
1105,
5096,
10008,
1104,
8219,
119,
1438,
117,
1175,
1138,
1136,
1151,
2567,
4580,
1115,
1138,
10510,
3622,
1114,
7328,
1106,
1672,
5402,
117,
1105,
1134,
1138,
4572,
1103,
10156,
14940,
1112,
5806,
1106,
1103,
4048,
119,
1130,
1142,
2526,
117,
1195,
1138,
2136,
170,
4301,
1396,
12231,
3189,
1114,
7328,
1106,
1103,
10923,
9932,
1678,
1121,
2166,
1844,
119,
1109,
3703,
1209,
3531,
170,
10923,
11309,
117,
1105,
1103,
9932,
3417,
19774,
1116,
1103,
4048,
1106,
1801,
1134,
3482,
1110,
5806,
1118,
10761,
1103,
14372,
4193,
117,
2308,
7740,
1105,
1103,
21073,
1181,
1540,
1104,
1103,
8050,
10704,
3113,
117,
1103,
2233,
2235,
117,
1846,
117,
7581,
117,
4048,
117,
1105,
5136,
119,
4428,
117,
1195,
3146,
1118,
11124,
1317,
1844,
7768,
1114,
7328,
1106,
1103,
10923,
11309,
119,
7443,
15573,
131,
3510,
7147,
1394,
132,
10923,
132,
4901,
21340,
1197,
132,
4901,
10923,
132,
10923,
14975,
146,
119,
15969,
23313,
15609,
21986,
21669,
11414,
138,
21340,
1197,
1110,
170,
4148,
8297,
1134,
2075,
1126,
2802,
1647,
1104,
14409,
119,
1370,
5374,
117,
170,
21340,
1197,
1209,
1647,
14409,
1206,
1317,
2595,
5482,
117,
1137,
4817,
10476,
1114,
1227,
3512,
119,
1760,
7631,
1104,
3510,
7147,
4935,
1110,
1115,
1103,
21340,
1197,
1110,
16498,
1906,
3665,
1113,
1593,
1155,
1103,
15029,
119,
9841,
117,
14409,
1132,
8968,
1154,
5511,
117,
1173,
25953,
1106,
1141,
1330,
119,
6589,
117,
1103,
4901,
21340,
1197,
1110,
170,
16498,
1906,
25337,
1178,
2233,
8297,
119,
138,
3510,
7147,
1394,
3471,
1114,
1103,
3288,
2231,
117,
1229,
1103,
21340,
1197,
3002,
1155,
1103,
1607,
1104,
1103,
16547,
7791,
119,
138,
5531,
11653,
4901,
21340,
1733,
1180,
1705,
6120,
1172,
1107,
2538,
1104,
1210,
5402,
119,
113,
138,
14566,
8355,
117,
1249,
9388,
117,
1105,
3291,
1394,
114,
119,
7245,
117,
1103,
4048,
1687,
1113,
1103,
1499,
1104,
1103,
21340,
1197,
23497,
1103
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"State",
"of",
"the",
"Art",
"and",
"Challenge",
"##s",
"F",
"##acing",
"Con",
"##sen",
"##sus",
"Protocol",
"##s",
"on",
"Block",
"##cha",
"##in",
"N",
"##utt",
"##hak",
"##orn",
"Cha",
"##la",
"##em",
"##won",
"##g",
"##wan",
"Information",
"Science",
"and",
"Technology",
"Ma",
"##hana",
"##kor",
"##n",
"University",
"of",
"Technology",
"Bangkok",
",",
"Thailand",
"nut",
"##tha",
"##kor",
"##n",
".",
"c",
"@",
"monster",
"##con",
"##nect",
".",
"co",
".",
"th",
"We",
"##ras",
"##ak",
"Ku",
"##ru",
"##ta",
"##ch",
"Information",
"Science",
"and",
"Technology",
"Ma",
"##hana",
"##kor",
"##n",
"University",
"of",
"Technology",
"Bangkok",
",",
"Thailand",
"we",
"##ras",
"##ak",
"@",
"m",
"##ut",
".",
"a",
"##c",
".",
"th",
"A",
"##bs",
"##tract",
"β",
"Nowadays",
",",
"the",
"block",
"##cha",
"##in",
"is",
"a",
"favorite",
"platform",
",",
"for",
"instance",
",",
"for",
"use",
"with",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
",",
"smart",
"contracts",
",",
"I",
"##o",
"##T",
",",
"and",
"so",
"forth",
".",
"Block",
"##cha",
"##ins",
"are",
"distributed",
"ledge",
"##rs",
"that",
"enable",
"parties",
"who",
"do",
"not",
"trust",
"each",
"other",
"to",
"maintain",
"states",
".",
"The",
"parties",
"agree",
"on",
"the",
"existence",
",",
"values",
",",
"and",
"histories",
"of",
"the",
"states",
".",
"The",
"block",
"##cha",
"##in",
"applies",
"the",
"consensus",
"protocol",
"to",
"verify",
"the",
"block",
"which",
"is",
"distributing",
"the",
"network",
"node",
".",
"Con",
"##sen",
"##sus",
"has",
"many",
"practices",
"such",
"as",
",",
"for",
"example",
",",
"Byzantine",
"general",
"problem",
",",
"Pro",
"##of",
"of",
"work",
",",
"and",
"Pro",
"##of",
"of",
"stake",
".",
"However",
",",
"there",
"have",
"not",
"been",
"numerous",
"papers",
"that",
"have",
"undertaken",
"analysis",
"with",
"regard",
"to",
"various",
"aspects",
",",
"and",
"which",
"have",
"incorporated",
"the",
"adoption",
"summary",
"as",
"appropriate",
"to",
"the",
"application",
".",
"In",
"this",
"paper",
",",
"we",
"have",
"provided",
"a",
"technical",
"ve",
"##rification",
"review",
"with",
"regard",
"to",
"the",
"consensus",
"algorithm",
"taken",
"from",
"previous",
"research",
".",
"The",
"audience",
"will",
"receive",
"a",
"consensus",
"protocol",
",",
"and",
"the",
"algorithm",
"typically",
"analyze",
"##s",
"the",
"application",
"to",
"match",
"which",
"platform",
"is",
"appropriate",
"by",
"viewing",
"the",
"node",
"identity",
",",
"energy",
"saving",
"and",
"the",
"tolerate",
"##d",
"power",
"of",
"the",
"ad",
"##vers",
"##ary",
",",
"the",
"data",
"model",
",",
"language",
",",
"execution",
",",
"application",
",",
"and",
"examples",
".",
"Finally",
",",
"we",
"finish",
"by",
"presenting",
"several",
"research",
"directions",
"with",
"regard",
"to",
"the",
"consensus",
"protocol",
".",
"Key",
"##words",
":",
"block",
"##cha",
"##in",
";",
"consensus",
";",
"distributed",
"ledge",
"##r",
";",
"distributed",
"consensus",
";",
"consensus",
"algorithms",
"I",
".",
"IN",
"##TR",
"##OD",
"##UC",
"##TI",
"##ON",
"A",
"ledge",
"##r",
"is",
"a",
"documentary",
"framework",
"which",
"includes",
"an",
"ordered",
"record",
"of",
"transactions",
".",
"For",
"instance",
",",
"a",
"ledge",
"##r",
"will",
"record",
"transactions",
"between",
"several",
"commercial",
"banks",
",",
"or",
"goods",
"exchanged",
"with",
"known",
"parties",
".",
"An",
"aspect",
"of",
"block",
"##cha",
"##ins",
"is",
"that",
"the",
"ledge",
"##r",
"is",
"replica",
"##ted",
"entirely",
"on",
"almost",
"all",
"the",
"nodes",
".",
"Moreover",
",",
"transactions",
"are",
"assembled",
"into",
"blocks",
",",
"then",
"chained",
"to",
"one",
"another",
".",
"Therefore",
",",
"the",
"distributed",
"ledge",
"##r",
"is",
"a",
"replica",
"##ted",
"attach",
"only",
"data",
"framework",
".",
"A",
"block",
"##cha",
"##in",
"begins",
"with",
"the",
"initial",
"states",
",",
"while",
"the",
"ledge",
"##r",
"records",
"all",
"the",
"history",
"of",
"the",
"revision",
"procedure",
".",
"A",
"technique",
"encouraging",
"distributed",
"ledge",
"##rs",
"could",
"class",
"##ify",
"them",
"in",
"terms",
"of",
"three",
"aspects",
".",
"(",
"A",
"##cco",
"##unt",
",",
"As",
"##set",
",",
"and",
"Co",
"##in",
")",
".",
"Initially",
",",
"the",
"application",
"created",
"on",
"the",
"top",
"of",
"the",
"ledge",
"##r",
"establishes",
"the"
] | State of the art and challenges facing consensus p | 106 |
so forth. Blockchains are distributed ledgers that enable
parties who do not trust each other to maintain states. The
parties agree on the existence, values, and histories of the states.
The blockchain applies the consensus protocol to verify the block
which is distributing the network node. Consensus has many
practices such as, for example, Byzantine general problem, Proof
of work, and Proof of stake. However, there have not been
numerous papers that have undertaken analysis with regard to | [
1869,
3665,
1107,
1216,
170,
1236,
1112,
1106,
1712,
1439,
1103,
21340,
1197,
138,
5354,
6451,
13335,
2149,
5123,
3457,
4048,
1209,
1329,
1106,
2561,
170,
4795,
3300,
1861,
1106,
1115,
1276,
1107,
7228,
9339,
119,
1109,
6247,
1110,
1115,
1122,
1110,
3014,
1106,
3076,
1105,
6058,
170,
2211,
1634,
2235,
1216,
1112,
1126,
1859,
1952,
1137,
170,
3607,
2860,
1112,
3025,
119,
2307,
117,
1103,
8458,
1449,
1547,
1138,
1141,
1137,
2299,
21340,
1733,
1134,
1169,
5088,
1106,
1141,
1330,
119,
138,
1415,
10614,
117,
1111,
5374,
117,
1336,
1138,
2967,
21340,
1733,
117,
1141,
1111,
1451,
2853,
1216,
1112,
3752,
117,
3813,
117,
3880,
4129,
117,
2653,
10747,
117,
1105,
1177,
5275,
119,
4428,
117,
21340,
1197,
6224,
1169,
23896,
5822,
20043,
5409,
1121,
1217,
5490,
3665,
1106,
1103,
1470,
1106,
1217,
5733,
2374,
1118,
1141,
14031,
119,
27400,
2528,
1394,
117,
1111,
5374,
117,
1108,
2756,
1105,
117,
1112,
170,
1871,
117,
2228,
1234,
1341,
1115,
1122,
1110,
18372,
1106,
4959,
1150,
1209,
11984,
1103,
1470,
21340,
1197,
119,
19585,
12298,
164,
122,
166,
3073,
2007,
27084,
1199,
5032,
1150,
14878,
1103,
1470,
21340,
1197,
2566,
1118,
5321,
1147,
8250,
1106,
1103,
5511,
119,
1109,
1869,
4049,
1107,
1103,
21340,
1197,
17798,
1103,
1607,
1104,
14409,
1146,
1106,
1103,
1954,
1159,
1194,
1103,
3510,
7147,
1394,
119,
3725,
20388,
1106,
1103,
21340,
1197,
1431,
1129,
9635,
1174,
1106,
1118,
1451,
14031,
119,
21325,
117,
1317,
6635,
1444,
1106,
5340,
1114,
170,
10923,
119,
152,
4832,
1200,
3970,
1134,
1122,
1110,
1336,
1136,
1129,
1103,
2820,
1276,
1107,
15696,
1842,
118,
1362,
4683,
1216,
1112,
170,
20497,
2980,
3539,
10202,
117,
1118,
1134,
170,
1423,
9127,
113,
174,
119,
176,
119,
117,
170,
3085,
1137,
170,
1433,
114,
6771,
1113,
1103,
15549,
119,
1109,
4495,
1104,
170,
3510,
7147,
1394,
5564,
1110,
2140,
1217,
1682,
1106,
2239,
1114,
1343,
15029,
1115,
1202,
1136,
3496,
1684,
1487,
117,
7713,
1134,
10986,
1547,
6297,
1107,
8377,
4698,
1785,
119,
1109,
10923,
11309,
14007,
2993,
1106,
19646,
8377,
2645,
119,
1109,
1844,
5336,
170,
5980,
1113,
10923,
1108,
8232,
117,
1105,
1175,
1132,
2567,
3827,
1104,
2331,
6315,
19755,
1115,
1138,
1151,
7227,
1111,
3510,
7147,
4935,
164,
123,
166,
119,
1636,
1180,
1129,
22429,
1107,
2538,
1104,
1147,
3490,
2079,
119,
3278,
2246,
18809,
5031,
2923,
1104,
9308,
3254,
19675,
118,
1359,
19755,
1107,
1134,
1103,
4713,
17573,
6777,
1104,
3254,
19675,
1106,
1525,
170,
14372,
1115,
170,
26281,
2875,
22190,
5264,
17579,
1103,
1397,
2805,
119,
27400,
2528,
1394,
112,
188,
5096,
10008,
1104,
1250,
113,
18959,
2924,
114,
1110,
170,
3014,
1859,
1104,
1103,
10923,
119,
1109,
1168,
5199,
1132,
9308,
4909,
118,
1359,
19755,
1111,
1134,
15029,
1138,
9901,
3667,
1105,
1576,
1194,
1317,
5720,
1104,
4909,
1106,
5515,
10923,
119,
1398,
19755,
117,
153,
18890,
8377,
143,
14045,
1706,
2879,
3923,
113,
153,
26447,
1942,
114,
164,
124,
166,
1217,
1103,
1436,
17011,
117,
1132,
3666,
1107,
2440,
25209,
1272,
1152,
1321,
16047,
2913,
15029,
119,
1130,
1103,
2243,
117,
1155,
3714,
1116,
1195,
1525,
3216
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
4,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
5,
6,
6,
6,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
4,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
5,
6,
6,
6,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"information",
"entirely",
"in",
"such",
"a",
"way",
"as",
"to",
"keep",
"within",
"the",
"ledge",
"##r",
"A",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"application",
"will",
"use",
"to",
"create",
"a",
"user",
"account",
"similar",
"to",
"that",
"found",
"in",
"conventional",
"banking",
".",
"The",
"intention",
"is",
"that",
"it",
"is",
"simple",
"to",
"build",
"and",
"apply",
"a",
"lower",
"level",
"model",
"such",
"as",
"an",
"example",
"table",
"or",
"a",
"critical",
"value",
"as",
"mentioned",
".",
"Second",
",",
"the",
"functional",
"system",
"might",
"have",
"one",
"or",
"higher",
"ledge",
"##rs",
"which",
"can",
"link",
"to",
"one",
"another",
".",
"A",
"large",
"enterprise",
",",
"for",
"instance",
",",
"may",
"have",
"multiple",
"ledge",
"##rs",
",",
"one",
"for",
"every",
"department",
"such",
"as",
"engineering",
",",
"sales",
",",
"supply",
"chain",
",",
"pay",
"##roll",
",",
"and",
"so",
"forth",
".",
"Finally",
",",
"ledge",
"##r",
"possession",
"can",
"flu",
"##ct",
"##uate",
"significantly",
"from",
"being",
"exposed",
"entirely",
"to",
"the",
"public",
"to",
"being",
"totally",
"managed",
"by",
"one",
"participant",
".",
"Bit",
"##co",
"##in",
",",
"for",
"instance",
",",
"was",
"presented",
"and",
",",
"as",
"a",
"result",
",",
"makes",
"people",
"think",
"that",
"it",
"is",
"costly",
"to",
"determine",
"who",
"will",
"update",
"the",
"public",
"ledge",
"##r",
".",
"Pa",
"##rity",
"[",
"1",
"]",
"pre",
"##de",
"##fines",
"some",
"owners",
"who",
"adjust",
"the",
"public",
"ledge",
"##r",
"simply",
"by",
"adding",
"their",
"signature",
"to",
"the",
"blocks",
".",
"The",
"information",
"contained",
"in",
"the",
"ledge",
"##r",
"demonstrates",
"the",
"history",
"of",
"transactions",
"up",
"to",
"the",
"current",
"time",
"through",
"the",
"block",
"##cha",
"##in",
".",
"Up",
"##dates",
"to",
"the",
"ledge",
"##r",
"should",
"be",
"consent",
"##ed",
"to",
"by",
"every",
"participant",
".",
"Specifically",
",",
"several",
"participants",
"need",
"to",
"agree",
"with",
"a",
"consensus",
".",
"O",
"##bs",
"##er",
"##ving",
"which",
"it",
"is",
"may",
"not",
"be",
"the",
"situation",
"found",
"in",
"countless",
"real",
"-",
"world",
"applications",
"such",
"as",
"a",
"fi",
"##at",
"digital",
"currency",
",",
"by",
"which",
"a",
"single",
"entity",
"(",
"e",
".",
"g",
".",
",",
"a",
"bank",
"or",
"a",
"government",
")",
"decides",
"on",
"the",
"updates",
".",
"The",
"importance",
"of",
"a",
"block",
"##cha",
"##in",
"strategy",
"is",
"actually",
"being",
"able",
"to",
"deal",
"with",
"those",
"nodes",
"that",
"do",
"not",
"trust",
"working",
"together",
",",
"indicating",
"which",
"variables",
"might",
"respond",
"in",
"Byzantine",
"formal",
"##ity",
".",
"The",
"consensus",
"protocol",
"consequently",
"needs",
"to",
"endure",
"Byzantine",
"problems",
".",
"The",
"research",
"involving",
"a",
"survey",
"on",
"consensus",
"was",
"comprehensive",
",",
"and",
"there",
"are",
"numerous",
"versions",
"of",
"previously",
"recommended",
"protocols",
"that",
"have",
"been",
"manufactured",
"for",
"block",
"##cha",
"##ins",
"[",
"2",
"]",
".",
"These",
"could",
"be",
"categorized",
"in",
"terms",
"of",
"their",
"combined",
"range",
".",
"Over",
"##w",
"##hel",
"##ming",
"consists",
"of",
"solely",
"com",
"##putation",
"-",
"based",
"protocols",
"in",
"which",
"the",
"users",
"utilize",
"proof",
"of",
"com",
"##putation",
"to",
"find",
"a",
"node",
"that",
"a",
"##rb",
"##it",
"##rar",
"##ily",
"determines",
"the",
"next",
"operation",
".",
"Bit",
"##co",
"##in",
"'",
"s",
"Pro",
"##of",
"of",
"work",
"(",
"Po",
"##W",
")",
"is",
"a",
"simple",
"example",
"of",
"the",
"consensus",
".",
"The",
"other",
"severe",
"are",
"solely",
"communication",
"-",
"based",
"protocols",
"for",
"which",
"nodes",
"have",
"matching",
"votes",
"and",
"run",
"through",
"several",
"rounds",
"of",
"communication",
"to",
"achieve",
"consensus",
".",
"All",
"protocols",
",",
"P",
"##ractical",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"(",
"P",
"##BF",
"##T",
")",
"[",
"3",
"]",
"being",
"the",
"best",
"illustration",
",",
"are",
"applied",
"in",
"particular",
"configurations",
"because",
"they",
"take",
"authentic",
"##ated",
"nodes",
".",
"In",
"the",
"middle",
",",
"all",
"opposite",
"##s",
"we",
"find",
"mixed"
] | State of the art and challenges facing consensus p | 107 |
so forth. Blockchains are distributed ledgers that enable
parties who do not trust each other to maintain states. The
parties agree on the existence, values, and histories of the states.
The blockchain applies the consensus protocol to verify the block
which is distributing the network node. Consensus has many
practices such as, for example, Byzantine general problem, Proof
of work, and Proof of stake. However, there have not been
numerous papers that have undertaken analysis with regard to | [
1869,
3665,
1107,
1216,
170,
1236,
1112,
1106,
1712,
1439,
1103,
21340,
1197,
138,
5354,
6451,
13335,
2149,
5123,
3457,
4048,
1209,
1329,
1106,
2561,
170,
4795,
3300,
1861,
1106,
1115,
1276,
1107,
7228,
9339,
119,
1109,
6247,
1110,
1115,
1122,
1110,
3014,
1106,
3076,
1105,
6058,
170,
2211,
1634,
2235,
1216,
1112,
1126,
1859,
1952,
1137,
170,
3607,
2860,
1112,
3025,
119,
2307,
117,
1103,
8458,
1449,
1547,
1138,
1141,
1137,
2299,
21340,
1733,
1134,
1169,
5088,
1106,
1141,
1330,
119,
138,
1415,
10614,
117,
1111,
5374,
117,
1336,
1138,
2967,
21340,
1733,
117,
1141,
1111,
1451,
2853,
1216,
1112,
3752,
117,
3813,
117,
3880,
4129,
117,
2653,
10747,
117,
1105,
1177,
5275,
119,
4428,
117,
21340,
1197,
6224,
1169,
23896,
5822,
20043,
5409,
1121,
1217,
5490,
3665,
1106,
1103,
1470,
1106,
1217,
5733,
2374,
1118,
1141,
14031,
119,
27400,
2528,
1394,
117,
1111,
5374,
117,
1108,
2756,
1105,
117,
1112,
170,
1871,
117,
2228,
1234,
1341,
1115,
1122,
1110,
18372,
1106,
4959,
1150,
1209,
11984,
1103,
1470,
21340,
1197,
119,
19585,
12298,
164,
122,
166,
3073,
2007,
27084,
1199,
5032,
1150,
14878,
1103,
1470,
21340,
1197,
2566,
1118,
5321,
1147,
8250,
1106,
1103,
5511,
119,
1109,
1869,
4049,
1107,
1103,
21340,
1197,
17798,
1103,
1607,
1104,
14409,
1146,
1106,
1103,
1954,
1159,
1194,
1103,
3510,
7147,
1394,
119,
3725,
20388,
1106,
1103,
21340,
1197,
1431,
1129,
9635,
1174,
1106,
1118,
1451,
14031,
119,
21325,
117,
1317,
6635,
1444,
1106,
5340,
1114,
170,
10923,
119,
152,
4832,
1200,
3970,
1134,
1122,
1110,
1336,
1136,
1129,
1103,
2820,
1276,
1107,
15696,
1842,
118,
1362,
4683,
1216,
1112,
170,
20497,
2980,
3539,
10202,
117,
1118,
1134,
170,
1423,
9127,
113,
174,
119,
176,
119,
117,
170,
3085,
1137,
170,
1433,
114,
6771,
1113,
1103,
15549,
119,
1109,
4495,
1104,
170,
3510,
7147,
1394,
5564,
1110,
2140,
1217,
1682,
1106,
2239,
1114,
1343,
15029,
1115,
1202,
1136,
3496,
1684,
1487,
117,
7713,
1134,
10986,
1547,
6297,
1107,
8377,
4698,
1785,
119,
1109,
10923,
11309,
14007,
2993,
1106,
19646,
8377,
2645,
119,
1109,
1844,
5336,
170,
5980,
1113,
10923,
1108,
8232,
117,
1105,
1175,
1132,
2567,
3827,
1104,
2331,
6315,
19755,
1115,
1138,
1151,
7227,
1111,
3510,
7147,
4935,
164,
123,
166,
119,
1636,
1180,
1129,
22429,
1107,
2538,
1104,
1147,
3490,
2079,
119,
3278,
2246,
18809,
5031,
2923,
1104,
9308,
3254,
19675,
118,
1359,
19755,
1107,
1134,
1103,
4713,
17573,
6777,
1104,
3254,
19675,
1106,
1525,
170,
14372,
1115,
170,
26281,
2875,
22190,
5264,
17579,
1103,
1397,
2805,
119,
27400,
2528,
1394,
112,
188,
5096,
10008,
1104,
1250,
113,
18959,
2924,
114,
1110,
170,
3014,
1859,
1104,
1103,
10923,
119,
1109,
1168,
5199,
1132,
9308,
4909,
118,
1359,
19755,
1111,
1134,
15029,
1138,
9901,
3667,
1105,
1576,
1194,
1317,
5720,
1104,
4909,
1106,
5515,
10923,
119,
1398,
19755,
117,
153,
18890,
8377,
143,
14045,
1706,
2879,
3923,
113,
153,
26447,
1942,
114,
164,
124,
166,
1217,
1103,
1436,
17011,
117,
1132,
3666,
1107,
2440,
25209,
1272,
1152,
1321,
16047,
2913,
15029,
119,
1130,
1103,
2243,
117,
1155,
3714,
1116,
1195,
1525,
3216
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
5,
6,
6,
5,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
5,
6,
6,
5,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"information",
"entirely",
"in",
"such",
"a",
"way",
"as",
"to",
"keep",
"within",
"the",
"ledge",
"##r",
"A",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"application",
"will",
"use",
"to",
"create",
"a",
"user",
"account",
"similar",
"to",
"that",
"found",
"in",
"conventional",
"banking",
".",
"The",
"intention",
"is",
"that",
"it",
"is",
"simple",
"to",
"build",
"and",
"apply",
"a",
"lower",
"level",
"model",
"such",
"as",
"an",
"example",
"table",
"or",
"a",
"critical",
"value",
"as",
"mentioned",
".",
"Second",
",",
"the",
"functional",
"system",
"might",
"have",
"one",
"or",
"higher",
"ledge",
"##rs",
"which",
"can",
"link",
"to",
"one",
"another",
".",
"A",
"large",
"enterprise",
",",
"for",
"instance",
",",
"may",
"have",
"multiple",
"ledge",
"##rs",
",",
"one",
"for",
"every",
"department",
"such",
"as",
"engineering",
",",
"sales",
",",
"supply",
"chain",
",",
"pay",
"##roll",
",",
"and",
"so",
"forth",
".",
"Finally",
",",
"ledge",
"##r",
"possession",
"can",
"flu",
"##ct",
"##uate",
"significantly",
"from",
"being",
"exposed",
"entirely",
"to",
"the",
"public",
"to",
"being",
"totally",
"managed",
"by",
"one",
"participant",
".",
"Bit",
"##co",
"##in",
",",
"for",
"instance",
",",
"was",
"presented",
"and",
",",
"as",
"a",
"result",
",",
"makes",
"people",
"think",
"that",
"it",
"is",
"costly",
"to",
"determine",
"who",
"will",
"update",
"the",
"public",
"ledge",
"##r",
".",
"Pa",
"##rity",
"[",
"1",
"]",
"pre",
"##de",
"##fines",
"some",
"owners",
"who",
"adjust",
"the",
"public",
"ledge",
"##r",
"simply",
"by",
"adding",
"their",
"signature",
"to",
"the",
"blocks",
".",
"The",
"information",
"contained",
"in",
"the",
"ledge",
"##r",
"demonstrates",
"the",
"history",
"of",
"transactions",
"up",
"to",
"the",
"current",
"time",
"through",
"the",
"block",
"##cha",
"##in",
".",
"Up",
"##dates",
"to",
"the",
"ledge",
"##r",
"should",
"be",
"consent",
"##ed",
"to",
"by",
"every",
"participant",
".",
"Specifically",
",",
"several",
"participants",
"need",
"to",
"agree",
"with",
"a",
"consensus",
".",
"O",
"##bs",
"##er",
"##ving",
"which",
"it",
"is",
"may",
"not",
"be",
"the",
"situation",
"found",
"in",
"countless",
"real",
"-",
"world",
"applications",
"such",
"as",
"a",
"fi",
"##at",
"digital",
"currency",
",",
"by",
"which",
"a",
"single",
"entity",
"(",
"e",
".",
"g",
".",
",",
"a",
"bank",
"or",
"a",
"government",
")",
"decides",
"on",
"the",
"updates",
".",
"The",
"importance",
"of",
"a",
"block",
"##cha",
"##in",
"strategy",
"is",
"actually",
"being",
"able",
"to",
"deal",
"with",
"those",
"nodes",
"that",
"do",
"not",
"trust",
"working",
"together",
",",
"indicating",
"which",
"variables",
"might",
"respond",
"in",
"Byzantine",
"formal",
"##ity",
".",
"The",
"consensus",
"protocol",
"consequently",
"needs",
"to",
"endure",
"Byzantine",
"problems",
".",
"The",
"research",
"involving",
"a",
"survey",
"on",
"consensus",
"was",
"comprehensive",
",",
"and",
"there",
"are",
"numerous",
"versions",
"of",
"previously",
"recommended",
"protocols",
"that",
"have",
"been",
"manufactured",
"for",
"block",
"##cha",
"##ins",
"[",
"2",
"]",
".",
"These",
"could",
"be",
"categorized",
"in",
"terms",
"of",
"their",
"combined",
"range",
".",
"Over",
"##w",
"##hel",
"##ming",
"consists",
"of",
"solely",
"com",
"##putation",
"-",
"based",
"protocols",
"in",
"which",
"the",
"users",
"utilize",
"proof",
"of",
"com",
"##putation",
"to",
"find",
"a",
"node",
"that",
"a",
"##rb",
"##it",
"##rar",
"##ily",
"determines",
"the",
"next",
"operation",
".",
"Bit",
"##co",
"##in",
"'",
"s",
"Pro",
"##of",
"of",
"work",
"(",
"Po",
"##W",
")",
"is",
"a",
"simple",
"example",
"of",
"the",
"consensus",
".",
"The",
"other",
"severe",
"are",
"solely",
"communication",
"-",
"based",
"protocols",
"for",
"which",
"nodes",
"have",
"matching",
"votes",
"and",
"run",
"through",
"several",
"rounds",
"of",
"communication",
"to",
"achieve",
"consensus",
".",
"All",
"protocols",
",",
"P",
"##ractical",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"(",
"P",
"##BF",
"##T",
")",
"[",
"3",
"]",
"being",
"the",
"best",
"illustration",
",",
"are",
"applied",
"in",
"particular",
"configurations",
"because",
"they",
"take",
"authentic",
"##ated",
"nodes",
".",
"In",
"the",
"middle",
",",
"all",
"opposite",
"##s",
"we",
"find",
"mixed"
] | State of the art and challenges facing consensus p | 108 |
various aspects, and which have incorporated the adoption
summary as appropriate to the application. In this paper, we
have provided a technical verification review with regard to the
consensus algorithm taken from previous research. The audience
will receive a consensus protocol, and the algorithm typically
analyzes the application to match which platform is appropriate
by viewing the node identity, energy saving and the tolerated
power of the adversary, the data model, language, executio | [
10923,
19755,
1115,
13938,
1106,
2773,
1103,
8096,
1104,
153,
26447,
1942,
1105,
18959,
2924,
119,
1249,
1126,
1859,
117,
5096,
10008,
1104,
2896,
11478,
5591,
2614,
22391,
1103,
1444,
1111,
18372,
5463,
1120,
18959,
2924,
1114,
1103,
1329,
1104,
5022,
1158,
10682,
5197,
119,
1109,
1168,
17011,
1110,
4573,
1559,
1580,
1559,
1604,
118,
122,
118,
4389,
22392,
118,
25325,
1568,
118,
123,
120,
1407,
120,
109,
1955,
119,
3135,
206,
10973,
15292,
16206,
146,
15678,
11607,
1857,
5096,
10008,
1104,
5987,
164,
125,
166,
1134,
6618,
153,
26447,
1942,
1118,
3073,
118,
4006,
9373,
15029,
1107,
1134,
4713,
2992,
1113,
1147,
1319,
1107,
1546,
1106,
5515,
10923,
119,
18872,
117,
12126,
1197,
164,
126,
166,
1105,
155,
9717,
7136,
164,
127,
166,
12686,
14294,
153,
26447,
1942,
1118,
11190,
10923,
1107,
2964,
6379,
119,
1130,
1103,
1397,
2237,
117,
1195,
2194,
2272,
1250,
2628,
1114,
10923,
11309,
119,
4539,
2684,
7155,
10923,
11309,
21329,
1134,
1132,
1215,
1107,
6177,
4191,
1111,
3622,
4998,
119,
6177,
159,
3272,
170,
6593,
1114,
7328,
1106,
1103,
5980,
1104,
10923,
19755,
117,
1105,
2237,
7118,
8927,
1114,
2174,
1844,
7768,
119,
1563,
119,
155,
21678,
13821,
10069,
160,
9565,
2428,
138,
119,
8784,
2101,
15840,
16996,
8784,
2101,
15840,
16996,
164,
128,
166,
1110,
170,
1449,
1115,
17114,
1116,
2967,
15029,
1115,
4282,
1887,
2233,
117,
1105,
2196,
1134,
4901,
2344,
1169,
2423,
13692,
1103,
1378,
1210,
4625,
131,
16752,
22398,
9517,
113,
140,
114,
1110,
170,
2781,
1118,
1134,
1296,
14372,
1144,
1103,
6270,
2233,
1120,
1103,
1269,
1159,
119,
11651,
8009,
5474,
113,
138,
114,
1110,
1103,
2781,
1187,
1251,
4290,
1104,
170,
2747,
14372,
1674,
1136,
6975,
1168,
15029,
119,
4539,
8934,
15745,
113,
153,
114,
1110,
1103,
2781,
1118,
1134,
15029,
1169,
2760,
2500,
117,
1256,
1114,
170,
4290,
1107,
1103,
2443,
119,
1109,
3510,
7147,
1394,
1110,
1141,
1104,
1103,
4901,
2344,
1134,
1169,
13692,
1241,
11731,
113,
138,
114,
1105,
16416,
15745,
113,
153,
114,
1133,
2834,
13692,
1103,
3879,
1104,
20904,
113,
140,
114,
119,
3743,
117,
1112,
1263,
1112,
1103,
8865,
1104,
1103,
2443,
1110,
1159,
118,
2609,
117,
1103,
1449,
1110,
4485,
1112,
8338,
1103,
10010,
20904,
119,
11618,
20904,
1110,
1103,
5564,
1115,
8469,
1106,
7290,
1191,
1122,
1110,
12095,
1191,
1103,
16117,
1110,
2028,
6018,
117,
1256,
1114,
1199,
1159,
2495,
5700,
119,
139,
119,
8377,
1615,
1116,
21710,
113,
139,
17095,
114,
8093,
7147,
1394,
1144,
4275,
1103,
2486,
1115,
15267,
1103,
2006,
2443,
1106,
9221,
2193,
14409,
1106,
4989,
1115,
2702,
5369,
1110,
11168,
119,
13197,
170,
14031,
26064,
1103,
2915,
1105,
24738,
1104,
1103,
13618,
1137,
1136,
117,
3162,
1538,
4392,
1122,
119,
1109,
3136,
13198,
1103,
1177,
118,
1270,
139,
17095,
164,
129,
166,
164,
130,
166,
119,
1188,
1110,
2272,
1106,
1103,
4506,
1104,
1106,
2879,
3798,
21688,
1107,
170,
4901,
3750,
119,
1556,
1103,
139,
17095,
1107,
1713,
117,
1103,
2304,
1104,
6014,
17409,
20251,
1118,
1134,
1126,
8050,
10704,
3113,
1180,
11885,
170,
156,
1183,
15197,
2035,
119,
2409,
4953,
117,
1103,
4795,
1547
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0
] | [
"consensus",
"protocols",
"that",
"intend",
"to",
"increase",
"the",
"efficiency",
"of",
"P",
"##BF",
"##T",
"and",
"Po",
"##W",
".",
"As",
"an",
"example",
",",
"Pro",
"##of",
"of",
"El",
"##ap",
"##sed",
"Time",
"removes",
"the",
"need",
"for",
"costly",
"mining",
"at",
"Po",
"##W",
"with",
"the",
"use",
"of",
"profit",
"##ing",
"reliable",
"devices",
".",
"The",
"other",
"illustration",
"is",
"95",
"##7",
"##9",
"##7",
"##8",
"-",
"1",
"-",
"53",
"##86",
"-",
"229",
"##0",
"-",
"2",
"/",
"18",
"/",
"$",
"31",
".",
"00",
"Β©",
"##20",
"##18",
"IEEE",
"I",
"##CO",
"##IN",
"2018",
"Pro",
"##of",
"of",
"Authority",
"[",
"4",
"]",
"which",
"helps",
"P",
"##BF",
"##T",
"by",
"pre",
"-",
"finding",
"trusted",
"nodes",
"in",
"which",
"users",
"vote",
"on",
"their",
"own",
"in",
"order",
"to",
"achieve",
"consensus",
".",
"Likewise",
",",
"Stella",
"##r",
"[",
"5",
"]",
"and",
"R",
"##ip",
"##ple",
"[",
"6",
"]",
"au",
"##gment",
"P",
"##BF",
"##T",
"by",
"achieving",
"consensus",
"in",
"smaller",
"networks",
".",
"In",
"the",
"next",
"section",
",",
"we",
"provide",
"related",
"work",
"associated",
"with",
"consensus",
"protocol",
".",
"Part",
"III",
"explains",
"consensus",
"protocol",
"comparisons",
"which",
"are",
"used",
"in",
"Section",
"IV",
"for",
"analysis",
"purposes",
".",
"Section",
"V",
"offers",
"a",
"conclusion",
"with",
"regard",
"to",
"the",
"survey",
"of",
"consensus",
"protocols",
",",
"and",
"section",
"VI",
"deals",
"with",
"future",
"research",
"directions",
".",
"II",
".",
"R",
"##EL",
"##AT",
"##ED",
"W",
"##OR",
"##K",
"A",
".",
"CA",
"##P",
"Theo",
"##rem",
"CA",
"##P",
"Theo",
"##rem",
"[",
"7",
"]",
"is",
"a",
"system",
"that",
"distribute",
"##s",
"multiple",
"nodes",
"that",
"handle",
"common",
"data",
",",
"and",
"shows",
"which",
"distributed",
"systems",
"can",
"completely",
"satisfy",
"the",
"following",
"three",
"properties",
":",
"Con",
"##sist",
"##ency",
"(",
"C",
")",
"is",
"a",
"status",
"by",
"which",
"each",
"node",
"has",
"the",
"latest",
"data",
"at",
"the",
"same",
"time",
".",
"Ava",
"##ila",
"##bility",
"(",
"A",
")",
"is",
"the",
"status",
"where",
"any",
"failure",
"of",
"a",
"specific",
"node",
"does",
"not",
"affect",
"other",
"nodes",
".",
"Part",
"##ition",
"tolerance",
"(",
"P",
")",
"is",
"the",
"status",
"by",
"which",
"nodes",
"can",
"continue",
"operations",
",",
"even",
"with",
"a",
"failure",
"in",
"the",
"network",
".",
"The",
"block",
"##cha",
"##in",
"is",
"one",
"of",
"the",
"distributed",
"systems",
"which",
"can",
"satisfy",
"both",
"availability",
"(",
"A",
")",
"and",
"partition",
"tolerance",
"(",
"P",
")",
"but",
"cannot",
"satisfy",
"the",
"condition",
"of",
"consistency",
"(",
"C",
")",
".",
"Instead",
",",
"as",
"long",
"as",
"the",
"separation",
"of",
"the",
"network",
"is",
"time",
"-",
"limited",
",",
"the",
"system",
"is",
"regarded",
"as",
"maintaining",
"the",
"ultimate",
"consistency",
".",
"Ultimate",
"consistency",
"is",
"the",
"strategy",
"that",
"aims",
"to",
"discover",
"if",
"it",
"is",
"acceptable",
"if",
"the",
"texture",
"is",
"eventually",
"preserved",
",",
"even",
"with",
"some",
"time",
"la",
"##gs",
".",
"B",
".",
"Byzantine",
"General",
"##s",
"Problem",
"(",
"B",
"##GP",
")",
"Block",
"##cha",
"##in",
"has",
"fixed",
"the",
"issue",
"that",
"permits",
"the",
"whole",
"network",
"to",
"valid",
"##ate",
"transactions",
"to",
"ensure",
"that",
"double",
"spending",
"is",
"detected",
".",
"Whether",
"a",
"participant",
"confirms",
"the",
"presence",
"and",
"authenticity",
"of",
"the",
"transaction",
"or",
"not",
",",
"Bob",
"must",
"accept",
"it",
".",
"The",
"approach",
"resembles",
"the",
"so",
"-",
"called",
"B",
"##GP",
"[",
"8",
"]",
"[",
"9",
"]",
".",
"This",
"is",
"related",
"to",
"the",
"challenge",
"of",
"to",
"##ler",
"##ating",
"faults",
"in",
"a",
"distributed",
"environment",
".",
"With",
"the",
"B",
"##GP",
"in",
"mind",
",",
"the",
"question",
"of",
"false",
"identities",
"arises",
"by",
"which",
"an",
"ad",
"##vers",
"##ary",
"could",
"mount",
"a",
"S",
"##y",
"##bil",
"attack",
".",
"Like",
"Alice",
",",
"the",
"user",
"might"
] | State of the art and challenges facing consensus p | 109 |
various aspects, and which have incorporated the adoption
summary as appropriate to the application. In this paper, we
have provided a technical verification review with regard to the
consensus algorithm taken from previous research. The audience
will receive a consensus protocol, and the algorithm typically
analyzes the application to match which platform is appropriate
by viewing the node identity, energy saving and the tolerated
power of the adversary, the data model, language, executio | [
10923,
19755,
1115,
13938,
1106,
2773,
1103,
8096,
1104,
153,
26447,
1942,
1105,
18959,
2924,
119,
1249,
1126,
1859,
117,
5096,
10008,
1104,
2896,
11478,
5591,
2614,
22391,
1103,
1444,
1111,
18372,
5463,
1120,
18959,
2924,
1114,
1103,
1329,
1104,
5022,
1158,
10682,
5197,
119,
1109,
1168,
17011,
1110,
4573,
1559,
1580,
1559,
1604,
118,
122,
118,
4389,
22392,
118,
25325,
1568,
118,
123,
120,
1407,
120,
109,
1955,
119,
3135,
206,
10973,
15292,
16206,
146,
15678,
11607,
1857,
5096,
10008,
1104,
5987,
164,
125,
166,
1134,
6618,
153,
26447,
1942,
1118,
3073,
118,
4006,
9373,
15029,
1107,
1134,
4713,
2992,
1113,
1147,
1319,
1107,
1546,
1106,
5515,
10923,
119,
18872,
117,
12126,
1197,
164,
126,
166,
1105,
155,
9717,
7136,
164,
127,
166,
12686,
14294,
153,
26447,
1942,
1118,
11190,
10923,
1107,
2964,
6379,
119,
1130,
1103,
1397,
2237,
117,
1195,
2194,
2272,
1250,
2628,
1114,
10923,
11309,
119,
4539,
2684,
7155,
10923,
11309,
21329,
1134,
1132,
1215,
1107,
6177,
4191,
1111,
3622,
4998,
119,
6177,
159,
3272,
170,
6593,
1114,
7328,
1106,
1103,
5980,
1104,
10923,
19755,
117,
1105,
2237,
7118,
8927,
1114,
2174,
1844,
7768,
119,
1563,
119,
155,
21678,
13821,
10069,
160,
9565,
2428,
138,
119,
8784,
2101,
15840,
16996,
8784,
2101,
15840,
16996,
164,
128,
166,
1110,
170,
1449,
1115,
17114,
1116,
2967,
15029,
1115,
4282,
1887,
2233,
117,
1105,
2196,
1134,
4901,
2344,
1169,
2423,
13692,
1103,
1378,
1210,
4625,
131,
16752,
22398,
9517,
113,
140,
114,
1110,
170,
2781,
1118,
1134,
1296,
14372,
1144,
1103,
6270,
2233,
1120,
1103,
1269,
1159,
119,
11651,
8009,
5474,
113,
138,
114,
1110,
1103,
2781,
1187,
1251,
4290,
1104,
170,
2747,
14372,
1674,
1136,
6975,
1168,
15029,
119,
4539,
8934,
15745,
113,
153,
114,
1110,
1103,
2781,
1118,
1134,
15029,
1169,
2760,
2500,
117,
1256,
1114,
170,
4290,
1107,
1103,
2443,
119,
1109,
3510,
7147,
1394,
1110,
1141,
1104,
1103,
4901,
2344,
1134,
1169,
13692,
1241,
11731,
113,
138,
114,
1105,
16416,
15745,
113,
153,
114,
1133,
2834,
13692,
1103,
3879,
1104,
20904,
113,
140,
114,
119,
3743,
117,
1112,
1263,
1112,
1103,
8865,
1104,
1103,
2443,
1110,
1159,
118,
2609,
117,
1103,
1449,
1110,
4485,
1112,
8338,
1103,
10010,
20904,
119,
11618,
20904,
1110,
1103,
5564,
1115,
8469,
1106,
7290,
1191,
1122,
1110,
12095,
1191,
1103,
16117,
1110,
2028,
6018,
117,
1256,
1114,
1199,
1159,
2495,
5700,
119,
139,
119,
8377,
1615,
1116,
21710,
113,
139,
17095,
114,
8093,
7147,
1394,
1144,
4275,
1103,
2486,
1115,
15267,
1103,
2006,
2443,
1106,
9221,
2193,
14409,
1106,
4989,
1115,
2702,
5369,
1110,
11168,
119,
13197,
170,
14031,
26064,
1103,
2915,
1105,
24738,
1104,
1103,
13618,
1137,
1136,
117,
3162,
1538,
4392,
1122,
119,
1109,
3136,
13198,
1103,
1177,
118,
1270,
139,
17095,
164,
129,
166,
164,
130,
166,
119,
1188,
1110,
2272,
1106,
1103,
4506,
1104,
1106,
2879,
3798,
21688,
1107,
170,
4901,
3750,
119,
1556,
1103,
139,
17095,
1107,
1713,
117,
1103,
2304,
1104,
6014,
17409,
20251,
1118,
1134,
1126,
8050,
10704,
3113,
1180,
11885,
170,
156,
1183,
15197,
2035,
119,
2409,
4953,
117,
1103,
4795,
1547
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"consensus",
"protocols",
"that",
"intend",
"to",
"increase",
"the",
"efficiency",
"of",
"P",
"##BF",
"##T",
"and",
"Po",
"##W",
".",
"As",
"an",
"example",
",",
"Pro",
"##of",
"of",
"El",
"##ap",
"##sed",
"Time",
"removes",
"the",
"need",
"for",
"costly",
"mining",
"at",
"Po",
"##W",
"with",
"the",
"use",
"of",
"profit",
"##ing",
"reliable",
"devices",
".",
"The",
"other",
"illustration",
"is",
"95",
"##7",
"##9",
"##7",
"##8",
"-",
"1",
"-",
"53",
"##86",
"-",
"229",
"##0",
"-",
"2",
"/",
"18",
"/",
"$",
"31",
".",
"00",
"Β©",
"##20",
"##18",
"IEEE",
"I",
"##CO",
"##IN",
"2018",
"Pro",
"##of",
"of",
"Authority",
"[",
"4",
"]",
"which",
"helps",
"P",
"##BF",
"##T",
"by",
"pre",
"-",
"finding",
"trusted",
"nodes",
"in",
"which",
"users",
"vote",
"on",
"their",
"own",
"in",
"order",
"to",
"achieve",
"consensus",
".",
"Likewise",
",",
"Stella",
"##r",
"[",
"5",
"]",
"and",
"R",
"##ip",
"##ple",
"[",
"6",
"]",
"au",
"##gment",
"P",
"##BF",
"##T",
"by",
"achieving",
"consensus",
"in",
"smaller",
"networks",
".",
"In",
"the",
"next",
"section",
",",
"we",
"provide",
"related",
"work",
"associated",
"with",
"consensus",
"protocol",
".",
"Part",
"III",
"explains",
"consensus",
"protocol",
"comparisons",
"which",
"are",
"used",
"in",
"Section",
"IV",
"for",
"analysis",
"purposes",
".",
"Section",
"V",
"offers",
"a",
"conclusion",
"with",
"regard",
"to",
"the",
"survey",
"of",
"consensus",
"protocols",
",",
"and",
"section",
"VI",
"deals",
"with",
"future",
"research",
"directions",
".",
"II",
".",
"R",
"##EL",
"##AT",
"##ED",
"W",
"##OR",
"##K",
"A",
".",
"CA",
"##P",
"Theo",
"##rem",
"CA",
"##P",
"Theo",
"##rem",
"[",
"7",
"]",
"is",
"a",
"system",
"that",
"distribute",
"##s",
"multiple",
"nodes",
"that",
"handle",
"common",
"data",
",",
"and",
"shows",
"which",
"distributed",
"systems",
"can",
"completely",
"satisfy",
"the",
"following",
"three",
"properties",
":",
"Con",
"##sist",
"##ency",
"(",
"C",
")",
"is",
"a",
"status",
"by",
"which",
"each",
"node",
"has",
"the",
"latest",
"data",
"at",
"the",
"same",
"time",
".",
"Ava",
"##ila",
"##bility",
"(",
"A",
")",
"is",
"the",
"status",
"where",
"any",
"failure",
"of",
"a",
"specific",
"node",
"does",
"not",
"affect",
"other",
"nodes",
".",
"Part",
"##ition",
"tolerance",
"(",
"P",
")",
"is",
"the",
"status",
"by",
"which",
"nodes",
"can",
"continue",
"operations",
",",
"even",
"with",
"a",
"failure",
"in",
"the",
"network",
".",
"The",
"block",
"##cha",
"##in",
"is",
"one",
"of",
"the",
"distributed",
"systems",
"which",
"can",
"satisfy",
"both",
"availability",
"(",
"A",
")",
"and",
"partition",
"tolerance",
"(",
"P",
")",
"but",
"cannot",
"satisfy",
"the",
"condition",
"of",
"consistency",
"(",
"C",
")",
".",
"Instead",
",",
"as",
"long",
"as",
"the",
"separation",
"of",
"the",
"network",
"is",
"time",
"-",
"limited",
",",
"the",
"system",
"is",
"regarded",
"as",
"maintaining",
"the",
"ultimate",
"consistency",
".",
"Ultimate",
"consistency",
"is",
"the",
"strategy",
"that",
"aims",
"to",
"discover",
"if",
"it",
"is",
"acceptable",
"if",
"the",
"texture",
"is",
"eventually",
"preserved",
",",
"even",
"with",
"some",
"time",
"la",
"##gs",
".",
"B",
".",
"Byzantine",
"General",
"##s",
"Problem",
"(",
"B",
"##GP",
")",
"Block",
"##cha",
"##in",
"has",
"fixed",
"the",
"issue",
"that",
"permits",
"the",
"whole",
"network",
"to",
"valid",
"##ate",
"transactions",
"to",
"ensure",
"that",
"double",
"spending",
"is",
"detected",
".",
"Whether",
"a",
"participant",
"confirms",
"the",
"presence",
"and",
"authenticity",
"of",
"the",
"transaction",
"or",
"not",
",",
"Bob",
"must",
"accept",
"it",
".",
"The",
"approach",
"resembles",
"the",
"so",
"-",
"called",
"B",
"##GP",
"[",
"8",
"]",
"[",
"9",
"]",
".",
"This",
"is",
"related",
"to",
"the",
"challenge",
"of",
"to",
"##ler",
"##ating",
"faults",
"in",
"a",
"distributed",
"environment",
".",
"With",
"the",
"B",
"##GP",
"in",
"mind",
",",
"the",
"question",
"of",
"false",
"identities",
"arises",
"by",
"which",
"an",
"ad",
"##vers",
"##ary",
"could",
"mount",
"a",
"S",
"##y",
"##bil",
"attack",
".",
"Like",
"Alice",
",",
"the",
"user",
"might"
] | State of the art and challenges facing consensus p | 110 |
n,
application, and examples. Finally, we finish by presenting
several research directions with regard to the consensus protocol.
Keywords: blockchain; consensus; distributed ledger;
distributed consensus; consensus algorithms
I. INTRODUCTION
A ledger is a documentary framework which includes an
ordered record of transactions. For instance, a ledger will
record transactions between several commercial banks, or
goods exchanged with known parties. An aspect of
blockchains is that the le | [
2561,
2967,
12409,
117,
1296,
21295,
1103,
13618,
119,
2711,
1103,
3958,
117,
1142,
1110,
170,
2702,
4511,
119,
3162,
1209,
3496,
1292,
117,
1173,
4392,
1103,
13618,
119,
140,
119,
153,
18890,
8377,
143,
14045,
1706,
2879,
3923,
113,
153,
26447,
1942,
114,
153,
26447,
1942,
164,
1275,
166,
1110,
1126,
9932,
1111,
15097,
170,
8377,
143,
14045,
3694,
1121,
170,
4290,
1107,
1459,
170,
10923,
2416,
1118,
1103,
139,
17095,
119,
1135,
1108,
1737,
1106,
1129,
170,
3021,
4506,
1106,
1508,
1103,
9932,
1106,
6691,
1329,
1496,
1106,
1103,
7883,
2971,
1104,
19218,
2320,
119,
8094,
117,
1103,
2072,
2971,
1104,
15029,
1444,
1129,
1227,
117,
1105,
1103,
4177,
2971,
1104,
5696,
15029,
2993,
1106,
1129,
1383,
119,
1636,
5420,
1294,
1122,
1662,
1106,
12912,
1142,
9932,
1114,
7328,
1106,
1470,
2344,
119,
153,
26447,
1110,
1971,
1215,
1107,
155,
9717,
7136,
1105,
12126,
1197,
119,
141,
119,
5096,
10008,
1104,
6955,
113,
18959,
2924,
114,
18959,
2924,
164,
1429,
166,
4431,
1106,
170,
6978,
1106,
12434,
170,
1825,
112,
188,
15025,
1118,
1515,
1172,
1202,
170,
1612,
1250,
1134,
1110,
16115,
6758,
1133,
21546,
119,
2857,
1152,
1138,
1694,
1142,
1250,
117,
1122,
1169,
1129,
1346,
22480,
119,
1370,
1859,
117,
1103,
18959,
2924,
9932,
3909,
10736,
1324,
21995,
1324,
1169,
1129,
5546,
1111,
5416,
24853,
119,
138,
2747,
1144,
1324,
19218,
1110,
3238,
1296,
1159,
1126,
10632,
1110,
1850,
117,
8267,
14243,
22620,
10951,
1116,
119,
27400,
2528,
1394,
2745,
18959,
2924,
1106,
3133,
170,
6978,
1134,
17356,
1103,
1940,
1116,
1874,
1643,
4894,
20936,
1104,
2233,
1105,
3840,
21379,
10772,
1443,
1103,
1444,
1111,
170,
2129,
3748,
117,
1105,
1134,
1169,
8333,
1103,
1449,
1222,
3690,
1118,
12477,
8031,
4179,
4713,
119,
142,
119,
5096,
10008,
1104,
1457,
9899,
113,
18959,
1708,
114,
18959,
1708,
164,
1367,
166,
1110,
1126,
4174,
6978,
1111,
18959,
2924,
1134,
8247,
1116,
1103,
1397,
5463,
14372,
1359,
1113,
1147,
2355,
1104,
1103,
2900,
3539,
10202,
1104,
1103,
3510,
7147,
1394,
2443,
119,
1370,
1859,
117,
1103,
13418,
1444,
1106,
5424,
1103,
5582,
1104,
170,
2218,
2971,
1104,
8536,
9584,
10202,
1107,
1546,
1106,
2317,
5511,
119,
18959,
2924,
164,
1492,
166,
5463,
1110,
1304,
18372,
119,
1109,
7791,
1110,
2108,
1540,
5827,
119,
18959,
1708,
1110,
5409,
11479,
1106,
20220,
1103,
11013,
1104,
5463,
119,
18959,
1708,
20421,
170,
1423,
3392,
117,
1105,
1870,
24573,
1103,
13544,
112,
188,
3819,
1106,
1129,
22127,
1193,
5236,
1106,
1103,
2317,
1197,
112,
188,
8219,
1107,
1103,
2443,
119,
138,
8219,
1110,
4444,
170,
6561,
5467,
3338,
170,
2440,
9397,
117,
13735,
1103,
2317,
1197,
112,
188,
13314,
1106,
8338,
1103,
2443,
119,
1188,
13267,
1103,
2672,
1134,
2502,
1171,
1103,
8219,
119,
10608,
117,
170,
2317,
1197,
1180,
3133,
1103,
6270,
3510,
1118,
1231,
24313,
3970,
1103,
13544,
119,
143,
119,
5096,
10008,
1104,
2173,
6366,
113,
18959,
1592,
114,
18959,
1708,
1144,
1242,
1167,
9118,
1115,
4444,
12864,
1113,
1103,
9584,
2553,
1134,
1180,
8803,
3709,
7674,
1107,
170,
9584,
8219,
13618,
1106,
3200,
22775,
119,
3291,
4935,
1850,
1106
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
1,
2,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
1,
2,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"create",
"multiple",
"instances",
",",
"each",
"confirming",
"the",
"transaction",
".",
"Despite",
"the",
"reality",
",",
"this",
"is",
"a",
"double",
"spend",
".",
"Bob",
"will",
"trust",
"these",
",",
"then",
"accept",
"the",
"transaction",
".",
"C",
".",
"P",
"##ractical",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"(",
"P",
"##BF",
"##T",
")",
"P",
"##BF",
"##T",
"[",
"10",
"]",
"is",
"an",
"algorithm",
"for",
"solving",
"a",
"Byzantine",
"F",
"##ault",
"resulting",
"from",
"a",
"failure",
"in",
"building",
"a",
"consensus",
"caused",
"by",
"the",
"B",
"##GP",
".",
"It",
"was",
"considered",
"to",
"be",
"a",
"serious",
"challenge",
"to",
"put",
"the",
"algorithm",
"to",
"practical",
"use",
"due",
"to",
"the",
"enormous",
"amount",
"of",
"calculation",
"required",
".",
"Nevertheless",
",",
"the",
"entire",
"amount",
"of",
"nodes",
"need",
"be",
"known",
",",
"and",
"the",
"maximum",
"amount",
"of",
"illegal",
"nodes",
"needs",
"to",
"be",
"set",
".",
"These",
"requirements",
"make",
"it",
"hard",
"to",
"employ",
"this",
"algorithm",
"with",
"regard",
"to",
"public",
"systems",
".",
"P",
"##BF",
"is",
"currently",
"used",
"in",
"R",
"##ip",
"##ple",
"and",
"Stella",
"##r",
".",
"D",
".",
"Pro",
"##of",
"of",
"Work",
"(",
"Po",
"##W",
")",
"Po",
"##W",
"[",
"11",
"]",
"refers",
"to",
"a",
"mechanism",
"to",
"confirm",
"a",
"person",
"'",
"s",
"innocence",
"by",
"having",
"them",
"do",
"a",
"sure",
"work",
"which",
"is",
"troubles",
"##ome",
"but",
"straightforward",
".",
"Once",
"they",
"have",
"done",
"this",
"work",
",",
"it",
"can",
"be",
"early",
"verified",
".",
"For",
"example",
",",
"the",
"Po",
"##W",
"algorithm",
"entitled",
"Has",
"##h",
"##cas",
"##h",
"can",
"be",
"adapted",
"for",
"sending",
"emails",
".",
"A",
"specific",
"has",
"##h",
"calculation",
"is",
"necessary",
"each",
"time",
"an",
"email",
"is",
"sent",
",",
"thereby",
"excluding",
"spa",
"##mmer",
"##s",
".",
"Bit",
"##co",
"##in",
"uses",
"Po",
"##W",
"to",
"produce",
"a",
"mechanism",
"which",
"prevents",
"the",
"mi",
"##s",
"##re",
"##p",
"##res",
"##entation",
"of",
"data",
"and",
"du",
"##plicate",
"payments",
"without",
"the",
"need",
"for",
"a",
"central",
"authority",
",",
"and",
"which",
"can",
"preserve",
"the",
"system",
"against",
"attacks",
"by",
"ma",
"##lic",
"##ious",
"users",
".",
"E",
".",
"Pro",
"##of",
"of",
"St",
"##ake",
"(",
"Po",
"##S",
")",
"Po",
"##S",
"[",
"12",
"]",
"is",
"an",
"alternative",
"mechanism",
"for",
"Po",
"##W",
"which",
"select",
"##s",
"the",
"next",
"mining",
"node",
"based",
"on",
"their",
"holding",
"of",
"the",
"native",
"digital",
"currency",
"of",
"the",
"block",
"##cha",
"##in",
"network",
".",
"For",
"example",
",",
"the",
"miners",
"need",
"to",
"prove",
"the",
"ownership",
"of",
"a",
"certain",
"amount",
"of",
"peer",
"coin",
"currency",
"in",
"order",
"to",
"mine",
"blocks",
".",
"Po",
"##W",
"[",
"13",
"]",
"mining",
"is",
"very",
"costly",
".",
"The",
"procedure",
"is",
"especially",
"power",
"intense",
".",
"Po",
"##S",
"is",
"significantly",
"projected",
"to",
"minimize",
"the",
"expense",
"of",
"mining",
".",
"Po",
"##S",
"preserves",
"a",
"single",
"branch",
",",
"and",
"yet",
"transforms",
"the",
"puzzle",
"'",
"s",
"trouble",
"to",
"be",
"inverse",
"##ly",
"relative",
"to",
"the",
"mine",
"##r",
"'",
"s",
"stake",
"in",
"the",
"network",
".",
"A",
"stake",
"is",
"ultimately",
"a",
"secured",
"membership",
"alongside",
"a",
"particular",
"stability",
",",
"addressing",
"the",
"mine",
"##r",
"'",
"s",
"dedication",
"to",
"maintaining",
"the",
"network",
".",
"This",
"enables",
"the",
"feature",
"which",
"comes",
"back",
"the",
"stake",
".",
"Subsequently",
",",
"a",
"mine",
"##r",
"could",
"produce",
"the",
"latest",
"block",
"by",
"re",
"##sol",
"##ving",
"the",
"puzzle",
".",
"F",
".",
"Pro",
"##of",
"of",
"Act",
"##ivity",
"(",
"Po",
"##A",
")",
"Po",
"##S",
"has",
"many",
"more",
"restrictions",
"that",
"ultimately",
"depend",
"on",
"the",
"coin",
"##age",
"which",
"could",
"involve",
"keeping",
"coins",
"in",
"a",
"coin",
"stake",
"transaction",
"to",
"ones",
"##elf",
".",
"Co",
"##ins",
"sent",
"to"
] | State of the art and challenges facing consensus p | 111 |
n,
application, and examples. Finally, we finish by presenting
several research directions with regard to the consensus protocol.
Keywords: blockchain; consensus; distributed ledger;
distributed consensus; consensus algorithms
I. INTRODUCTION
A ledger is a documentary framework which includes an
ordered record of transactions. For instance, a ledger will
record transactions between several commercial banks, or
goods exchanged with known parties. An aspect of
blockchains is that the le | [
2561,
2967,
12409,
117,
1296,
21295,
1103,
13618,
119,
2711,
1103,
3958,
117,
1142,
1110,
170,
2702,
4511,
119,
3162,
1209,
3496,
1292,
117,
1173,
4392,
1103,
13618,
119,
140,
119,
153,
18890,
8377,
143,
14045,
1706,
2879,
3923,
113,
153,
26447,
1942,
114,
153,
26447,
1942,
164,
1275,
166,
1110,
1126,
9932,
1111,
15097,
170,
8377,
143,
14045,
3694,
1121,
170,
4290,
1107,
1459,
170,
10923,
2416,
1118,
1103,
139,
17095,
119,
1135,
1108,
1737,
1106,
1129,
170,
3021,
4506,
1106,
1508,
1103,
9932,
1106,
6691,
1329,
1496,
1106,
1103,
7883,
2971,
1104,
19218,
2320,
119,
8094,
117,
1103,
2072,
2971,
1104,
15029,
1444,
1129,
1227,
117,
1105,
1103,
4177,
2971,
1104,
5696,
15029,
2993,
1106,
1129,
1383,
119,
1636,
5420,
1294,
1122,
1662,
1106,
12912,
1142,
9932,
1114,
7328,
1106,
1470,
2344,
119,
153,
26447,
1110,
1971,
1215,
1107,
155,
9717,
7136,
1105,
12126,
1197,
119,
141,
119,
5096,
10008,
1104,
6955,
113,
18959,
2924,
114,
18959,
2924,
164,
1429,
166,
4431,
1106,
170,
6978,
1106,
12434,
170,
1825,
112,
188,
15025,
1118,
1515,
1172,
1202,
170,
1612,
1250,
1134,
1110,
16115,
6758,
1133,
21546,
119,
2857,
1152,
1138,
1694,
1142,
1250,
117,
1122,
1169,
1129,
1346,
22480,
119,
1370,
1859,
117,
1103,
18959,
2924,
9932,
3909,
10736,
1324,
21995,
1324,
1169,
1129,
5546,
1111,
5416,
24853,
119,
138,
2747,
1144,
1324,
19218,
1110,
3238,
1296,
1159,
1126,
10632,
1110,
1850,
117,
8267,
14243,
22620,
10951,
1116,
119,
27400,
2528,
1394,
2745,
18959,
2924,
1106,
3133,
170,
6978,
1134,
17356,
1103,
1940,
1116,
1874,
1643,
4894,
20936,
1104,
2233,
1105,
3840,
21379,
10772,
1443,
1103,
1444,
1111,
170,
2129,
3748,
117,
1105,
1134,
1169,
8333,
1103,
1449,
1222,
3690,
1118,
12477,
8031,
4179,
4713,
119,
142,
119,
5096,
10008,
1104,
1457,
9899,
113,
18959,
1708,
114,
18959,
1708,
164,
1367,
166,
1110,
1126,
4174,
6978,
1111,
18959,
2924,
1134,
8247,
1116,
1103,
1397,
5463,
14372,
1359,
1113,
1147,
2355,
1104,
1103,
2900,
3539,
10202,
1104,
1103,
3510,
7147,
1394,
2443,
119,
1370,
1859,
117,
1103,
13418,
1444,
1106,
5424,
1103,
5582,
1104,
170,
2218,
2971,
1104,
8536,
9584,
10202,
1107,
1546,
1106,
2317,
5511,
119,
18959,
2924,
164,
1492,
166,
5463,
1110,
1304,
18372,
119,
1109,
7791,
1110,
2108,
1540,
5827,
119,
18959,
1708,
1110,
5409,
11479,
1106,
20220,
1103,
11013,
1104,
5463,
119,
18959,
1708,
20421,
170,
1423,
3392,
117,
1105,
1870,
24573,
1103,
13544,
112,
188,
3819,
1106,
1129,
22127,
1193,
5236,
1106,
1103,
2317,
1197,
112,
188,
8219,
1107,
1103,
2443,
119,
138,
8219,
1110,
4444,
170,
6561,
5467,
3338,
170,
2440,
9397,
117,
13735,
1103,
2317,
1197,
112,
188,
13314,
1106,
8338,
1103,
2443,
119,
1188,
13267,
1103,
2672,
1134,
2502,
1171,
1103,
8219,
119,
10608,
117,
170,
2317,
1197,
1180,
3133,
1103,
6270,
3510,
1118,
1231,
24313,
3970,
1103,
13544,
119,
143,
119,
5096,
10008,
1104,
2173,
6366,
113,
18959,
1592,
114,
18959,
1708,
1144,
1242,
1167,
9118,
1115,
4444,
12864,
1113,
1103,
9584,
2553,
1134,
1180,
8803,
3709,
7674,
1107,
170,
9584,
8219,
13618,
1106,
3200,
22775,
119,
3291,
4935,
1850,
1106
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
5,
6,
6,
5,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
5,
6,
6,
5,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"create",
"multiple",
"instances",
",",
"each",
"confirming",
"the",
"transaction",
".",
"Despite",
"the",
"reality",
",",
"this",
"is",
"a",
"double",
"spend",
".",
"Bob",
"will",
"trust",
"these",
",",
"then",
"accept",
"the",
"transaction",
".",
"C",
".",
"P",
"##ractical",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"(",
"P",
"##BF",
"##T",
")",
"P",
"##BF",
"##T",
"[",
"10",
"]",
"is",
"an",
"algorithm",
"for",
"solving",
"a",
"Byzantine",
"F",
"##ault",
"resulting",
"from",
"a",
"failure",
"in",
"building",
"a",
"consensus",
"caused",
"by",
"the",
"B",
"##GP",
".",
"It",
"was",
"considered",
"to",
"be",
"a",
"serious",
"challenge",
"to",
"put",
"the",
"algorithm",
"to",
"practical",
"use",
"due",
"to",
"the",
"enormous",
"amount",
"of",
"calculation",
"required",
".",
"Nevertheless",
",",
"the",
"entire",
"amount",
"of",
"nodes",
"need",
"be",
"known",
",",
"and",
"the",
"maximum",
"amount",
"of",
"illegal",
"nodes",
"needs",
"to",
"be",
"set",
".",
"These",
"requirements",
"make",
"it",
"hard",
"to",
"employ",
"this",
"algorithm",
"with",
"regard",
"to",
"public",
"systems",
".",
"P",
"##BF",
"is",
"currently",
"used",
"in",
"R",
"##ip",
"##ple",
"and",
"Stella",
"##r",
".",
"D",
".",
"Pro",
"##of",
"of",
"Work",
"(",
"Po",
"##W",
")",
"Po",
"##W",
"[",
"11",
"]",
"refers",
"to",
"a",
"mechanism",
"to",
"confirm",
"a",
"person",
"'",
"s",
"innocence",
"by",
"having",
"them",
"do",
"a",
"sure",
"work",
"which",
"is",
"troubles",
"##ome",
"but",
"straightforward",
".",
"Once",
"they",
"have",
"done",
"this",
"work",
",",
"it",
"can",
"be",
"early",
"verified",
".",
"For",
"example",
",",
"the",
"Po",
"##W",
"algorithm",
"entitled",
"Has",
"##h",
"##cas",
"##h",
"can",
"be",
"adapted",
"for",
"sending",
"emails",
".",
"A",
"specific",
"has",
"##h",
"calculation",
"is",
"necessary",
"each",
"time",
"an",
"email",
"is",
"sent",
",",
"thereby",
"excluding",
"spa",
"##mmer",
"##s",
".",
"Bit",
"##co",
"##in",
"uses",
"Po",
"##W",
"to",
"produce",
"a",
"mechanism",
"which",
"prevents",
"the",
"mi",
"##s",
"##re",
"##p",
"##res",
"##entation",
"of",
"data",
"and",
"du",
"##plicate",
"payments",
"without",
"the",
"need",
"for",
"a",
"central",
"authority",
",",
"and",
"which",
"can",
"preserve",
"the",
"system",
"against",
"attacks",
"by",
"ma",
"##lic",
"##ious",
"users",
".",
"E",
".",
"Pro",
"##of",
"of",
"St",
"##ake",
"(",
"Po",
"##S",
")",
"Po",
"##S",
"[",
"12",
"]",
"is",
"an",
"alternative",
"mechanism",
"for",
"Po",
"##W",
"which",
"select",
"##s",
"the",
"next",
"mining",
"node",
"based",
"on",
"their",
"holding",
"of",
"the",
"native",
"digital",
"currency",
"of",
"the",
"block",
"##cha",
"##in",
"network",
".",
"For",
"example",
",",
"the",
"miners",
"need",
"to",
"prove",
"the",
"ownership",
"of",
"a",
"certain",
"amount",
"of",
"peer",
"coin",
"currency",
"in",
"order",
"to",
"mine",
"blocks",
".",
"Po",
"##W",
"[",
"13",
"]",
"mining",
"is",
"very",
"costly",
".",
"The",
"procedure",
"is",
"especially",
"power",
"intense",
".",
"Po",
"##S",
"is",
"significantly",
"projected",
"to",
"minimize",
"the",
"expense",
"of",
"mining",
".",
"Po",
"##S",
"preserves",
"a",
"single",
"branch",
",",
"and",
"yet",
"transforms",
"the",
"puzzle",
"'",
"s",
"trouble",
"to",
"be",
"inverse",
"##ly",
"relative",
"to",
"the",
"mine",
"##r",
"'",
"s",
"stake",
"in",
"the",
"network",
".",
"A",
"stake",
"is",
"ultimately",
"a",
"secured",
"membership",
"alongside",
"a",
"particular",
"stability",
",",
"addressing",
"the",
"mine",
"##r",
"'",
"s",
"dedication",
"to",
"maintaining",
"the",
"network",
".",
"This",
"enables",
"the",
"feature",
"which",
"comes",
"back",
"the",
"stake",
".",
"Subsequently",
",",
"a",
"mine",
"##r",
"could",
"produce",
"the",
"latest",
"block",
"by",
"re",
"##sol",
"##ving",
"the",
"puzzle",
".",
"F",
".",
"Pro",
"##of",
"of",
"Act",
"##ivity",
"(",
"Po",
"##A",
")",
"Po",
"##S",
"has",
"many",
"more",
"restrictions",
"that",
"ultimately",
"depend",
"on",
"the",
"coin",
"##age",
"which",
"could",
"involve",
"keeping",
"coins",
"in",
"a",
"coin",
"stake",
"transaction",
"to",
"ones",
"##elf",
".",
"Co",
"##ins",
"sent",
"to"
] | State of the art and challenges facing consensus p | 112 |
dger is replicated entirely on almost
all the nodes. Moreover, transactions are assembled into
blocks, then chained to one another. Therefore, the distributed
ledger is a replicated attach only data framework. A
blockchain begins with the initial states, while the ledger
records all the history of the revision procedure.
A technique encouraging distributed ledgers could classify
them in terms of three aspects. (Account, Asset, and Coin).
Initially, the application created on the top of the | [
2530,
14409,
27430,
1158,
7674,
1106,
1832,
1748,
10677,
1103,
9584,
2553,
117,
1133,
1132,
1136,
1529,
1107,
1103,
18959,
1708,
119,
1438,
117,
1103,
1514,
11477,
1110,
1115,
9584,
2553,
19213,
7747,
1103,
14372,
1674,
1136,
5088,
1106,
1103,
2443,
119,
1109,
14372,
1110,
6664,
7747,
15029,
2845,
3294,
2121,
1105,
8513,
1111,
1147,
23692,
117,
7097,
1106,
1301,
1228,
2568,
1254,
2886,
119,
1109,
1236,
1122,
1759,
1674,
1871,
1107,
21254,
1104,
23692,
23190,
3402,
1106,
1103,
2820,
18115,
15029,
10861,
2760,
3294,
164,
1489,
166,
119,
8094,
117,
1103,
26027,
1930,
1202,
4392,
1103,
9386,
119,
1760,
14733,
2971,
1104,
3294,
15029,
117,
1649,
117,
11000,
1116,
3690,
119,
144,
119,
5096,
10008,
1104,
2710,
1891,
113,
18959,
2101,
114,
138,
1159,
118,
13182,
1158,
1555,
2790,
1551,
20284,
3491,
1114,
7328,
1106,
3539,
3002,
1134,
7487,
9032,
9437,
1104,
1103,
4573,
1604,
3707,
1105,
15156,
1159,
1104,
1103,
1647,
119,
1247,
1132,
170,
1295,
1104,
1672,
1159,
13182,
1158,
4884,
117,
1259,
153,
2428,
2240,
1359,
25864,
1826,
119,
1636,
3002,
1105,
1551,
20284,
3491,
1132,
1144,
8961,
1105,
6561,
1194,
170,
2029,
2501,
9770,
119,
16097,
117,
1103,
16096,
1180,
1171,
9216,
3002,
6150,
1229,
1144,
8840,
1105,
6086,
1763,
1551,
20284,
3491,
164,
1405,
166,
119,
1706,
11407,
1142,
2486,
117,
1175,
1138,
1151,
1872,
1177,
118,
1270,
5128,
1551,
20284,
3491,
119,
4081,
1159,
13182,
10890,
2515,
170,
2166,
1144,
1324,
3510,
119,
1188,
14955,
1116,
170,
2335,
1546,
1104,
3002,
1256,
1107,
1103,
1692,
1104,
18238,
24998,
119,
9841,
117,
1122,
3272,
15870,
8406,
21487,
1134,
1132,
1136,
25667,
1165,
1122,
2502,
1106,
1231,
8005,
19667,
1193,
6755,
3002,
1107,
170,
5128,
4129,
1104,
1159,
13321,
119,
145,
119,
5096,
10008,
1104,
16915,
113,
18959,
2064,
114,
18959,
2064,
164,
1479,
166,
1110,
170,
1304,
1218,
118,
1227,
1105,
15668,
6806,
1111,
10348,
119,
6240,
11309,
2607,
1216,
1112,
22475,
3798,
170,
2166,
13618,
1336,
13639,
170,
2991,
13097,
1133,
3337,
2760,
8740,
12173,
6963,
7550,
1547,
5340,
1106,
4392,
14409,
1115,
1132,
4485,
1112,
1217,
18238,
2258,
1207,
4683,
6596,
119,
1706,
10407,
1103,
2607,
117,
1211,
1104,
1103,
13418,
1431,
12764,
119,
9139,
1733,
1547,
1329,
12783,
1540,
1118,
3780,
5511,
1134,
1547,
1129,
5164,
1118,
1168,
15029,
119,
23104,
117,
13418,
4282,
1106,
16315,
13676,
20889,
3558,
1103,
1211,
6246,
1116,
119,
146,
119,
5096,
10008,
1104,
11336,
19091,
12853,
5474,
113,
18959,
2069,
114,
153,
9565,
164,
1542,
166,
1110,
1861,
1106,
1103,
6777,
1104,
6790,
1133,
6986,
1103,
2912,
1106,
2194,
5250,
12598,
8268,
19755,
1118,
6103,
22965,
1105,
1231,
19091,
12853,
5474,
1115,
1169,
1129,
1215,
1106,
27842,
11928,
1112,
1122,
18381,
1106,
11858,
4412,
2200,
4956,
5092,
119,
147,
119,
5096,
10008,
1104,
2896,
11478,
5591,
2614,
113,
18959,
11943,
114,
18959,
11943,
164,
1407,
166,
164,
1627,
166,
22974,
18959,
2924,
1112,
170,
1167,
7856,
11309,
119,
16409,
16891,
1193,
117,
18959,
11943,
5049,
1107,
170,
4921,
4035,
16768,
119,
1188,
1110,
7087,
1118,
12713,
170,
3510,
1105,
7758,
117,
3780,
170,
7091,
9355
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"standard",
"transactions",
"assign",
"##ing",
"coins",
"to",
"rest",
"further",
"ruin",
"the",
"coin",
"##age",
",",
"but",
"are",
"not",
"included",
"in",
"the",
"Po",
"##S",
".",
"However",
",",
"the",
"main",
"weakness",
"is",
"that",
"coin",
"##age",
"collects",
"whenever",
"the",
"node",
"does",
"not",
"link",
"to",
"the",
"network",
".",
"The",
"node",
"is",
"sufficient",
"whenever",
"nodes",
"appear",
"online",
"sometimes",
"and",
"delay",
"for",
"their",
"incentive",
",",
"exclusively",
"to",
"go",
"off",
"##line",
"again",
"subsequently",
".",
"The",
"way",
"it",
"works",
"does",
"result",
"in",
"bursts",
"of",
"incentive",
"distributions",
"compared",
"to",
"the",
"situation",
"wherein",
"nodes",
"continuously",
"continue",
"online",
"[",
"14",
"]",
".",
"Nevertheless",
",",
"the",
"stakeholders",
"probably",
"do",
"accept",
"the",
"outcome",
".",
"An",
"insufficient",
"amount",
"of",
"online",
"nodes",
",",
"however",
",",
"facilitate",
"##s",
"attacks",
".",
"G",
".",
"Pro",
"##of",
"of",
"Public",
"##ation",
"(",
"Po",
"##P",
")",
"A",
"time",
"-",
"stamp",
"##ing",
"service",
"provides",
"times",
"##tam",
"##ps",
"with",
"regard",
"to",
"digital",
"records",
"which",
"firmly",
"maintains",
"monitoring",
"of",
"the",
"95",
"##8",
"creation",
"and",
"modification",
"time",
"of",
"the",
"record",
".",
"There",
"are",
"a",
"number",
"of",
"various",
"time",
"stamp",
"##ing",
"techniques",
",",
"including",
"P",
"##K",
"##I",
"based",
"centralized",
"services",
".",
"These",
"records",
"and",
"times",
"##tam",
"##ps",
"are",
"has",
"##hed",
"and",
"secured",
"through",
"a",
"private",
"key",
"server",
".",
"Nonetheless",
",",
"the",
"servers",
"could",
"back",
"##date",
"records",
"perfectly",
"while",
"has",
"##hing",
"and",
"signing",
"past",
"times",
"##tam",
"##ps",
"[",
"15",
"]",
".",
"To",
"tackle",
"this",
"issue",
",",
"there",
"have",
"been",
"developed",
"so",
"-",
"called",
"linked",
"times",
"##tam",
"##ps",
".",
"Every",
"time",
"stamp",
"certificate",
"contains",
"a",
"previous",
"has",
"##h",
"block",
".",
"This",
"assure",
"##s",
"a",
"complete",
"order",
"of",
"records",
"even",
"in",
"the",
"case",
"of",
"incorrect",
"clocks",
".",
"Moreover",
",",
"it",
"offers",
"hardened",
"fake",
"certificates",
"which",
"are",
"not",
"feasible",
"when",
"it",
"comes",
"to",
"re",
"##tro",
"##active",
"##ly",
"connecting",
"records",
"in",
"a",
"linked",
"chain",
"of",
"time",
"stamps",
".",
"H",
".",
"Pro",
"##of",
"of",
"Burn",
"(",
"Po",
"##B",
")",
"Po",
"##B",
"[",
"16",
"]",
"is",
"a",
"very",
"well",
"-",
"known",
"and",
"viable",
"tool",
"for",
"migration",
".",
"Natural",
"protocol",
"changes",
"such",
"as",
"invalid",
"##ating",
"a",
"previous",
"transaction",
"may",
"incorporate",
"a",
"soft",
"fork",
"but",
"commonly",
"continue",
"backward",
"compatible",
"Former",
"clients",
"might",
"agree",
"to",
"accept",
"transactions",
"that",
"are",
"regarded",
"as",
"being",
"incorrect",
"via",
"new",
"applications",
"releases",
".",
"To",
"implement",
"the",
"changes",
",",
"most",
"of",
"the",
"miners",
"should",
"upgrade",
".",
"Mine",
"##rs",
"might",
"use",
"computing",
"power",
"by",
"creating",
"blocks",
"which",
"might",
"be",
"rejected",
"by",
"other",
"nodes",
".",
"Alternatively",
",",
"miners",
"handle",
"to",
"oppose",
"resistant",
"upgrades",
"providing",
"the",
"most",
"decline",
"##s",
".",
"I",
".",
"Pro",
"##of",
"of",
"Re",
"##tri",
"##eva",
"##bility",
"(",
"Po",
"##R",
")",
"P",
"##OR",
"[",
"17",
"]",
"is",
"similar",
"to",
"the",
"proof",
"of",
"burn",
"but",
"increases",
"the",
"ability",
"to",
"provide",
"pro",
"##vable",
"commitment",
"protocols",
"by",
"considering",
"bandwidth",
"and",
"re",
"##tri",
"##eva",
"##bility",
"that",
"can",
"be",
"used",
"to",
"repay",
"expenses",
"as",
"it",
"proposes",
"to",
"decent",
"##ral",
"##ized",
"file",
"storage",
".",
"J",
".",
"Pro",
"##of",
"of",
"El",
"##ap",
"##sed",
"Time",
"(",
"Po",
"##ET",
")",
"Po",
"##ET",
"[",
"18",
"]",
"[",
"19",
"]",
"replaces",
"Po",
"##W",
"as",
"a",
"more",
"efficient",
"protocol",
".",
"Ex",
"##clusive",
"##ly",
",",
"Po",
"##ET",
"operates",
"in",
"a",
"protected",
"en",
"##clave",
".",
"This",
"is",
"initiated",
"by",
"generating",
"a",
"block",
"and",
"input",
",",
"creating",
"a",
"random",
"duration"
] | State of the art and challenges facing consensus p | 113 |
dger is replicated entirely on almost
all the nodes. Moreover, transactions are assembled into
blocks, then chained to one another. Therefore, the distributed
ledger is a replicated attach only data framework. A
blockchain begins with the initial states, while the ledger
records all the history of the revision procedure.
A technique encouraging distributed ledgers could classify
them in terms of three aspects. (Account, Asset, and Coin).
Initially, the application created on the top of the | [
2530,
14409,
27430,
1158,
7674,
1106,
1832,
1748,
10677,
1103,
9584,
2553,
117,
1133,
1132,
1136,
1529,
1107,
1103,
18959,
1708,
119,
1438,
117,
1103,
1514,
11477,
1110,
1115,
9584,
2553,
19213,
7747,
1103,
14372,
1674,
1136,
5088,
1106,
1103,
2443,
119,
1109,
14372,
1110,
6664,
7747,
15029,
2845,
3294,
2121,
1105,
8513,
1111,
1147,
23692,
117,
7097,
1106,
1301,
1228,
2568,
1254,
2886,
119,
1109,
1236,
1122,
1759,
1674,
1871,
1107,
21254,
1104,
23692,
23190,
3402,
1106,
1103,
2820,
18115,
15029,
10861,
2760,
3294,
164,
1489,
166,
119,
8094,
117,
1103,
26027,
1930,
1202,
4392,
1103,
9386,
119,
1760,
14733,
2971,
1104,
3294,
15029,
117,
1649,
117,
11000,
1116,
3690,
119,
144,
119,
5096,
10008,
1104,
2710,
1891,
113,
18959,
2101,
114,
138,
1159,
118,
13182,
1158,
1555,
2790,
1551,
20284,
3491,
1114,
7328,
1106,
3539,
3002,
1134,
7487,
9032,
9437,
1104,
1103,
4573,
1604,
3707,
1105,
15156,
1159,
1104,
1103,
1647,
119,
1247,
1132,
170,
1295,
1104,
1672,
1159,
13182,
1158,
4884,
117,
1259,
153,
2428,
2240,
1359,
25864,
1826,
119,
1636,
3002,
1105,
1551,
20284,
3491,
1132,
1144,
8961,
1105,
6561,
1194,
170,
2029,
2501,
9770,
119,
16097,
117,
1103,
16096,
1180,
1171,
9216,
3002,
6150,
1229,
1144,
8840,
1105,
6086,
1763,
1551,
20284,
3491,
164,
1405,
166,
119,
1706,
11407,
1142,
2486,
117,
1175,
1138,
1151,
1872,
1177,
118,
1270,
5128,
1551,
20284,
3491,
119,
4081,
1159,
13182,
10890,
2515,
170,
2166,
1144,
1324,
3510,
119,
1188,
14955,
1116,
170,
2335,
1546,
1104,
3002,
1256,
1107,
1103,
1692,
1104,
18238,
24998,
119,
9841,
117,
1122,
3272,
15870,
8406,
21487,
1134,
1132,
1136,
25667,
1165,
1122,
2502,
1106,
1231,
8005,
19667,
1193,
6755,
3002,
1107,
170,
5128,
4129,
1104,
1159,
13321,
119,
145,
119,
5096,
10008,
1104,
16915,
113,
18959,
2064,
114,
18959,
2064,
164,
1479,
166,
1110,
170,
1304,
1218,
118,
1227,
1105,
15668,
6806,
1111,
10348,
119,
6240,
11309,
2607,
1216,
1112,
22475,
3798,
170,
2166,
13618,
1336,
13639,
170,
2991,
13097,
1133,
3337,
2760,
8740,
12173,
6963,
7550,
1547,
5340,
1106,
4392,
14409,
1115,
1132,
4485,
1112,
1217,
18238,
2258,
1207,
4683,
6596,
119,
1706,
10407,
1103,
2607,
117,
1211,
1104,
1103,
13418,
1431,
12764,
119,
9139,
1733,
1547,
1329,
12783,
1540,
1118,
3780,
5511,
1134,
1547,
1129,
5164,
1118,
1168,
15029,
119,
23104,
117,
13418,
4282,
1106,
16315,
13676,
20889,
3558,
1103,
1211,
6246,
1116,
119,
146,
119,
5096,
10008,
1104,
11336,
19091,
12853,
5474,
113,
18959,
2069,
114,
153,
9565,
164,
1542,
166,
1110,
1861,
1106,
1103,
6777,
1104,
6790,
1133,
6986,
1103,
2912,
1106,
2194,
5250,
12598,
8268,
19755,
1118,
6103,
22965,
1105,
1231,
19091,
12853,
5474,
1115,
1169,
1129,
1215,
1106,
27842,
11928,
1112,
1122,
18381,
1106,
11858,
4412,
2200,
4956,
5092,
119,
147,
119,
5096,
10008,
1104,
2896,
11478,
5591,
2614,
113,
18959,
11943,
114,
18959,
11943,
164,
1407,
166,
164,
1627,
166,
22974,
18959,
2924,
1112,
170,
1167,
7856,
11309,
119,
16409,
16891,
1193,
117,
18959,
11943,
5049,
1107,
170,
4921,
4035,
16768,
119,
1188,
1110,
7087,
1118,
12713,
170,
3510,
1105,
7758,
117,
3780,
170,
7091,
9355
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"standard",
"transactions",
"assign",
"##ing",
"coins",
"to",
"rest",
"further",
"ruin",
"the",
"coin",
"##age",
",",
"but",
"are",
"not",
"included",
"in",
"the",
"Po",
"##S",
".",
"However",
",",
"the",
"main",
"weakness",
"is",
"that",
"coin",
"##age",
"collects",
"whenever",
"the",
"node",
"does",
"not",
"link",
"to",
"the",
"network",
".",
"The",
"node",
"is",
"sufficient",
"whenever",
"nodes",
"appear",
"online",
"sometimes",
"and",
"delay",
"for",
"their",
"incentive",
",",
"exclusively",
"to",
"go",
"off",
"##line",
"again",
"subsequently",
".",
"The",
"way",
"it",
"works",
"does",
"result",
"in",
"bursts",
"of",
"incentive",
"distributions",
"compared",
"to",
"the",
"situation",
"wherein",
"nodes",
"continuously",
"continue",
"online",
"[",
"14",
"]",
".",
"Nevertheless",
",",
"the",
"stakeholders",
"probably",
"do",
"accept",
"the",
"outcome",
".",
"An",
"insufficient",
"amount",
"of",
"online",
"nodes",
",",
"however",
",",
"facilitate",
"##s",
"attacks",
".",
"G",
".",
"Pro",
"##of",
"of",
"Public",
"##ation",
"(",
"Po",
"##P",
")",
"A",
"time",
"-",
"stamp",
"##ing",
"service",
"provides",
"times",
"##tam",
"##ps",
"with",
"regard",
"to",
"digital",
"records",
"which",
"firmly",
"maintains",
"monitoring",
"of",
"the",
"95",
"##8",
"creation",
"and",
"modification",
"time",
"of",
"the",
"record",
".",
"There",
"are",
"a",
"number",
"of",
"various",
"time",
"stamp",
"##ing",
"techniques",
",",
"including",
"P",
"##K",
"##I",
"based",
"centralized",
"services",
".",
"These",
"records",
"and",
"times",
"##tam",
"##ps",
"are",
"has",
"##hed",
"and",
"secured",
"through",
"a",
"private",
"key",
"server",
".",
"Nonetheless",
",",
"the",
"servers",
"could",
"back",
"##date",
"records",
"perfectly",
"while",
"has",
"##hing",
"and",
"signing",
"past",
"times",
"##tam",
"##ps",
"[",
"15",
"]",
".",
"To",
"tackle",
"this",
"issue",
",",
"there",
"have",
"been",
"developed",
"so",
"-",
"called",
"linked",
"times",
"##tam",
"##ps",
".",
"Every",
"time",
"stamp",
"certificate",
"contains",
"a",
"previous",
"has",
"##h",
"block",
".",
"This",
"assure",
"##s",
"a",
"complete",
"order",
"of",
"records",
"even",
"in",
"the",
"case",
"of",
"incorrect",
"clocks",
".",
"Moreover",
",",
"it",
"offers",
"hardened",
"fake",
"certificates",
"which",
"are",
"not",
"feasible",
"when",
"it",
"comes",
"to",
"re",
"##tro",
"##active",
"##ly",
"connecting",
"records",
"in",
"a",
"linked",
"chain",
"of",
"time",
"stamps",
".",
"H",
".",
"Pro",
"##of",
"of",
"Burn",
"(",
"Po",
"##B",
")",
"Po",
"##B",
"[",
"16",
"]",
"is",
"a",
"very",
"well",
"-",
"known",
"and",
"viable",
"tool",
"for",
"migration",
".",
"Natural",
"protocol",
"changes",
"such",
"as",
"invalid",
"##ating",
"a",
"previous",
"transaction",
"may",
"incorporate",
"a",
"soft",
"fork",
"but",
"commonly",
"continue",
"backward",
"compatible",
"Former",
"clients",
"might",
"agree",
"to",
"accept",
"transactions",
"that",
"are",
"regarded",
"as",
"being",
"incorrect",
"via",
"new",
"applications",
"releases",
".",
"To",
"implement",
"the",
"changes",
",",
"most",
"of",
"the",
"miners",
"should",
"upgrade",
".",
"Mine",
"##rs",
"might",
"use",
"computing",
"power",
"by",
"creating",
"blocks",
"which",
"might",
"be",
"rejected",
"by",
"other",
"nodes",
".",
"Alternatively",
",",
"miners",
"handle",
"to",
"oppose",
"resistant",
"upgrades",
"providing",
"the",
"most",
"decline",
"##s",
".",
"I",
".",
"Pro",
"##of",
"of",
"Re",
"##tri",
"##eva",
"##bility",
"(",
"Po",
"##R",
")",
"P",
"##OR",
"[",
"17",
"]",
"is",
"similar",
"to",
"the",
"proof",
"of",
"burn",
"but",
"increases",
"the",
"ability",
"to",
"provide",
"pro",
"##vable",
"commitment",
"protocols",
"by",
"considering",
"bandwidth",
"and",
"re",
"##tri",
"##eva",
"##bility",
"that",
"can",
"be",
"used",
"to",
"repay",
"expenses",
"as",
"it",
"proposes",
"to",
"decent",
"##ral",
"##ized",
"file",
"storage",
".",
"J",
".",
"Pro",
"##of",
"of",
"El",
"##ap",
"##sed",
"Time",
"(",
"Po",
"##ET",
")",
"Po",
"##ET",
"[",
"18",
"]",
"[",
"19",
"]",
"replaces",
"Po",
"##W",
"as",
"a",
"more",
"efficient",
"protocol",
".",
"Ex",
"##clusive",
"##ly",
",",
"Po",
"##ET",
"operates",
"in",
"a",
"protected",
"en",
"##clave",
".",
"This",
"is",
"initiated",
"by",
"generating",
"a",
"block",
"and",
"input",
",",
"creating",
"a",
"random",
"duration"
] | State of the art and challenges facing consensus p | 114 |
ledger
establishes the information entirely in such a way as to keep
within the ledger A cryptocurrency application will use to
create a user account similar to that found in conventional
banking. The intention is that it is simple to build and apply a
lower level model such as an example table or a critical value
as mentioned. Second, the functional system might have one
or higher ledgers which can link to one another. A large
enterprise, for instance, may have multiple ledgers, one for | [
1159,
119,
2611,
117,
1142,
1180,
1129,
1215,
1106,
3076,
21487,
117,
2951,
8985,
1293,
1677,
9355,
9032,
3175,
1165,
1103,
1159,
1197,
3471,
119,
138,
14372,
1134,
18959,
11943,
6570,
170,
1374,
1551,
1180,
12647,
6696,
1103,
3510,
117,
1517,
1103,
1159,
1197,
4252,
20082,
1116,
119,
1370,
1859,
117,
1103,
14372,
1180,
7543,
1147,
18959,
11943,
10890,
1106,
1103,
3510,
117,
19148,
3558,
1115,
1159,
1108,
1159,
7681,
1190,
1184,
1687,
1114,
1251,
1168,
14372,
1103,
3510,
1110,
4092,
119,
148,
119,
5096,
10008,
1104,
17212,
19905,
113,
18959,
1658,
114,
18959,
1658,
164,
1406,
166,
164,
1626,
166,
2745,
10682,
3204,
1106,
9711,
1103,
1295,
1104,
16498,
1116,
2320,
1106,
21073,
4290,
119,
1109,
151,
118,
14372,
2443,
1169,
1208,
21073,
1146,
1106,
151,
134,
123,
8050,
10704,
11315,
1233,
15029,
117,
1112,
4151,
1106,
151,
134,
124,
8050,
10704,
11315,
1233,
15029,
1107,
1103,
1560,
153,
26447,
1942,
119,
149,
119,
5096,
10008,
1104,
146,
24729,
16242,
3633,
113,
18959,
2240,
114,
18959,
2240,
164,
128,
166,
2745,
170,
3442,
1115,
13687,
15029,
1194,
13618,
10873,
3622,
117,
19105,
1103,
13618,
12709,
1105,
1103,
5233,
1116,
1104,
2510,
15029,
1112,
24091,
117,
13170,
1103,
4495,
1104,
1296,
14372,
1105,
1902,
3798,
1103,
9830,
1606,
1144,
1324,
3254,
19675,
1116,
1106,
1167,
2418,
15029,
119,
140,
23225,
1158,
1110,
2637,
1106,
1294,
1122,
25667,
1106,
11552,
15029,
1134,
1132,
3566,
6713,
1106,
10836,
5696,
14409,
119,
150,
119,
5096,
10008,
1104,
13432,
1468,
3157,
113,
18959,
2346,
114,
18959,
2346,
164,
1659,
166,
1110,
1737,
1114,
7328,
1106,
1672,
4817,
1105,
2266,
1107,
2538,
1104,
4172,
1826,
113,
5582,
117,
1268,
1106,
1329,
117,
1105,
1177,
5275,
114,
119,
1135,
1110,
1136,
2609,
1106,
2860,
118,
2272,
1869,
119,
151,
119,
5096,
10008,
1104,
4525,
113,
18959,
1708,
1643,
114,
18959,
1708,
1643,
164,
1695,
166,
1110,
14299,
11858,
4412,
2734,
1107,
5463,
14372,
1907,
1105,
15816,
1103,
1108,
11535,
1104,
19903,
1250,
1107,
1103,
1449,
119,
152,
119,
9352,
12606,
2913,
5096,
10008,
1104,
1457,
9899,
113,
141,
23329,
1708,
114,
141,
23329,
1708,
164,
1572,
166,
1110,
170,
2698,
117,
6548,
117,
11858,
4412,
2200,
117,
1105,
14785,
10923,
2235,
119,
141,
23329,
1708,
24242,
1103,
2308,
1106,
8219,
14507,
22843,
6612,
117,
1107,
1546,
1106,
9474,
10923,
2645,
1107,
170,
9483,
1105,
22338,
4758,
119,
1398,
14372,
1714,
2619,
8803,
3510,
11491,
1105,
1472,
13618,
10855,
119,
1220,
1169,
1129,
8054,
1194,
170,
3468,
13715,
119,
6712,
3510,
9263,
9396,
14409,
1106,
1129,
22480,
1107,
1213,
122,
1248,
119,
18959,
5208,
16764,
1193,
117,
1807,
1155,
117,
1103,
10923,
11309,
1108,
1687,
1106,
3244,
1155,
2833,
1114,
7328,
1106,
5576,
18766,
9739,
12638,
19019,
1116,
119,
153,
119,
155,
9717,
7136,
155,
9717,
7136,
164,
127,
166,
1110,
1842,
118,
1159,
10272,
3433,
1449,
113,
155,
1942,
13472,
114,
8616,
1106,
10202,
16845,
1105,
1231,
9084,
5108,
2093,
6379,
119,
1135,
1110,
1932,
1227,
1112,
155,
9717,
7136,
13809,
15022,
17580,
113,
155,
1942,
3190,
2101,
114,
119,
155,
9717,
7136,
1108,
1687,
1170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"time",
".",
"Later",
",",
"this",
"could",
"be",
"used",
"to",
"build",
"certificates",
",",
"sign",
"##ifying",
"how",
"far",
"duration",
"maintains",
"transferred",
"when",
"the",
"time",
"##r",
"begins",
".",
"A",
"node",
"which",
"Po",
"##ET",
"produces",
"a",
"few",
"times",
"could",
"app",
"##end",
"the",
"block",
",",
"once",
"the",
"time",
"##r",
"ex",
"##pire",
"##s",
".",
"For",
"example",
",",
"the",
"node",
"could",
"connect",
"their",
"Po",
"##ET",
"certificate",
"to",
"the",
"block",
",",
"additionally",
"providing",
"that",
"time",
"was",
"time",
"shorter",
"than",
"what",
"created",
"with",
"any",
"other",
"node",
"the",
"block",
"is",
"approved",
".",
"K",
".",
"Pro",
"##of",
"of",
"Cap",
"##acity",
"(",
"Po",
"##C",
")",
"Po",
"##C",
"[",
"20",
"]",
"[",
"21",
"]",
"uses",
"reliable",
"equipment",
"to",
"decrease",
"the",
"number",
"of",
"replica",
"##s",
"required",
"to",
"tolerate",
"failure",
".",
"The",
"N",
"-",
"node",
"network",
"can",
"now",
"tolerate",
"up",
"to",
"N",
"=",
"2",
"ad",
"##vers",
"##aria",
"##l",
"nodes",
",",
"as",
"opposed",
"to",
"N",
"=",
"3",
"ad",
"##vers",
"##aria",
"##l",
"nodes",
"in",
"the",
"original",
"P",
"##BF",
"##T",
".",
"L",
".",
"Pro",
"##of",
"of",
"I",
"##mpo",
"##rta",
"##nce",
"(",
"Po",
"##I",
")",
"Po",
"##I",
"[",
"7",
"]",
"uses",
"a",
"method",
"that",
"clusters",
"nodes",
"through",
"transaction",
"graph",
"analysis",
",",
"utilizing",
"the",
"transaction",
"quantities",
"and",
"the",
"balance",
"##s",
"of",
"individual",
"nodes",
"as",
"indicators",
",",
"determining",
"the",
"importance",
"of",
"each",
"node",
"and",
"design",
"##ating",
"the",
"priority",
"using",
"has",
"##h",
"com",
"##putation",
"##s",
"to",
"more",
"significant",
"nodes",
".",
"C",
"##luster",
"##ing",
"is",
"expected",
"to",
"make",
"it",
"feasible",
"to",
"detect",
"nodes",
"which",
"are",
"possibly",
"attempting",
"to",
"commit",
"illegal",
"transactions",
".",
"M",
".",
"Pro",
"##of",
"of",
"Own",
"##ers",
"##hip",
"(",
"Po",
"##O",
")",
"Po",
"##O",
"[",
"22",
"]",
"is",
"considered",
"with",
"regard",
"to",
"various",
"goods",
"and",
"rights",
"in",
"terms",
"of",
"receiving",
"services",
"(",
"ownership",
",",
"right",
"to",
"use",
",",
"and",
"so",
"forth",
")",
".",
"It",
"is",
"not",
"limited",
"to",
"value",
"-",
"related",
"information",
".",
"N",
".",
"Pro",
"##of",
"of",
"Space",
"(",
"Po",
"##S",
"##p",
")",
"Po",
"##S",
"##p",
"[",
"23",
"]",
"is",
"recovering",
"decent",
"##ral",
"##ization",
"in",
"mining",
"node",
"available",
"and",
"limiting",
"the",
"was",
"##tage",
"of",
"computational",
"work",
"in",
"the",
"system",
".",
"O",
".",
"Del",
"##eg",
"##ated",
"Pro",
"##of",
"of",
"St",
"##ake",
"(",
"D",
"##PO",
"##S",
")",
"D",
"##PO",
"##S",
"[",
"24",
"]",
"is",
"a",
"fast",
",",
"excellent",
",",
"decent",
"##ral",
"##ized",
",",
"and",
"convenient",
"consensus",
"model",
".",
"D",
"##PO",
"##S",
"utilizes",
"the",
"energy",
"to",
"stake",
"##holder",
"endorsement",
"voting",
",",
"in",
"order",
"to",
"solve",
"consensus",
"problems",
"in",
"a",
"reasonable",
"and",
"fashionable",
"manner",
".",
"All",
"node",
"free",
"activities",
"involve",
"block",
"timing",
"and",
"different",
"transaction",
"sizes",
".",
"They",
"can",
"be",
"updated",
"through",
"a",
"chosen",
"delegate",
".",
"Collection",
"block",
"manufacturers",
"enable",
"transactions",
"to",
"be",
"verified",
"in",
"around",
"1",
"second",
".",
"Po",
"##ten",
"##tial",
"##ly",
",",
"above",
"all",
",",
"the",
"consensus",
"protocol",
"was",
"created",
"to",
"protect",
"all",
"individuals",
"with",
"regard",
"to",
"und",
"##esi",
"##rable",
"regulatory",
"disturbance",
"##s",
".",
"P",
".",
"R",
"##ip",
"##ple",
"R",
"##ip",
"##ple",
"[",
"6",
"]",
"is",
"real",
"-",
"time",
"gross",
"settlement",
"system",
"(",
"R",
"##T",
"##GS",
")",
"relating",
"to",
"currency",
"transfers",
"and",
"re",
"##mit",
"##tan",
"##ce",
"networks",
".",
"It",
"is",
"usually",
"known",
"as",
"R",
"##ip",
"##ple",
"Trans",
"##action",
"Protocol",
"(",
"R",
"##T",
"##X",
"##P",
")",
".",
"R",
"##ip",
"##ple",
"was",
"created",
"after"
] | State of the art and challenges facing consensus p | 115 |
ledger
establishes the information entirely in such a way as to keep
within the ledger A cryptocurrency application will use to
create a user account similar to that found in conventional
banking. The intention is that it is simple to build and apply a
lower level model such as an example table or a critical value
as mentioned. Second, the functional system might have one
or higher ledgers which can link to one another. A large
enterprise, for instance, may have multiple ledgers, one for | [
1159,
119,
2611,
117,
1142,
1180,
1129,
1215,
1106,
3076,
21487,
117,
2951,
8985,
1293,
1677,
9355,
9032,
3175,
1165,
1103,
1159,
1197,
3471,
119,
138,
14372,
1134,
18959,
11943,
6570,
170,
1374,
1551,
1180,
12647,
6696,
1103,
3510,
117,
1517,
1103,
1159,
1197,
4252,
20082,
1116,
119,
1370,
1859,
117,
1103,
14372,
1180,
7543,
1147,
18959,
11943,
10890,
1106,
1103,
3510,
117,
19148,
3558,
1115,
1159,
1108,
1159,
7681,
1190,
1184,
1687,
1114,
1251,
1168,
14372,
1103,
3510,
1110,
4092,
119,
148,
119,
5096,
10008,
1104,
17212,
19905,
113,
18959,
1658,
114,
18959,
1658,
164,
1406,
166,
164,
1626,
166,
2745,
10682,
3204,
1106,
9711,
1103,
1295,
1104,
16498,
1116,
2320,
1106,
21073,
4290,
119,
1109,
151,
118,
14372,
2443,
1169,
1208,
21073,
1146,
1106,
151,
134,
123,
8050,
10704,
11315,
1233,
15029,
117,
1112,
4151,
1106,
151,
134,
124,
8050,
10704,
11315,
1233,
15029,
1107,
1103,
1560,
153,
26447,
1942,
119,
149,
119,
5096,
10008,
1104,
146,
24729,
16242,
3633,
113,
18959,
2240,
114,
18959,
2240,
164,
128,
166,
2745,
170,
3442,
1115,
13687,
15029,
1194,
13618,
10873,
3622,
117,
19105,
1103,
13618,
12709,
1105,
1103,
5233,
1116,
1104,
2510,
15029,
1112,
24091,
117,
13170,
1103,
4495,
1104,
1296,
14372,
1105,
1902,
3798,
1103,
9830,
1606,
1144,
1324,
3254,
19675,
1116,
1106,
1167,
2418,
15029,
119,
140,
23225,
1158,
1110,
2637,
1106,
1294,
1122,
25667,
1106,
11552,
15029,
1134,
1132,
3566,
6713,
1106,
10836,
5696,
14409,
119,
150,
119,
5096,
10008,
1104,
13432,
1468,
3157,
113,
18959,
2346,
114,
18959,
2346,
164,
1659,
166,
1110,
1737,
1114,
7328,
1106,
1672,
4817,
1105,
2266,
1107,
2538,
1104,
4172,
1826,
113,
5582,
117,
1268,
1106,
1329,
117,
1105,
1177,
5275,
114,
119,
1135,
1110,
1136,
2609,
1106,
2860,
118,
2272,
1869,
119,
151,
119,
5096,
10008,
1104,
4525,
113,
18959,
1708,
1643,
114,
18959,
1708,
1643,
164,
1695,
166,
1110,
14299,
11858,
4412,
2734,
1107,
5463,
14372,
1907,
1105,
15816,
1103,
1108,
11535,
1104,
19903,
1250,
1107,
1103,
1449,
119,
152,
119,
9352,
12606,
2913,
5096,
10008,
1104,
1457,
9899,
113,
141,
23329,
1708,
114,
141,
23329,
1708,
164,
1572,
166,
1110,
170,
2698,
117,
6548,
117,
11858,
4412,
2200,
117,
1105,
14785,
10923,
2235,
119,
141,
23329,
1708,
24242,
1103,
2308,
1106,
8219,
14507,
22843,
6612,
117,
1107,
1546,
1106,
9474,
10923,
2645,
1107,
170,
9483,
1105,
22338,
4758,
119,
1398,
14372,
1714,
2619,
8803,
3510,
11491,
1105,
1472,
13618,
10855,
119,
1220,
1169,
1129,
8054,
1194,
170,
3468,
13715,
119,
6712,
3510,
9263,
9396,
14409,
1106,
1129,
22480,
1107,
1213,
122,
1248,
119,
18959,
5208,
16764,
1193,
117,
1807,
1155,
117,
1103,
10923,
11309,
1108,
1687,
1106,
3244,
1155,
2833,
1114,
7328,
1106,
5576,
18766,
9739,
12638,
19019,
1116,
119,
153,
119,
155,
9717,
7136,
155,
9717,
7136,
164,
127,
166,
1110,
1842,
118,
1159,
10272,
3433,
1449,
113,
155,
1942,
13472,
114,
8616,
1106,
10202,
16845,
1105,
1231,
9084,
5108,
2093,
6379,
119,
1135,
1110,
1932,
1227,
1112,
155,
9717,
7136,
13809,
15022,
17580,
113,
155,
1942,
3190,
2101,
114,
119,
155,
9717,
7136,
1108,
1687,
1170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"time",
".",
"Later",
",",
"this",
"could",
"be",
"used",
"to",
"build",
"certificates",
",",
"sign",
"##ifying",
"how",
"far",
"duration",
"maintains",
"transferred",
"when",
"the",
"time",
"##r",
"begins",
".",
"A",
"node",
"which",
"Po",
"##ET",
"produces",
"a",
"few",
"times",
"could",
"app",
"##end",
"the",
"block",
",",
"once",
"the",
"time",
"##r",
"ex",
"##pire",
"##s",
".",
"For",
"example",
",",
"the",
"node",
"could",
"connect",
"their",
"Po",
"##ET",
"certificate",
"to",
"the",
"block",
",",
"additionally",
"providing",
"that",
"time",
"was",
"time",
"shorter",
"than",
"what",
"created",
"with",
"any",
"other",
"node",
"the",
"block",
"is",
"approved",
".",
"K",
".",
"Pro",
"##of",
"of",
"Cap",
"##acity",
"(",
"Po",
"##C",
")",
"Po",
"##C",
"[",
"20",
"]",
"[",
"21",
"]",
"uses",
"reliable",
"equipment",
"to",
"decrease",
"the",
"number",
"of",
"replica",
"##s",
"required",
"to",
"tolerate",
"failure",
".",
"The",
"N",
"-",
"node",
"network",
"can",
"now",
"tolerate",
"up",
"to",
"N",
"=",
"2",
"ad",
"##vers",
"##aria",
"##l",
"nodes",
",",
"as",
"opposed",
"to",
"N",
"=",
"3",
"ad",
"##vers",
"##aria",
"##l",
"nodes",
"in",
"the",
"original",
"P",
"##BF",
"##T",
".",
"L",
".",
"Pro",
"##of",
"of",
"I",
"##mpo",
"##rta",
"##nce",
"(",
"Po",
"##I",
")",
"Po",
"##I",
"[",
"7",
"]",
"uses",
"a",
"method",
"that",
"clusters",
"nodes",
"through",
"transaction",
"graph",
"analysis",
",",
"utilizing",
"the",
"transaction",
"quantities",
"and",
"the",
"balance",
"##s",
"of",
"individual",
"nodes",
"as",
"indicators",
",",
"determining",
"the",
"importance",
"of",
"each",
"node",
"and",
"design",
"##ating",
"the",
"priority",
"using",
"has",
"##h",
"com",
"##putation",
"##s",
"to",
"more",
"significant",
"nodes",
".",
"C",
"##luster",
"##ing",
"is",
"expected",
"to",
"make",
"it",
"feasible",
"to",
"detect",
"nodes",
"which",
"are",
"possibly",
"attempting",
"to",
"commit",
"illegal",
"transactions",
".",
"M",
".",
"Pro",
"##of",
"of",
"Own",
"##ers",
"##hip",
"(",
"Po",
"##O",
")",
"Po",
"##O",
"[",
"22",
"]",
"is",
"considered",
"with",
"regard",
"to",
"various",
"goods",
"and",
"rights",
"in",
"terms",
"of",
"receiving",
"services",
"(",
"ownership",
",",
"right",
"to",
"use",
",",
"and",
"so",
"forth",
")",
".",
"It",
"is",
"not",
"limited",
"to",
"value",
"-",
"related",
"information",
".",
"N",
".",
"Pro",
"##of",
"of",
"Space",
"(",
"Po",
"##S",
"##p",
")",
"Po",
"##S",
"##p",
"[",
"23",
"]",
"is",
"recovering",
"decent",
"##ral",
"##ization",
"in",
"mining",
"node",
"available",
"and",
"limiting",
"the",
"was",
"##tage",
"of",
"computational",
"work",
"in",
"the",
"system",
".",
"O",
".",
"Del",
"##eg",
"##ated",
"Pro",
"##of",
"of",
"St",
"##ake",
"(",
"D",
"##PO",
"##S",
")",
"D",
"##PO",
"##S",
"[",
"24",
"]",
"is",
"a",
"fast",
",",
"excellent",
",",
"decent",
"##ral",
"##ized",
",",
"and",
"convenient",
"consensus",
"model",
".",
"D",
"##PO",
"##S",
"utilizes",
"the",
"energy",
"to",
"stake",
"##holder",
"endorsement",
"voting",
",",
"in",
"order",
"to",
"solve",
"consensus",
"problems",
"in",
"a",
"reasonable",
"and",
"fashionable",
"manner",
".",
"All",
"node",
"free",
"activities",
"involve",
"block",
"timing",
"and",
"different",
"transaction",
"sizes",
".",
"They",
"can",
"be",
"updated",
"through",
"a",
"chosen",
"delegate",
".",
"Collection",
"block",
"manufacturers",
"enable",
"transactions",
"to",
"be",
"verified",
"in",
"around",
"1",
"second",
".",
"Po",
"##ten",
"##tial",
"##ly",
",",
"above",
"all",
",",
"the",
"consensus",
"protocol",
"was",
"created",
"to",
"protect",
"all",
"individuals",
"with",
"regard",
"to",
"und",
"##esi",
"##rable",
"regulatory",
"disturbance",
"##s",
".",
"P",
".",
"R",
"##ip",
"##ple",
"R",
"##ip",
"##ple",
"[",
"6",
"]",
"is",
"real",
"-",
"time",
"gross",
"settlement",
"system",
"(",
"R",
"##T",
"##GS",
")",
"relating",
"to",
"currency",
"transfers",
"and",
"re",
"##mit",
"##tan",
"##ce",
"networks",
".",
"It",
"is",
"usually",
"known",
"as",
"R",
"##ip",
"##ple",
"Trans",
"##action",
"Protocol",
"(",
"R",
"##T",
"##X",
"##P",
")",
".",
"R",
"##ip",
"##ple",
"was",
"created",
"after"
] | State of the art and challenges facing consensus p | 116 |
every department such as engineering, sales, supply chain,
payroll, and so forth. Finally, ledger possession can fluctuate
significantly from being exposed entirely to the public to
being totally managed by one participant. Bitcoin, for
instance, was presented and, as a result, makes people think
that it is costly to determine who will update the public ledger.
Parity [1] predefines some owners who adjust the public
ledger simply by adding their signature to the blocks.
The information c | [
1103,
2819,
1104,
1501,
2674,
4639,
19755,
119,
155,
9717,
7136,
13267,
2699,
117,
1110,
2698,
117,
1105,
3272,
1714,
4529,
15997,
14409,
1114,
1185,
2965,
11713,
119,
1188,
23078,
22559,
1116,
1115,
4248,
8050,
9380,
13923,
117,
5354,
6451,
13335,
2149,
5123,
3457,
117,
26279,
1137,
170,
2079,
1104,
1472,
6245,
119,
2082,
16246,
117,
155,
9717,
7136,
1108,
15695,
4901,
1470,
21340,
1197,
1104,
1103,
1912,
1115,
24242,
10923,
8826,
1134,
9154,
10772,
117,
17755,
117,
1105,
1231,
9084,
5108,
7723,
119,
154,
119,
5157,
2692,
7937,
1204,
5157,
2692,
7937,
1204,
164,
1512,
166,
2923,
1104,
4683,
5336,
1103,
5343,
1105,
2366,
25544,
1104,
1126,
4048,
1113,
2967,
15029,
119,
1284,
5343,
1134,
5157,
2692,
7937,
1204,
5049,
3081,
119,
3236,
110,
1104,
15029,
8693,
1134,
1155,
1907,
15029,
2781,
1103,
1269,
13618,
1647,
1105,
3254,
22662,
1116,
1103,
1269,
1352,
119,
22087,
22712,
1105,
4836,
25544,
1108,
1126,
10311,
2486,
1113,
4901,
6379,
119,
1188,
13395,
7770,
10383,
1126,
6818,
3053,
1107,
2538,
1104,
6088,
15745,
119,
2684,
119,
18732,
12347,
12426,
6258,
11414,
1130,
1142,
2237,
117,
1195,
1138,
3402,
3510,
7147,
1394,
10923,
19755,
6995,
170,
2436,
1104,
8148,
3510,
7147,
1394,
5924,
119,
1636,
3322,
1104,
5924,
13639,
14372,
4193,
117,
2308,
7740,
117,
21073,
1181,
1540,
1104,
8050,
10704,
3113,
117,
2233,
2235,
117,
1846,
117,
7581,
117,
4048,
117,
1859,
1105,
1540,
1104,
4573,
1580,
1103,
8050,
10704,
3113,
117,
2443,
188,
27250,
8167,
10031,
19129,
117,
1105,
117,
1314,
1133,
1136,
1655,
117,
1103,
3796,
1104,
5663,
1757,
6777,
1116,
1104,
19755,
10311,
3510,
7147,
1394,
119,
1188,
1383,
1104,
4625,
1110,
1930,
1136,
16287,
2109,
117,
1133,
1195,
2059,
1122,
1110,
4702,
1111,
15089,
1155,
10923,
19755,
119,
1130,
1103,
1832,
1104,
1142,
2237,
117,
1195,
17794,
11389,
146,
119,
1107,
1167,
6505,
119,
4191,
119,
23096,
12507,
3663,
13882,
1708,
138,
119,
16752,
3792,
14410,
14975,
7577,
9311,
10923,
14975,
1138,
1472,
23347,
1105,
3282,
11713,
119,
11389,
146,
119,
7100,
1126,
8670,
1213,
1672,
10923,
14975,
117,
1105,
1195,
1329,
1103,
4625,
6103,
1378,
119,
2586,
18791,
7088,
1306,
1302,
2007,
22855,
5514,
17784,
3970,
1706,
2879,
2913,
1540,
1104,
8050,
10704,
3113,
7154,
2235,
6828,
16409,
10294,
16065,
1186,
183,
22491,
16409,
26671,
8784,
2101,
164,
128,
166,
7219,
1302,
1851,
110,
24442,
1431,
1129,
7443,
118,
24076,
156,
22825,
117,
23334,
117,
9155,
117,
3414,
156,
22825,
117,
1302,
156,
22825,
22929,
117,
2562,
7154,
117,
1457,
27611,
22401,
2758,
2137,
2064,
117,
16645,
117,
10978,
138,
26395,
1457,
27611,
139,
17095,
164,
129,
117,
130,
166,
7219,
2160,
3081,
119,
124,
110,
143,
11922,
7443,
118,
24076,
6291,
151,
120,
138,
1615,
20603,
1615,
153,
26447,
1942,
164,
1275,
166,
7219,
2160,
3081,
119,
124,
110,
143,
14045,
1183,
20777,
9538,
1116,
7443,
118,
24076,
3414,
19514,
117,
9155,
20115,
1468,
1615,
20603,
145,
24312,
19693,
1197,
18959,
2924,
164,
1429,
166,
2710,
1302,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
3,
4,
0,
0,
0,
13,
14,
14,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
3,
0,
3,
0,
3,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
0,
3,
0,
0,
3,
4,
4,
4,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
3,
4,
0,
0,
0,
13,
14,
14,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
3,
0,
3,
0,
3,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
0,
3,
0,
0,
3,
4,
4,
4,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"spread",
"of",
"open",
"source",
"Internet",
"protocols",
".",
"R",
"##ip",
"##ple",
"enables",
"security",
",",
"is",
"fast",
",",
"and",
"offers",
"free",
"worldwide",
"monetary",
"transactions",
"with",
"no",
"charge",
"##backs",
".",
"This",
"aids",
"token",
"##s",
"that",
"represent",
"ad",
"##ju",
"##dication",
",",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
",",
"commodities",
"or",
"a",
"range",
"of",
"different",
"benefits",
".",
"Most",
"importantly",
",",
"R",
"##ip",
"##ple",
"was",
"structured",
"distributed",
"public",
"ledge",
"##r",
"of",
"the",
"kind",
"that",
"utilizes",
"consensus",
"procedures",
"which",
"permit",
"payments",
",",
"exchanges",
",",
"and",
"re",
"##mit",
"##tan",
"##ces",
".",
"Q",
".",
"Ten",
"##der",
"##min",
"##t",
"Ten",
"##der",
"##min",
"##t",
"[",
"25",
"]",
"consists",
"of",
"applications",
"involving",
"the",
"secure",
"and",
"regular",
"replication",
"of",
"an",
"application",
"on",
"multiple",
"nodes",
".",
"We",
"secure",
"which",
"Ten",
"##der",
"##min",
"##t",
"operates",
"33",
".",
"34",
"%",
"of",
"nodes",
"fail",
"which",
"all",
"available",
"nodes",
"status",
"the",
"same",
"transaction",
"record",
"and",
"com",
"##pute",
"##s",
"the",
"same",
"state",
".",
"Se",
"##cure",
"and",
"constant",
"replication",
"was",
"an",
"underlying",
"issue",
"on",
"distributed",
"networks",
".",
"This",
"tech",
"##nic",
"performs",
"an",
"essential",
"function",
"in",
"terms",
"of",
"fault",
"tolerance",
".",
"III",
".",
"CO",
"##MP",
"##AR",
"##IS",
"##ON",
"In",
"this",
"section",
",",
"we",
"have",
"compared",
"block",
"##cha",
"##in",
"consensus",
"protocols",
"concerning",
"a",
"collection",
"of",
"fundamental",
"block",
"##cha",
"##in",
"characteristics",
".",
"These",
"types",
"of",
"characteristics",
"incorporate",
"node",
"identity",
",",
"energy",
"saving",
",",
"tolerate",
"##d",
"power",
"of",
"ad",
"##vers",
"##ary",
",",
"data",
"model",
",",
"language",
",",
"execution",
",",
"application",
",",
"example",
"and",
"power",
"of",
"95",
"##9",
"the",
"ad",
"##vers",
"##ary",
",",
"network",
"s",
"##ync",
"##hr",
"##ony",
"assumptions",
",",
"and",
",",
"last",
"but",
"not",
"least",
",",
"the",
"existence",
"of",
"correct",
"##ness",
"proof",
"##s",
"of",
"protocols",
"underlying",
"block",
"##cha",
"##in",
".",
"This",
"set",
"of",
"properties",
"is",
"probably",
"not",
"exhaust",
"##ive",
",",
"but",
"we",
"believe",
"it",
"is",
"representative",
"for",
"comparing",
"all",
"consensus",
"protocols",
".",
"In",
"the",
"rest",
"of",
"this",
"section",
",",
"we",
"propose",
"Table",
"I",
".",
"in",
"more",
"detail",
".",
"IV",
".",
"AN",
"##AL",
"##Y",
"##SI",
"##S",
"A",
".",
"Con",
"##sen",
"##sus",
"algorithms",
"comparison",
"Various",
"consensus",
"algorithms",
"have",
"different",
"strengths",
"and",
"draw",
"##backs",
".",
"Table",
"I",
".",
"brings",
"an",
"assessment",
"around",
"various",
"consensus",
"algorithms",
",",
"and",
"we",
"use",
"the",
"properties",
"considering",
"following",
".",
"Al",
"##gor",
"##ith",
"##m",
"No",
"##de",
"Identity",
"Energy",
"Sa",
"##ving",
"To",
"##ler",
"##ated",
"power",
"of",
"ad",
"##vers",
"##ary",
"Data",
"model",
"Language",
"Ex",
"##ec",
"##uti",
"##o",
"n",
"Application",
"Ex",
"##ample",
"CA",
"##P",
"[",
"7",
"]",
"Private",
"No",
"50",
"%",
"Rate",
"should",
"be",
"Key",
"-",
"Value",
"S",
"##QL",
",",
"Python",
",",
"Java",
",",
"Go",
"S",
"##QL",
",",
"No",
"S",
"##QL",
"Database",
",",
"Big",
"Data",
",",
"St",
"##orage",
"Mon",
"##go",
"##D",
"##B",
",",
"Cassandra",
",",
"MS",
"A",
"##zure",
"St",
"##orage",
"B",
"##GP",
"[",
"8",
",",
"9",
"]",
"Private",
"Yes",
"33",
".",
"3",
"%",
"F",
"##ail",
"Key",
"-",
"Value",
"Any",
"N",
"/",
"A",
"General",
"Applications",
"General",
"P",
"##BF",
"##T",
"[",
"10",
"]",
"Private",
"Yes",
"33",
".",
"3",
"%",
"F",
"##ault",
"##y",
"Rep",
"##lica",
"##s",
"Key",
"-",
"Value",
"Go",
"##lang",
",",
"Java",
"Dock",
"##ers",
"General",
"Applications",
"H",
"##yper",
"##ledge",
"##r",
"Po",
"##W",
"[",
"11",
"]",
"Public",
"No",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+"
] | State of the art and challenges facing consensus p | 117 |
every department such as engineering, sales, supply chain,
payroll, and so forth. Finally, ledger possession can fluctuate
significantly from being exposed entirely to the public to
being totally managed by one participant. Bitcoin, for
instance, was presented and, as a result, makes people think
that it is costly to determine who will update the public ledger.
Parity [1] predefines some owners who adjust the public
ledger simply by adding their signature to the blocks.
The information c | [
1103,
2819,
1104,
1501,
2674,
4639,
19755,
119,
155,
9717,
7136,
13267,
2699,
117,
1110,
2698,
117,
1105,
3272,
1714,
4529,
15997,
14409,
1114,
1185,
2965,
11713,
119,
1188,
23078,
22559,
1116,
1115,
4248,
8050,
9380,
13923,
117,
5354,
6451,
13335,
2149,
5123,
3457,
117,
26279,
1137,
170,
2079,
1104,
1472,
6245,
119,
2082,
16246,
117,
155,
9717,
7136,
1108,
15695,
4901,
1470,
21340,
1197,
1104,
1103,
1912,
1115,
24242,
10923,
8826,
1134,
9154,
10772,
117,
17755,
117,
1105,
1231,
9084,
5108,
7723,
119,
154,
119,
5157,
2692,
7937,
1204,
5157,
2692,
7937,
1204,
164,
1512,
166,
2923,
1104,
4683,
5336,
1103,
5343,
1105,
2366,
25544,
1104,
1126,
4048,
1113,
2967,
15029,
119,
1284,
5343,
1134,
5157,
2692,
7937,
1204,
5049,
3081,
119,
3236,
110,
1104,
15029,
8693,
1134,
1155,
1907,
15029,
2781,
1103,
1269,
13618,
1647,
1105,
3254,
22662,
1116,
1103,
1269,
1352,
119,
22087,
22712,
1105,
4836,
25544,
1108,
1126,
10311,
2486,
1113,
4901,
6379,
119,
1188,
13395,
7770,
10383,
1126,
6818,
3053,
1107,
2538,
1104,
6088,
15745,
119,
2684,
119,
18732,
12347,
12426,
6258,
11414,
1130,
1142,
2237,
117,
1195,
1138,
3402,
3510,
7147,
1394,
10923,
19755,
6995,
170,
2436,
1104,
8148,
3510,
7147,
1394,
5924,
119,
1636,
3322,
1104,
5924,
13639,
14372,
4193,
117,
2308,
7740,
117,
21073,
1181,
1540,
1104,
8050,
10704,
3113,
117,
2233,
2235,
117,
1846,
117,
7581,
117,
4048,
117,
1859,
1105,
1540,
1104,
4573,
1580,
1103,
8050,
10704,
3113,
117,
2443,
188,
27250,
8167,
10031,
19129,
117,
1105,
117,
1314,
1133,
1136,
1655,
117,
1103,
3796,
1104,
5663,
1757,
6777,
1116,
1104,
19755,
10311,
3510,
7147,
1394,
119,
1188,
1383,
1104,
4625,
1110,
1930,
1136,
16287,
2109,
117,
1133,
1195,
2059,
1122,
1110,
4702,
1111,
15089,
1155,
10923,
19755,
119,
1130,
1103,
1832,
1104,
1142,
2237,
117,
1195,
17794,
11389,
146,
119,
1107,
1167,
6505,
119,
4191,
119,
23096,
12507,
3663,
13882,
1708,
138,
119,
16752,
3792,
14410,
14975,
7577,
9311,
10923,
14975,
1138,
1472,
23347,
1105,
3282,
11713,
119,
11389,
146,
119,
7100,
1126,
8670,
1213,
1672,
10923,
14975,
117,
1105,
1195,
1329,
1103,
4625,
6103,
1378,
119,
2586,
18791,
7088,
1306,
1302,
2007,
22855,
5514,
17784,
3970,
1706,
2879,
2913,
1540,
1104,
8050,
10704,
3113,
7154,
2235,
6828,
16409,
10294,
16065,
1186,
183,
22491,
16409,
26671,
8784,
2101,
164,
128,
166,
7219,
1302,
1851,
110,
24442,
1431,
1129,
7443,
118,
24076,
156,
22825,
117,
23334,
117,
9155,
117,
3414,
156,
22825,
117,
1302,
156,
22825,
22929,
117,
2562,
7154,
117,
1457,
27611,
22401,
2758,
2137,
2064,
117,
16645,
117,
10978,
138,
26395,
1457,
27611,
139,
17095,
164,
129,
117,
130,
166,
7219,
2160,
3081,
119,
124,
110,
143,
11922,
7443,
118,
24076,
6291,
151,
120,
138,
1615,
20603,
1615,
153,
26447,
1942,
164,
1275,
166,
7219,
2160,
3081,
119,
124,
110,
143,
14045,
1183,
20777,
9538,
1116,
7443,
118,
24076,
3414,
19514,
117,
9155,
20115,
1468,
1615,
20603,
145,
24312,
19693,
1197,
18959,
2924,
164,
1429,
166,
2710,
1302,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"spread",
"of",
"open",
"source",
"Internet",
"protocols",
".",
"R",
"##ip",
"##ple",
"enables",
"security",
",",
"is",
"fast",
",",
"and",
"offers",
"free",
"worldwide",
"monetary",
"transactions",
"with",
"no",
"charge",
"##backs",
".",
"This",
"aids",
"token",
"##s",
"that",
"represent",
"ad",
"##ju",
"##dication",
",",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
",",
"commodities",
"or",
"a",
"range",
"of",
"different",
"benefits",
".",
"Most",
"importantly",
",",
"R",
"##ip",
"##ple",
"was",
"structured",
"distributed",
"public",
"ledge",
"##r",
"of",
"the",
"kind",
"that",
"utilizes",
"consensus",
"procedures",
"which",
"permit",
"payments",
",",
"exchanges",
",",
"and",
"re",
"##mit",
"##tan",
"##ces",
".",
"Q",
".",
"Ten",
"##der",
"##min",
"##t",
"Ten",
"##der",
"##min",
"##t",
"[",
"25",
"]",
"consists",
"of",
"applications",
"involving",
"the",
"secure",
"and",
"regular",
"replication",
"of",
"an",
"application",
"on",
"multiple",
"nodes",
".",
"We",
"secure",
"which",
"Ten",
"##der",
"##min",
"##t",
"operates",
"33",
".",
"34",
"%",
"of",
"nodes",
"fail",
"which",
"all",
"available",
"nodes",
"status",
"the",
"same",
"transaction",
"record",
"and",
"com",
"##pute",
"##s",
"the",
"same",
"state",
".",
"Se",
"##cure",
"and",
"constant",
"replication",
"was",
"an",
"underlying",
"issue",
"on",
"distributed",
"networks",
".",
"This",
"tech",
"##nic",
"performs",
"an",
"essential",
"function",
"in",
"terms",
"of",
"fault",
"tolerance",
".",
"III",
".",
"CO",
"##MP",
"##AR",
"##IS",
"##ON",
"In",
"this",
"section",
",",
"we",
"have",
"compared",
"block",
"##cha",
"##in",
"consensus",
"protocols",
"concerning",
"a",
"collection",
"of",
"fundamental",
"block",
"##cha",
"##in",
"characteristics",
".",
"These",
"types",
"of",
"characteristics",
"incorporate",
"node",
"identity",
",",
"energy",
"saving",
",",
"tolerate",
"##d",
"power",
"of",
"ad",
"##vers",
"##ary",
",",
"data",
"model",
",",
"language",
",",
"execution",
",",
"application",
",",
"example",
"and",
"power",
"of",
"95",
"##9",
"the",
"ad",
"##vers",
"##ary",
",",
"network",
"s",
"##ync",
"##hr",
"##ony",
"assumptions",
",",
"and",
",",
"last",
"but",
"not",
"least",
",",
"the",
"existence",
"of",
"correct",
"##ness",
"proof",
"##s",
"of",
"protocols",
"underlying",
"block",
"##cha",
"##in",
".",
"This",
"set",
"of",
"properties",
"is",
"probably",
"not",
"exhaust",
"##ive",
",",
"but",
"we",
"believe",
"it",
"is",
"representative",
"for",
"comparing",
"all",
"consensus",
"protocols",
".",
"In",
"the",
"rest",
"of",
"this",
"section",
",",
"we",
"propose",
"Table",
"I",
".",
"in",
"more",
"detail",
".",
"IV",
".",
"AN",
"##AL",
"##Y",
"##SI",
"##S",
"A",
".",
"Con",
"##sen",
"##sus",
"algorithms",
"comparison",
"Various",
"consensus",
"algorithms",
"have",
"different",
"strengths",
"and",
"draw",
"##backs",
".",
"Table",
"I",
".",
"brings",
"an",
"assessment",
"around",
"various",
"consensus",
"algorithms",
",",
"and",
"we",
"use",
"the",
"properties",
"considering",
"following",
".",
"Al",
"##gor",
"##ith",
"##m",
"No",
"##de",
"Identity",
"Energy",
"Sa",
"##ving",
"To",
"##ler",
"##ated",
"power",
"of",
"ad",
"##vers",
"##ary",
"Data",
"model",
"Language",
"Ex",
"##ec",
"##uti",
"##o",
"n",
"Application",
"Ex",
"##ample",
"CA",
"##P",
"[",
"7",
"]",
"Private",
"No",
"50",
"%",
"Rate",
"should",
"be",
"Key",
"-",
"Value",
"S",
"##QL",
",",
"Python",
",",
"Java",
",",
"Go",
"S",
"##QL",
",",
"No",
"S",
"##QL",
"Database",
",",
"Big",
"Data",
",",
"St",
"##orage",
"Mon",
"##go",
"##D",
"##B",
",",
"Cassandra",
",",
"MS",
"A",
"##zure",
"St",
"##orage",
"B",
"##GP",
"[",
"8",
",",
"9",
"]",
"Private",
"Yes",
"33",
".",
"3",
"%",
"F",
"##ail",
"Key",
"-",
"Value",
"Any",
"N",
"/",
"A",
"General",
"Applications",
"General",
"P",
"##BF",
"##T",
"[",
"10",
"]",
"Private",
"Yes",
"33",
".",
"3",
"%",
"F",
"##ault",
"##y",
"Rep",
"##lica",
"##s",
"Key",
"-",
"Value",
"Go",
"##lang",
",",
"Java",
"Dock",
"##ers",
"General",
"Applications",
"H",
"##yper",
"##ledge",
"##r",
"Po",
"##W",
"[",
"11",
"]",
"Public",
"No",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+"
] | State of the art and challenges facing consensus p | 118 |
ontained in the ledger demonstrates the
history of transactions up to the current time through the
blockchain. Updates to the ledger should be consented to by
every participant. Specifically, several participants need to
agree with a consensus. Observing which it is may not be the
situation found in countless real-world applications such as a
fiat digital currency, by which a single entity (e.g., a bank or a
government) decides on the updates.
The importance of a blockchain strategy is | [
117,
20375,
1785,
117,
19536,
22083,
117,
12427,
2162,
4363,
117,
142,
2559,
2107,
15586,
6451,
1186,
118,
10202,
117,
1615,
20603,
27400,
2528,
1394,
117,
5255,
19000,
8136,
1179,
117,
163,
1658,
10733,
117,
142,
8420,
14136,
18959,
1708,
164,
1367,
117,
1492,
166,
2710,
4539,
2916,
1851,
110,
1457,
9899,
138,
14566,
8355,
118,
7457,
12107,
17436,
20071,
4363,
12107,
17436,
20071,
20603,
153,
8284,
2528,
1394,
117,
12008,
6112,
1116,
117,
5157,
2692,
7937,
1204,
18959,
1592,
164,
1489,
166,
2710,
4539,
2916,
1851,
110,
1104,
3294,
8219,
138,
14566,
8355,
118,
7457,
20375,
1785,
117,
9155,
117,
23334,
142,
2559,
2107,
117,
20115,
1468,
15586,
6451,
1186,
118,
10202,
19585,
12298,
18959,
2101,
164,
1405,
166,
7219,
1302,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116,
117,
20375,
1785,
117,
19536,
22083,
117,
12427,
2162,
4363,
117,
142,
2559,
2107,
15586,
6451,
1186,
118,
10202,
117,
1615,
20603,
27400,
2528,
1394,
18959,
2064,
164,
1479,
166,
2710,
1302,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116,
117,
20375,
1785,
117,
19536,
22083,
117,
12427,
2162,
4363,
117,
142,
2559,
2107,
15586,
6451,
1186,
118,
10202,
117,
1615,
20603,
22191,
2528,
1394,
18959,
2069,
164,
1542,
166,
2710,
2160,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116,
117,
20375,
1785,
117,
19536,
22083,
117,
12427,
2162,
4363,
117,
142,
2559,
2107,
3929,
7301,
2149,
2093,
1457,
27611,
25647,
156,
22705,
18959,
11943,
164,
1407,
117,
1627,
166,
2710,
2160,
16285,
7443,
118,
24076,
23334,
4363,
1615,
20603,
20318,
21590,
2161,
18959,
1658,
164,
1406,
117,
1626,
166,
2710,
1302,
16285,
7443,
118,
24076,
16285,
12118,
1377,
2728,
2246,
183,
3929,
7301,
2149,
2093,
1457,
27611,
25647,
156,
22705,
18959,
2240,
164,
128,
166,
2710,
117,
7219,
2160,
16285,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
9155,
26546,
2107,
8093,
7147,
1394,
17742,
161,
15577,
18959,
2346,
164,
1659,
166,
2710,
117,
7219,
1302,
16285,
138,
14566,
8355,
118,
7457,
6291,
140,
108,
7154,
24664,
3740,
5783,
1457,
19471,
1200,
18959,
1708,
1643,
1665,
164,
1695,
166,
2710,
1302,
1512,
110,
20463,
3794,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
3414,
19514,
117,
140,
116,
116,
117,
20375,
1785,
117,
19536,
22083,
117,
12427,
2162,
4363,
117,
142,
2559,
2107,
11508,
117,
20777,
15012,
2116,
4326,
117,
1457,
27611,
8329,
118,
22620,
1306,
141,
23329,
1708,
164,
1572,
166,
2710,
4539,
2916,
133,
4062,
110,
12226,
6859,
5067,
13809,
15022,
118,
7457,
117,
138,
14566,
8355,
118,
7457,
1302,
20452,
16669,
1916,
4363,
13063,
3452,
4412,
2200,
7855,
27400,
5480,
4894,
155,
9717,
7136,
164,
1512,
166,
2710,
2160,
133,
1406,
110,
143,
14045,
1183,
1302,
4704,
1107,
7414,
2162,
138,
14566,
8355,
118,
7457,
9155,
117,
3414,
117,
140,
116,
116,
1302,
2007,
119,
179,
1116,
117,
151,
14808,
6082,
1249,
27948,
117,
22531,
1880
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
3,
4,
0,
3,
4,
0,
3,
4,
0,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
1,
2,
2,
2,
0,
1,
2,
2,
0,
1,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
1,
2,
2,
0,
5,
6,
6,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
0,
3,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
6,
0,
19,
20,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
4,
0,
3,
4,
19,
20,
20,
0,
0,
0
] | [
0,
3,
4,
0,
3,
4,
0,
3,
4,
0,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
1,
2,
2,
2,
0,
1,
2,
2,
0,
1,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
1,
2,
2,
0,
5,
6,
6,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
0,
3,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
6,
0,
19,
20,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
4,
4,
0,
3,
4,
19,
20,
20,
0,
0,
0
] | [
",",
"Solid",
"##ity",
",",
"Ser",
"##pent",
",",
"LL",
"##L",
"Native",
",",
"E",
"##V",
"##M",
"Cry",
"##pt",
"##o",
"-",
"currency",
",",
"General",
"Applications",
"Bit",
"##co",
"##in",
",",
"Li",
"##tec",
"##oi",
"##n",
",",
"Z",
"##C",
"##ash",
",",
"E",
"##ther",
"##eum",
"Po",
"##S",
"[",
"12",
",",
"13",
"]",
"Public",
"Part",
"##ial",
"50",
"%",
"St",
"##ake",
"A",
"##cco",
"##unt",
"-",
"Based",
"Mi",
"##chal",
"##eson",
"Native",
"Mi",
"##chal",
"##eson",
"Applications",
"P",
"##eer",
"##co",
"##in",
",",
"Te",
"##zo",
"##s",
",",
"Ten",
"##der",
"##min",
"##t",
"Po",
"##A",
"[",
"14",
"]",
"Public",
"Part",
"##ial",
"50",
"%",
"of",
"online",
"stake",
"A",
"##cco",
"##unt",
"-",
"Based",
"Solid",
"##ity",
",",
"Java",
",",
"Python",
"E",
"##V",
"##M",
",",
"Dock",
"##ers",
"Cry",
"##pt",
"##o",
"-",
"currency",
"Pa",
"##rity",
"Po",
"##P",
"[",
"15",
"]",
"Private",
"No",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+",
",",
"Solid",
"##ity",
",",
"Ser",
"##pent",
",",
"LL",
"##L",
"Native",
",",
"E",
"##V",
"##M",
"Cry",
"##pt",
"##o",
"-",
"currency",
",",
"General",
"Applications",
"Bit",
"##co",
"##in",
"Po",
"##B",
"[",
"16",
"]",
"Public",
"No",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+",
",",
"Solid",
"##ity",
",",
"Ser",
"##pent",
",",
"LL",
"##L",
"Native",
",",
"E",
"##V",
"##M",
"Cry",
"##pt",
"##o",
"-",
"currency",
",",
"General",
"Applications",
"Slim",
"##co",
"##in",
"Po",
"##R",
"[",
"17",
"]",
"Public",
"Yes",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+",
",",
"Solid",
"##ity",
",",
"Ser",
"##pent",
",",
"LL",
"##L",
"Native",
",",
"E",
"##V",
"##M",
"Out",
"##so",
"##ur",
"##ce",
"St",
"##orage",
"File",
"S",
"##hare",
"Po",
"##ET",
"[",
"18",
",",
"19",
"]",
"Public",
"Yes",
"Unknown",
"Key",
"-",
"Value",
"Python",
"Native",
"General",
"Applications",
"Saw",
"##tooth",
"Lake",
"Po",
"##C",
"[",
"20",
",",
"21",
"]",
"Public",
"No",
"Unknown",
"Key",
"-",
"Value",
"Unknown",
"Un",
"##k",
"##no",
"##w",
"n",
"Out",
"##so",
"##ur",
"##ce",
"St",
"##orage",
"File",
"S",
"##hare",
"Po",
"##I",
"[",
"7",
"]",
"Public",
",",
"Private",
"Yes",
"Unknown",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Java",
"NE",
"##M",
"Block",
"##cha",
"##in",
"Platform",
"X",
"##EM",
"Po",
"##O",
"[",
"22",
"]",
"Public",
",",
"Private",
"No",
"Unknown",
"A",
"##cco",
"##unt",
"-",
"Based",
"Any",
"C",
"#",
"Data",
"Ce",
"##rt",
"##ification",
"St",
"##amp",
"##er",
"Po",
"##S",
"##p",
"##c",
"[",
"23",
"]",
"Public",
"No",
"25",
"%",
"Computing",
"Power",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"Go",
"##lang",
",",
"C",
"+",
"+",
",",
"Solid",
"##ity",
",",
"Ser",
"##pent",
",",
"LL",
"##L",
"Native",
",",
"E",
"##V",
"##M",
"Mail",
",",
"Rep",
"##uta",
"##tion",
"Services",
",",
"St",
"##orage",
"Anti",
"-",
"spa",
"##m",
"D",
"##PO",
"##S",
"[",
"24",
"]",
"Public",
"Part",
"##ial",
"<",
"51",
"%",
"Val",
"##ida",
"##tors",
"Trans",
"##action",
"-",
"Based",
",",
"A",
"##cco",
"##unt",
"-",
"Based",
"No",
"Sc",
"##rip",
"##ting",
"Native",
"Dec",
"##ent",
"##ral",
"##ized",
"Exchange",
"Bit",
"##sha",
"##res",
"R",
"##ip",
"##ple",
"[",
"25",
"]",
"Public",
"Yes",
"<",
"20",
"%",
"F",
"##ault",
"##y",
"No",
"##des",
"in",
"UN",
"##L",
"A",
"##cco",
"##unt",
"-",
"Based",
"Java",
",",
"Go",
",",
"C",
"+",
"+",
"No",
"##de",
".",
"j",
"##s",
",",
"N",
"##PM",
"Digital",
"As",
"##sets",
",",
"Pay",
"##ment"
] | State of the art and challenges facing consensus p | 119 |
actually being
able to deal with those nodes that do not trust working
together, indicating which variables might respond in
Byzantine formality. The consensus protocol consequently
needs to endure Byzantine problems. The research involving a
survey on consensus was comprehensive, and there are
numerous versions of previously recommended protocols that
have been manufactured for blockchains [2]. These could be
categorized in terms of their combined range. Overwhelming
consists of solely | [
155,
9717,
7136,
5157,
2692,
7937,
1204,
164,
1744,
166,
7219,
2160,
133,
3081,
119,
124,
110,
8377,
159,
13460,
3794,
138,
14566,
8355,
118,
7457,
20375,
1785,
142,
2559,
2107,
1615,
20603,
5157,
2692,
7937,
1204,
117,
15706,
1775,
11389,
146,
119,
3291,
8223,
26464,
1320,
1104,
3510,
7147,
1394,
10923,
19755,
1111,
170,
1383,
1104,
6818,
3510,
7147,
1394,
4625,
119,
122,
114,
1302,
2007,
22855,
131,
2993,
1106,
2437,
1103,
4193,
1104,
1451,
2317,
1197,
1106,
8247,
170,
1514,
1107,
1155,
8287,
2443,
119,
1438,
117,
5157,
2692,
7937,
1204,
117,
1105,
18959,
2101,
1444,
1106,
2437,
1103,
9221,
11664,
1107,
1546,
1106,
1129,
1682,
1106,
3368,
170,
17794,
1197,
1107,
1451,
1668,
119,
1556,
7328,
1106,
18959,
2924,
117,
18959,
1708,
117,
141,
23329,
1708,
117,
1105,
155,
9717,
7136,
117,
15029,
1547,
1129,
2628,
1114,
10681,
2443,
119,
5306,
1568,
123,
114,
5514,
17784,
3970,
131,
7323,
18959,
2924,
117,
13418,
1144,
1324,
1103,
3510,
23103,
10861,
1106,
15225,
1103,
6349,
3869,
119,
1249,
170,
1871,
117,
1103,
2971,
1104,
6538,
2308,
1834,
1106,
1965,
1103,
1250,
1110,
14934,
119,
1556,
7328,
1106,
18959,
1708,
1105,
141,
23329,
1708,
117,
13418,
1132,
4857,
2320,
1106,
1144,
1324,
1103,
3510,
23103,
1106,
3403,
1111,
6245,
117,
1133,
1103,
1250,
2412,
19377,
1112,
1103,
3403,
1282,
1110,
1666,
1106,
1129,
7458,
119,
23840,
153,
26447,
1942,
117,
155,
9717,
7136,
117,
1105,
5157,
2692,
7937,
1204,
117,
1175,
1110,
1185,
5463,
1107,
2538,
1104,
10923,
5564,
119,
6589,
1122,
14419,
1540,
12235,
119,
124,
114,
1706,
2879,
2913,
1540,
1104,
8050,
10704,
3113,
131,
6869,
1193,
4062,
110,
1104,
1144,
1324,
1540,
1110,
4628,
1229,
1103,
11810,
1106,
1141,
1106,
9703,
4282,
1104,
1103,
2443,
119,
8094,
117,
1103,
15589,
5463,
5564,
1107,
18959,
2924,
5660,
1336,
6043,
13418,
1106,
5515,
1167,
18155,
1229,
1606,
1178,
1512,
110,
1104,
1103,
1144,
8840,
1540,
119,
153,
26447,
1942,
1105,
5157,
2692,
7937,
1204,
1132,
7227,
1106,
5494,
1146,
1106,
3081,
119,
3236,
23912,
2109,
15029,
119,
155,
9717,
7136,
1110,
2602,
1106,
4731,
5663,
1757,
1165,
1103,
10807,
1104,
6088,
1183,
15029,
1107,
170,
3527,
14372,
2190,
1132,
2211,
1190,
1406,
110,
119,
125,
114,
7154,
2235,
131,
170,
2233,
2235,
1110,
170,
13618,
1115,
7203,
1113,
6661,
119,
1398,
2344,
4752,
2440,
25209,
117,
1114,
2567,
3722,
1217,
1682,
1106,
6898,
1146,
170,
2443,
1106,
3670,
6661,
1114,
1296,
1168,
119,
1636,
3722,
1132,
1103,
21340,
1197,
5032,
119,
1135,
1110,
4701,
1111,
1172,
1106,
1138,
1167,
1190,
1141,
21340,
1197,
5336,
1155,
1104,
1172,
119,
12126,
1197,
117,
155,
9717,
7136,
1105,
146,
14697,
1592,
2486,
1147,
1319,
22559,
1116,
6661,
1105,
2194,
1147,
21340,
1733,
1112,
170,
3442,
1104,
3670,
117,
1137,
1112,
170,
3482,
1111,
17599,
4163,
26911,
5240,
119,
146,
14697,
1592,
117,
4418,
117,
13267,
6756,
7216,
17599,
4163,
26911,
5240,
2258,
1157,
22559,
1116,
117,
1134,
8743,
3869,
21053,
21340,
1733,
1111,
16845,
1621,
146,
1186,
1942,
3204,
119,
1109,
21340,
1733,
1107,
1292,
2344,
11258,
3300,
118,
1359,
2233,
3584
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
13,
14,
14,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
13,
14,
14,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
3,
4,
4,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"R",
"##ip",
"##ple",
"Ten",
"##der",
"##min",
"##t",
"[",
"26",
"]",
"Private",
"Yes",
"<",
"33",
".",
"3",
"%",
"Byzantine",
"V",
"##oting",
"Power",
"A",
"##cco",
"##unt",
"-",
"Based",
"Solid",
"##ity",
"E",
"##V",
"##M",
"General",
"Applications",
"Ten",
"##der",
"##min",
"##t",
",",
"Mona",
"##x",
"Table",
"I",
".",
"Co",
"##mp",
"##aris",
"##on",
"of",
"block",
"##cha",
"##in",
"consensus",
"protocols",
"for",
"a",
"set",
"of",
"essential",
"block",
"##cha",
"##in",
"properties",
".",
"1",
")",
"No",
"##de",
"Identity",
":",
"needs",
"to",
"understand",
"the",
"identity",
"of",
"every",
"mine",
"##r",
"to",
"select",
"a",
"main",
"in",
"all",
"circular",
"network",
".",
"However",
",",
"Ten",
"##der",
"##min",
"##t",
",",
"and",
"Po",
"##P",
"need",
"to",
"understand",
"the",
"valid",
"##ators",
"in",
"order",
"to",
"be",
"able",
"to",
"pick",
"a",
"propose",
"##r",
"in",
"every",
"round",
".",
"With",
"regard",
"to",
"Po",
"##W",
",",
"Po",
"##S",
",",
"D",
"##PO",
"##S",
",",
"and",
"R",
"##ip",
"##ple",
",",
"nodes",
"might",
"be",
"associated",
"with",
"##the",
"network",
".",
"96",
"##0",
"2",
")",
"Energy",
"Sa",
"##ving",
":",
"Inside",
"Po",
"##W",
",",
"miners",
"has",
"##h",
"the",
"block",
"header",
"continuously",
"to",
"accomplish",
"the",
"preferred",
"worth",
".",
"As",
"a",
"result",
",",
"the",
"amount",
"of",
"electrical",
"energy",
"needed",
"to",
"process",
"the",
"work",
"is",
"immense",
".",
"With",
"regard",
"to",
"Po",
"##S",
"and",
"D",
"##PO",
"##S",
",",
"miners",
"are",
"regularly",
"required",
"to",
"has",
"##h",
"the",
"block",
"header",
"to",
"search",
"for",
"benefits",
",",
"but",
"the",
"work",
"generally",
"decreases",
"as",
"the",
"search",
"place",
"is",
"produced",
"to",
"be",
"restricted",
".",
"Regarding",
"P",
"##BF",
"##T",
",",
"R",
"##ip",
"##ple",
",",
"and",
"Ten",
"##der",
"##min",
"##t",
",",
"there",
"is",
"no",
"mining",
"in",
"terms",
"of",
"consensus",
"strategy",
".",
"Therefore",
"it",
"saves",
"power",
"dramatically",
".",
"3",
")",
"To",
"##ler",
"##ated",
"power",
"of",
"ad",
"##vers",
"##ary",
":",
"Common",
"##ly",
"51",
"%",
"of",
"has",
"##h",
"power",
"is",
"understood",
"while",
"the",
"threshold",
"to",
"one",
"to",
"acquire",
"handle",
"of",
"the",
"network",
".",
"Nevertheless",
",",
"the",
"selfish",
"mining",
"strategy",
"in",
"Po",
"##W",
"practices",
"may",
"assist",
"miners",
"to",
"achieve",
"more",
"earnings",
"while",
"using",
"only",
"25",
"%",
"of",
"the",
"has",
"##hing",
"power",
".",
"P",
"##BF",
"##T",
"and",
"Ten",
"##der",
"##min",
"##t",
"are",
"manufactured",
"to",
"manage",
"up",
"to",
"33",
".",
"34",
"defect",
"##ive",
"nodes",
".",
"R",
"##ip",
"##ple",
"is",
"shown",
"to",
"maintain",
"correct",
"##ness",
"when",
"the",
"proportion",
"of",
"fault",
"##y",
"nodes",
"in",
"a",
"unique",
"node",
"list",
"are",
"lower",
"than",
"20",
"%",
".",
"4",
")",
"Data",
"model",
":",
"a",
"data",
"model",
"is",
"a",
"transaction",
"that",
"focuses",
"on",
"assets",
".",
"All",
"systems",
"require",
"particular",
"configurations",
",",
"with",
"numerous",
"organizations",
"being",
"able",
"to",
"spin",
"up",
"a",
"network",
"to",
"exchange",
"assets",
"with",
"each",
"other",
".",
"These",
"organizations",
"are",
"the",
"ledge",
"##r",
"owners",
".",
"It",
"is",
"typical",
"for",
"them",
"to",
"have",
"more",
"than",
"one",
"ledge",
"##r",
"involving",
"all",
"of",
"them",
".",
"Stella",
"##r",
",",
"R",
"##ip",
"##ple",
"and",
"I",
"##OT",
"##A",
"issue",
"their",
"own",
"token",
"##s",
"assets",
"and",
"provide",
"their",
"ledge",
"##rs",
"as",
"a",
"method",
"of",
"exchange",
",",
"or",
"as",
"a",
"platform",
"for",
"micro",
"##pa",
"##yme",
"##nts",
".",
"I",
"##OT",
"##A",
",",
"specifically",
",",
"enables",
"zero",
"fee",
"micro",
"##pa",
"##yme",
"##nts",
"via",
"its",
"token",
"##s",
",",
"which",
"creates",
"worth",
"##while",
"ledge",
"##rs",
"for",
"transfers",
"among",
"I",
"##o",
"##T",
"equipment",
".",
"The",
"ledge",
"##rs",
"in",
"these",
"systems",
"adopt",
"account",
"-",
"based",
"data",
"models"
] | State of the art and challenges facing consensus p | 120 |
actually being
able to deal with those nodes that do not trust working
together, indicating which variables might respond in
Byzantine formality. The consensus protocol consequently
needs to endure Byzantine problems. The research involving a
survey on consensus was comprehensive, and there are
numerous versions of previously recommended protocols that
have been manufactured for blockchains [2]. These could be
categorized in terms of their combined range. Overwhelming
consists of solely | [
155,
9717,
7136,
5157,
2692,
7937,
1204,
164,
1744,
166,
7219,
2160,
133,
3081,
119,
124,
110,
8377,
159,
13460,
3794,
138,
14566,
8355,
118,
7457,
20375,
1785,
142,
2559,
2107,
1615,
20603,
5157,
2692,
7937,
1204,
117,
15706,
1775,
11389,
146,
119,
3291,
8223,
26464,
1320,
1104,
3510,
7147,
1394,
10923,
19755,
1111,
170,
1383,
1104,
6818,
3510,
7147,
1394,
4625,
119,
122,
114,
1302,
2007,
22855,
131,
2993,
1106,
2437,
1103,
4193,
1104,
1451,
2317,
1197,
1106,
8247,
170,
1514,
1107,
1155,
8287,
2443,
119,
1438,
117,
5157,
2692,
7937,
1204,
117,
1105,
18959,
2101,
1444,
1106,
2437,
1103,
9221,
11664,
1107,
1546,
1106,
1129,
1682,
1106,
3368,
170,
17794,
1197,
1107,
1451,
1668,
119,
1556,
7328,
1106,
18959,
2924,
117,
18959,
1708,
117,
141,
23329,
1708,
117,
1105,
155,
9717,
7136,
117,
15029,
1547,
1129,
2628,
1114,
10681,
2443,
119,
5306,
1568,
123,
114,
5514,
17784,
3970,
131,
7323,
18959,
2924,
117,
13418,
1144,
1324,
1103,
3510,
23103,
10861,
1106,
15225,
1103,
6349,
3869,
119,
1249,
170,
1871,
117,
1103,
2971,
1104,
6538,
2308,
1834,
1106,
1965,
1103,
1250,
1110,
14934,
119,
1556,
7328,
1106,
18959,
1708,
1105,
141,
23329,
1708,
117,
13418,
1132,
4857,
2320,
1106,
1144,
1324,
1103,
3510,
23103,
1106,
3403,
1111,
6245,
117,
1133,
1103,
1250,
2412,
19377,
1112,
1103,
3403,
1282,
1110,
1666,
1106,
1129,
7458,
119,
23840,
153,
26447,
1942,
117,
155,
9717,
7136,
117,
1105,
5157,
2692,
7937,
1204,
117,
1175,
1110,
1185,
5463,
1107,
2538,
1104,
10923,
5564,
119,
6589,
1122,
14419,
1540,
12235,
119,
124,
114,
1706,
2879,
2913,
1540,
1104,
8050,
10704,
3113,
131,
6869,
1193,
4062,
110,
1104,
1144,
1324,
1540,
1110,
4628,
1229,
1103,
11810,
1106,
1141,
1106,
9703,
4282,
1104,
1103,
2443,
119,
8094,
117,
1103,
15589,
5463,
5564,
1107,
18959,
2924,
5660,
1336,
6043,
13418,
1106,
5515,
1167,
18155,
1229,
1606,
1178,
1512,
110,
1104,
1103,
1144,
8840,
1540,
119,
153,
26447,
1942,
1105,
5157,
2692,
7937,
1204,
1132,
7227,
1106,
5494,
1146,
1106,
3081,
119,
3236,
23912,
2109,
15029,
119,
155,
9717,
7136,
1110,
2602,
1106,
4731,
5663,
1757,
1165,
1103,
10807,
1104,
6088,
1183,
15029,
1107,
170,
3527,
14372,
2190,
1132,
2211,
1190,
1406,
110,
119,
125,
114,
7154,
2235,
131,
170,
2233,
2235,
1110,
170,
13618,
1115,
7203,
1113,
6661,
119,
1398,
2344,
4752,
2440,
25209,
117,
1114,
2567,
3722,
1217,
1682,
1106,
6898,
1146,
170,
2443,
1106,
3670,
6661,
1114,
1296,
1168,
119,
1636,
3722,
1132,
1103,
21340,
1197,
5032,
119,
1135,
1110,
4701,
1111,
1172,
1106,
1138,
1167,
1190,
1141,
21340,
1197,
5336,
1155,
1104,
1172,
119,
12126,
1197,
117,
155,
9717,
7136,
1105,
146,
14697,
1592,
2486,
1147,
1319,
22559,
1116,
6661,
1105,
2194,
1147,
21340,
1733,
1112,
170,
3442,
1104,
3670,
117,
1137,
1112,
170,
3482,
1111,
17599,
4163,
26911,
5240,
119,
146,
14697,
1592,
117,
4418,
117,
13267,
6756,
7216,
17599,
4163,
26911,
5240,
2258,
1157,
22559,
1116,
117,
1134,
8743,
3869,
21053,
21340,
1733,
1111,
16845,
1621,
146,
1186,
1942,
3204,
119,
1109,
21340,
1733,
1107,
1292,
2344,
11258,
3300,
118,
1359,
2233,
3584
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"R",
"##ip",
"##ple",
"Ten",
"##der",
"##min",
"##t",
"[",
"26",
"]",
"Private",
"Yes",
"<",
"33",
".",
"3",
"%",
"Byzantine",
"V",
"##oting",
"Power",
"A",
"##cco",
"##unt",
"-",
"Based",
"Solid",
"##ity",
"E",
"##V",
"##M",
"General",
"Applications",
"Ten",
"##der",
"##min",
"##t",
",",
"Mona",
"##x",
"Table",
"I",
".",
"Co",
"##mp",
"##aris",
"##on",
"of",
"block",
"##cha",
"##in",
"consensus",
"protocols",
"for",
"a",
"set",
"of",
"essential",
"block",
"##cha",
"##in",
"properties",
".",
"1",
")",
"No",
"##de",
"Identity",
":",
"needs",
"to",
"understand",
"the",
"identity",
"of",
"every",
"mine",
"##r",
"to",
"select",
"a",
"main",
"in",
"all",
"circular",
"network",
".",
"However",
",",
"Ten",
"##der",
"##min",
"##t",
",",
"and",
"Po",
"##P",
"need",
"to",
"understand",
"the",
"valid",
"##ators",
"in",
"order",
"to",
"be",
"able",
"to",
"pick",
"a",
"propose",
"##r",
"in",
"every",
"round",
".",
"With",
"regard",
"to",
"Po",
"##W",
",",
"Po",
"##S",
",",
"D",
"##PO",
"##S",
",",
"and",
"R",
"##ip",
"##ple",
",",
"nodes",
"might",
"be",
"associated",
"with",
"##the",
"network",
".",
"96",
"##0",
"2",
")",
"Energy",
"Sa",
"##ving",
":",
"Inside",
"Po",
"##W",
",",
"miners",
"has",
"##h",
"the",
"block",
"header",
"continuously",
"to",
"accomplish",
"the",
"preferred",
"worth",
".",
"As",
"a",
"result",
",",
"the",
"amount",
"of",
"electrical",
"energy",
"needed",
"to",
"process",
"the",
"work",
"is",
"immense",
".",
"With",
"regard",
"to",
"Po",
"##S",
"and",
"D",
"##PO",
"##S",
",",
"miners",
"are",
"regularly",
"required",
"to",
"has",
"##h",
"the",
"block",
"header",
"to",
"search",
"for",
"benefits",
",",
"but",
"the",
"work",
"generally",
"decreases",
"as",
"the",
"search",
"place",
"is",
"produced",
"to",
"be",
"restricted",
".",
"Regarding",
"P",
"##BF",
"##T",
",",
"R",
"##ip",
"##ple",
",",
"and",
"Ten",
"##der",
"##min",
"##t",
",",
"there",
"is",
"no",
"mining",
"in",
"terms",
"of",
"consensus",
"strategy",
".",
"Therefore",
"it",
"saves",
"power",
"dramatically",
".",
"3",
")",
"To",
"##ler",
"##ated",
"power",
"of",
"ad",
"##vers",
"##ary",
":",
"Common",
"##ly",
"51",
"%",
"of",
"has",
"##h",
"power",
"is",
"understood",
"while",
"the",
"threshold",
"to",
"one",
"to",
"acquire",
"handle",
"of",
"the",
"network",
".",
"Nevertheless",
",",
"the",
"selfish",
"mining",
"strategy",
"in",
"Po",
"##W",
"practices",
"may",
"assist",
"miners",
"to",
"achieve",
"more",
"earnings",
"while",
"using",
"only",
"25",
"%",
"of",
"the",
"has",
"##hing",
"power",
".",
"P",
"##BF",
"##T",
"and",
"Ten",
"##der",
"##min",
"##t",
"are",
"manufactured",
"to",
"manage",
"up",
"to",
"33",
".",
"34",
"defect",
"##ive",
"nodes",
".",
"R",
"##ip",
"##ple",
"is",
"shown",
"to",
"maintain",
"correct",
"##ness",
"when",
"the",
"proportion",
"of",
"fault",
"##y",
"nodes",
"in",
"a",
"unique",
"node",
"list",
"are",
"lower",
"than",
"20",
"%",
".",
"4",
")",
"Data",
"model",
":",
"a",
"data",
"model",
"is",
"a",
"transaction",
"that",
"focuses",
"on",
"assets",
".",
"All",
"systems",
"require",
"particular",
"configurations",
",",
"with",
"numerous",
"organizations",
"being",
"able",
"to",
"spin",
"up",
"a",
"network",
"to",
"exchange",
"assets",
"with",
"each",
"other",
".",
"These",
"organizations",
"are",
"the",
"ledge",
"##r",
"owners",
".",
"It",
"is",
"typical",
"for",
"them",
"to",
"have",
"more",
"than",
"one",
"ledge",
"##r",
"involving",
"all",
"of",
"them",
".",
"Stella",
"##r",
",",
"R",
"##ip",
"##ple",
"and",
"I",
"##OT",
"##A",
"issue",
"their",
"own",
"token",
"##s",
"assets",
"and",
"provide",
"their",
"ledge",
"##rs",
"as",
"a",
"method",
"of",
"exchange",
",",
"or",
"as",
"a",
"platform",
"for",
"micro",
"##pa",
"##yme",
"##nts",
".",
"I",
"##OT",
"##A",
",",
"specifically",
",",
"enables",
"zero",
"fee",
"micro",
"##pa",
"##yme",
"##nts",
"via",
"its",
"token",
"##s",
",",
"which",
"creates",
"worth",
"##while",
"ledge",
"##rs",
"for",
"transfers",
"among",
"I",
"##o",
"##T",
"equipment",
".",
"The",
"ledge",
"##rs",
"in",
"these",
"systems",
"adopt",
"account",
"-",
"based",
"data",
"models"
] | State of the art and challenges facing consensus p | 121 |
computation-based protocols in which the
users utilize proof of computation to find a node that
arbitrarily determines the next operation. Bitcoin's Proof of
work (PoW) is a simple example of the consensus. The other
severe are solely communication-based protocols for which
nodes have matching votes and run through several rounds of
communication to achieve consensus. All protocols, Practical
Byzantine Fault Tolerance (PBFT) [3] being the best
illustration, are applied in particular config | [
119,
1448,
21340,
1197,
5903,
1679,
1501,
2818,
119,
126,
114,
16409,
10294,
12964,
131,
138,
6866,
2329,
1679,
22748,
1106,
170,
3254,
19675,
1982,
1517,
170,
13618,
1144,
1678,
1282,
119,
138,
6866,
2329,
1180,
1129,
4485,
1112,
170,
7905,
7791,
1107,
18891,
1113,
170,
2239,
119,
1109,
22743,
117,
5964,
1116,
117,
1105,
2781,
20968,
1118,
1103,
7581,
1104,
170,
6866,
2329,
6268,
9635,
1113,
1155,
14372,
119,
127,
114,
22491,
131,
11099,
2894,
5354,
6451,
13335,
2149,
5123,
3457,
1105,
13274,
2635,
117,
1199,
21340,
1733,
1619,
1919,
1704,
117,
4795,
118,
3393,
3254,
19675,
1116,
113,
1137,
1560,
8216,
114,
119,
142,
8420,
14136,
1105,
1157,
18952,
117,
8199,
145,
19429,
19366,
10390,
1179,
117,
154,
11848,
5697,
117,
15706,
1775,
117,
19585,
12298,
117,
1105,
3177,
24415,
1519,
4713,
3593,
16439,
1671,
8738,
5858,
1113,
1499,
1104,
1103,
21340,
1197,
119,
1370,
1859,
117,
142,
8420,
14136,
8216,
2079,
1121,
3014,
3515,
14703,
17038,
7827,
1106,
1343,
5336,
5151,
4381,
1176,
1103,
141,
1592,
2346,
119,
3177,
24415,
3272,
170,
2747,
1912,
1104,
3311,
1107,
2538,
1104,
12711,
11069,
1115,
17542,
1842,
118,
1362,
2995,
1852,
142,
8420,
14136,
118,
1176,
3510,
7147,
4935,
119,
145,
24312,
19693,
1197,
1105,
1157,
1601,
5009,
117,
20318,
21590,
2161,
117,
15869,
1619,
1919,
14283,
1403,
118,
2335,
3463,
119,
1220,
2906,
170,
2501,
118,
2860,
2233,
2235,
117,
1114,
1134,
1103,
4683,
1169,
2561,
1105,
11984,
2501,
118,
2860,
189,
4455,
2897,
1113,
1103,
3510,
7147,
1394,
119,
128,
114,
16409,
26671,
131,
27400,
2528,
1394,
1110,
1771,
1113,
18959,
2924,
1780,
153,
8284,
2528,
1394,
1110,
170,
1207,
8536,
118,
1106,
118,
8536,
18959,
1708,
5354,
6451,
13335,
2149,
5123,
3457,
119,
7282,
117,
145,
24312,
19693,
1197,
143,
6639,
4907,
2745,
153,
26447,
1942,
1106,
5515,
10923,
119,
27400,
5480,
4894,
117,
170,
6866,
2329,
3482,
117,
16001,
141,
23329,
1708,
1112,
1147,
10923,
9932,
119,
155,
9717,
7136,
24935,
1103,
155,
9717,
7136,
11309,
117,
1229,
5157,
2692,
7937,
1204,
2228,
1329,
1104,
1103,
5157,
2692,
7937,
1204,
11309,
119,
153,
26447,
1942,
1105,
5157,
2692,
7937,
1204,
1132,
6156,
1116,
19755,
119,
1302,
2007,
17409,
1132,
2637,
1106,
1129,
1227,
1111,
1103,
2006,
2443,
1177,
1115,
1152,
1547,
1129,
1215,
1107,
170,
2595,
5418,
1897,
1190,
170,
1470,
1141,
119,
18959,
2924,
1105,
18959,
1708,
1132,
6736,
1111,
1470,
3510,
7147,
4935,
119,
25222,
1137,
2029,
3510,
7147,
4935,
1547,
1138,
170,
12629,
1111,
153,
26447,
1942,
117,
5157,
2692,
7937,
1204,
117,
141,
23329,
1708,
117,
1137,
155,
9717,
7136,
119,
139,
119,
25308,
10923,
14975,
138,
2265,
10923,
9932,
5401,
2099,
117,
2699,
117,
1105,
16670,
119,
15088,
117,
170,
1363,
2239,
1104,
3098,
1144,
1151,
1508,
1154,
9248,
10923,
14975,
1107,
1103,
3510,
7147,
1394,
119,
1203,
10923,
14975,
1138,
1151,
1872,
1114,
1103,
6457,
1104,
15097,
1199,
2747,
4267,
23397,
1116,
1276,
1114,
7328,
1106,
1103,
3510,
7147,
1394,
119,
1109,
2425,
3136,
1104,
153,
8284,
1658,
5026,
1361,
1110,
1106,
1260,
2528,
4455,
1513,
3510,
1707,
1105,
13618
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
0,
1,
2,
2,
0,
1,
2,
0,
1,
2,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
5,
6,
0,
1,
2,
2,
2,
0,
0,
0,
5,
6,
6,
6,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
2,
0,
5,
6,
6,
0,
0,
5,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
13,
14,
14,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
0,
1,
2,
2,
0,
1,
2,
0,
1,
2,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
5,
6,
0,
1,
2,
2,
2,
0,
0,
0,
5,
6,
6,
6,
6,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
2,
0,
5,
6,
6,
0,
0,
5,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
13,
14,
14,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
".",
"One",
"ledge",
"##r",
"exists",
"per",
"open",
"policy",
".",
"5",
")",
"Ex",
"##ec",
"##ution",
":",
"A",
"smart",
"contract",
"per",
"##tains",
"to",
"a",
"com",
"##putation",
"performed",
"once",
"a",
"transaction",
"has",
"taken",
"place",
".",
"A",
"smart",
"contract",
"could",
"be",
"regarded",
"as",
"a",
"stored",
"procedure",
"in",
"##voked",
"on",
"a",
"deal",
".",
"The",
"inputs",
",",
"output",
"##s",
",",
"and",
"status",
"impacted",
"by",
"the",
"execution",
"of",
"a",
"smart",
"contract",
"obtain",
"consent",
"on",
"all",
"node",
".",
"6",
")",
"Application",
":",
"Going",
"beyond",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"and",
"asset",
"management",
",",
"some",
"ledge",
"##rs",
"support",
"running",
"general",
",",
"user",
"-",
"defined",
"com",
"##putation",
"##s",
"(",
"or",
"original",
"contracts",
")",
".",
"E",
"##ther",
"##eum",
"and",
"its",
"derivatives",
",",
"namely",
"H",
"##yd",
"##rac",
"##hai",
"##n",
",",
"Q",
"##uo",
"##rum",
",",
"Mona",
"##x",
",",
"Pa",
"##rity",
",",
"and",
"De",
"##finity",
"let",
"users",
"write",
"arbitrary",
"business",
"logic",
"executed",
"on",
"top",
"of",
"the",
"ledge",
"##r",
".",
"For",
"example",
",",
"E",
"##ther",
"##eum",
"contracts",
"range",
"from",
"simple",
"crowd",
"##fu",
"##nding",
"campaigns",
"to",
"those",
"involving",
"investment",
"funds",
"like",
"the",
"D",
"##A",
"##O",
".",
"De",
"##finity",
"offers",
"a",
"specific",
"kind",
"of",
"agreement",
"in",
"terms",
"of",
"governance",
"agreements",
"that",
"enforce",
"real",
"-",
"world",
"rules",
"upon",
"E",
"##ther",
"##eum",
"-",
"like",
"block",
"##cha",
"##ins",
".",
"H",
"##yper",
"##ledge",
"##r",
"and",
"its",
"close",
"cousin",
",",
"Saw",
"##tooth",
"Lake",
",",
"likewise",
"support",
"running",
"Turin",
"##g",
"-",
"complete",
"code",
".",
"They",
"offer",
"a",
"key",
"-",
"value",
"data",
"model",
",",
"with",
"which",
"the",
"applications",
"can",
"create",
"and",
"update",
"key",
"-",
"value",
"t",
"##up",
"##les",
"on",
"the",
"block",
"##cha",
"##in",
".",
"7",
")",
"Ex",
"##ample",
":",
"Bit",
"##co",
"##in",
"is",
"founded",
"on",
"Po",
"##W",
"although",
"P",
"##eer",
"##co",
"##in",
"is",
"a",
"new",
"peer",
"-",
"to",
"-",
"peer",
"Po",
"##S",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
".",
"Furthermore",
",",
"H",
"##yper",
"##ledge",
"##r",
"F",
"##ab",
"##ric",
"uses",
"P",
"##BF",
"##T",
"to",
"achieve",
"consensus",
".",
"Bit",
"##sha",
"##res",
",",
"a",
"smart",
"contract",
"platform",
",",
"explores",
"D",
"##PO",
"##S",
"as",
"their",
"consensus",
"algorithm",
".",
"R",
"##ip",
"##ple",
"implements",
"the",
"R",
"##ip",
"##ple",
"protocol",
",",
"while",
"Ten",
"##der",
"##min",
"##t",
"makes",
"use",
"of",
"the",
"Ten",
"##der",
"##min",
"##t",
"protocol",
".",
"P",
"##BF",
"##T",
"and",
"Ten",
"##der",
"##min",
"##t",
"are",
"permission",
"##s",
"protocols",
".",
"No",
"##de",
"identities",
"are",
"expected",
"to",
"be",
"known",
"for",
"the",
"whole",
"network",
"so",
"that",
"they",
"might",
"be",
"used",
"in",
"a",
"commercial",
"mode",
"rather",
"than",
"a",
"public",
"one",
".",
"Po",
"##W",
"and",
"Po",
"##S",
"are",
"suitable",
"for",
"public",
"block",
"##cha",
"##ins",
".",
"Consortium",
"or",
"private",
"block",
"##cha",
"##ins",
"might",
"have",
"a",
"preference",
"for",
"P",
"##BF",
"##T",
",",
"Ten",
"##der",
"##min",
"##t",
",",
"D",
"##PO",
"##S",
",",
"or",
"R",
"##ip",
"##ple",
".",
"B",
".",
"Advances",
"consensus",
"algorithms",
"A",
"successful",
"consensus",
"algorithm",
"suggests",
"performance",
",",
"security",
",",
"and",
"convenience",
".",
"Recently",
",",
"a",
"good",
"deal",
"of",
"effort",
"has",
"been",
"put",
"into",
"improving",
"consensus",
"algorithms",
"in",
"the",
"block",
"##cha",
"##in",
".",
"New",
"consensus",
"algorithms",
"have",
"been",
"developed",
"with",
"the",
"aim",
"of",
"solving",
"some",
"specific",
"di",
"##lemma",
"##s",
"found",
"with",
"regard",
"to",
"the",
"block",
"##cha",
"##in",
".",
"The",
"primary",
"approach",
"of",
"P",
"##eer",
"##C",
"##ens",
"##us",
"is",
"to",
"de",
"##co",
"##up",
"##le",
"block",
"production",
"and",
"transaction"
] | State of the art and challenges facing consensus p | 122 |
computation-based protocols in which the
users utilize proof of computation to find a node that
arbitrarily determines the next operation. Bitcoin's Proof of
work (PoW) is a simple example of the consensus. The other
severe are solely communication-based protocols for which
nodes have matching votes and run through several rounds of
communication to achieve consensus. All protocols, Practical
Byzantine Fault Tolerance (PBFT) [3] being the best
illustration, are applied in particular config | [
119,
1448,
21340,
1197,
5903,
1679,
1501,
2818,
119,
126,
114,
16409,
10294,
12964,
131,
138,
6866,
2329,
1679,
22748,
1106,
170,
3254,
19675,
1982,
1517,
170,
13618,
1144,
1678,
1282,
119,
138,
6866,
2329,
1180,
1129,
4485,
1112,
170,
7905,
7791,
1107,
18891,
1113,
170,
2239,
119,
1109,
22743,
117,
5964,
1116,
117,
1105,
2781,
20968,
1118,
1103,
7581,
1104,
170,
6866,
2329,
6268,
9635,
1113,
1155,
14372,
119,
127,
114,
22491,
131,
11099,
2894,
5354,
6451,
13335,
2149,
5123,
3457,
1105,
13274,
2635,
117,
1199,
21340,
1733,
1619,
1919,
1704,
117,
4795,
118,
3393,
3254,
19675,
1116,
113,
1137,
1560,
8216,
114,
119,
142,
8420,
14136,
1105,
1157,
18952,
117,
8199,
145,
19429,
19366,
10390,
1179,
117,
154,
11848,
5697,
117,
15706,
1775,
117,
19585,
12298,
117,
1105,
3177,
24415,
1519,
4713,
3593,
16439,
1671,
8738,
5858,
1113,
1499,
1104,
1103,
21340,
1197,
119,
1370,
1859,
117,
142,
8420,
14136,
8216,
2079,
1121,
3014,
3515,
14703,
17038,
7827,
1106,
1343,
5336,
5151,
4381,
1176,
1103,
141,
1592,
2346,
119,
3177,
24415,
3272,
170,
2747,
1912,
1104,
3311,
1107,
2538,
1104,
12711,
11069,
1115,
17542,
1842,
118,
1362,
2995,
1852,
142,
8420,
14136,
118,
1176,
3510,
7147,
4935,
119,
145,
24312,
19693,
1197,
1105,
1157,
1601,
5009,
117,
20318,
21590,
2161,
117,
15869,
1619,
1919,
14283,
1403,
118,
2335,
3463,
119,
1220,
2906,
170,
2501,
118,
2860,
2233,
2235,
117,
1114,
1134,
1103,
4683,
1169,
2561,
1105,
11984,
2501,
118,
2860,
189,
4455,
2897,
1113,
1103,
3510,
7147,
1394,
119,
128,
114,
16409,
26671,
131,
27400,
2528,
1394,
1110,
1771,
1113,
18959,
2924,
1780,
153,
8284,
2528,
1394,
1110,
170,
1207,
8536,
118,
1106,
118,
8536,
18959,
1708,
5354,
6451,
13335,
2149,
5123,
3457,
119,
7282,
117,
145,
24312,
19693,
1197,
143,
6639,
4907,
2745,
153,
26447,
1942,
1106,
5515,
10923,
119,
27400,
5480,
4894,
117,
170,
6866,
2329,
3482,
117,
16001,
141,
23329,
1708,
1112,
1147,
10923,
9932,
119,
155,
9717,
7136,
24935,
1103,
155,
9717,
7136,
11309,
117,
1229,
5157,
2692,
7937,
1204,
2228,
1329,
1104,
1103,
5157,
2692,
7937,
1204,
11309,
119,
153,
26447,
1942,
1105,
5157,
2692,
7937,
1204,
1132,
6156,
1116,
19755,
119,
1302,
2007,
17409,
1132,
2637,
1106,
1129,
1227,
1111,
1103,
2006,
2443,
1177,
1115,
1152,
1547,
1129,
1215,
1107,
170,
2595,
5418,
1897,
1190,
170,
1470,
1141,
119,
18959,
2924,
1105,
18959,
1708,
1132,
6736,
1111,
1470,
3510,
7147,
4935,
119,
25222,
1137,
2029,
3510,
7147,
4935,
1547,
1138,
170,
12629,
1111,
153,
26447,
1942,
117,
5157,
2692,
7937,
1204,
117,
141,
23329,
1708,
117,
1137,
155,
9717,
7136,
119,
139,
119,
25308,
10923,
14975,
138,
2265,
10923,
9932,
5401,
2099,
117,
2699,
117,
1105,
16670,
119,
15088,
117,
170,
1363,
2239,
1104,
3098,
1144,
1151,
1508,
1154,
9248,
10923,
14975,
1107,
1103,
3510,
7147,
1394,
119,
1203,
10923,
14975,
1138,
1151,
1872,
1114,
1103,
6457,
1104,
15097,
1199,
2747,
4267,
23397,
1116,
1276,
1114,
7328,
1106,
1103,
3510,
7147,
1394,
119,
1109,
2425,
3136,
1104,
153,
8284,
1658,
5026,
1361,
1110,
1106,
1260,
2528,
4455,
1513,
3510,
1707,
1105,
13618
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
".",
"One",
"ledge",
"##r",
"exists",
"per",
"open",
"policy",
".",
"5",
")",
"Ex",
"##ec",
"##ution",
":",
"A",
"smart",
"contract",
"per",
"##tains",
"to",
"a",
"com",
"##putation",
"performed",
"once",
"a",
"transaction",
"has",
"taken",
"place",
".",
"A",
"smart",
"contract",
"could",
"be",
"regarded",
"as",
"a",
"stored",
"procedure",
"in",
"##voked",
"on",
"a",
"deal",
".",
"The",
"inputs",
",",
"output",
"##s",
",",
"and",
"status",
"impacted",
"by",
"the",
"execution",
"of",
"a",
"smart",
"contract",
"obtain",
"consent",
"on",
"all",
"node",
".",
"6",
")",
"Application",
":",
"Going",
"beyond",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"and",
"asset",
"management",
",",
"some",
"ledge",
"##rs",
"support",
"running",
"general",
",",
"user",
"-",
"defined",
"com",
"##putation",
"##s",
"(",
"or",
"original",
"contracts",
")",
".",
"E",
"##ther",
"##eum",
"and",
"its",
"derivatives",
",",
"namely",
"H",
"##yd",
"##rac",
"##hai",
"##n",
",",
"Q",
"##uo",
"##rum",
",",
"Mona",
"##x",
",",
"Pa",
"##rity",
",",
"and",
"De",
"##finity",
"let",
"users",
"write",
"arbitrary",
"business",
"logic",
"executed",
"on",
"top",
"of",
"the",
"ledge",
"##r",
".",
"For",
"example",
",",
"E",
"##ther",
"##eum",
"contracts",
"range",
"from",
"simple",
"crowd",
"##fu",
"##nding",
"campaigns",
"to",
"those",
"involving",
"investment",
"funds",
"like",
"the",
"D",
"##A",
"##O",
".",
"De",
"##finity",
"offers",
"a",
"specific",
"kind",
"of",
"agreement",
"in",
"terms",
"of",
"governance",
"agreements",
"that",
"enforce",
"real",
"-",
"world",
"rules",
"upon",
"E",
"##ther",
"##eum",
"-",
"like",
"block",
"##cha",
"##ins",
".",
"H",
"##yper",
"##ledge",
"##r",
"and",
"its",
"close",
"cousin",
",",
"Saw",
"##tooth",
"Lake",
",",
"likewise",
"support",
"running",
"Turin",
"##g",
"-",
"complete",
"code",
".",
"They",
"offer",
"a",
"key",
"-",
"value",
"data",
"model",
",",
"with",
"which",
"the",
"applications",
"can",
"create",
"and",
"update",
"key",
"-",
"value",
"t",
"##up",
"##les",
"on",
"the",
"block",
"##cha",
"##in",
".",
"7",
")",
"Ex",
"##ample",
":",
"Bit",
"##co",
"##in",
"is",
"founded",
"on",
"Po",
"##W",
"although",
"P",
"##eer",
"##co",
"##in",
"is",
"a",
"new",
"peer",
"-",
"to",
"-",
"peer",
"Po",
"##S",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
".",
"Furthermore",
",",
"H",
"##yper",
"##ledge",
"##r",
"F",
"##ab",
"##ric",
"uses",
"P",
"##BF",
"##T",
"to",
"achieve",
"consensus",
".",
"Bit",
"##sha",
"##res",
",",
"a",
"smart",
"contract",
"platform",
",",
"explores",
"D",
"##PO",
"##S",
"as",
"their",
"consensus",
"algorithm",
".",
"R",
"##ip",
"##ple",
"implements",
"the",
"R",
"##ip",
"##ple",
"protocol",
",",
"while",
"Ten",
"##der",
"##min",
"##t",
"makes",
"use",
"of",
"the",
"Ten",
"##der",
"##min",
"##t",
"protocol",
".",
"P",
"##BF",
"##T",
"and",
"Ten",
"##der",
"##min",
"##t",
"are",
"permission",
"##s",
"protocols",
".",
"No",
"##de",
"identities",
"are",
"expected",
"to",
"be",
"known",
"for",
"the",
"whole",
"network",
"so",
"that",
"they",
"might",
"be",
"used",
"in",
"a",
"commercial",
"mode",
"rather",
"than",
"a",
"public",
"one",
".",
"Po",
"##W",
"and",
"Po",
"##S",
"are",
"suitable",
"for",
"public",
"block",
"##cha",
"##ins",
".",
"Consortium",
"or",
"private",
"block",
"##cha",
"##ins",
"might",
"have",
"a",
"preference",
"for",
"P",
"##BF",
"##T",
",",
"Ten",
"##der",
"##min",
"##t",
",",
"D",
"##PO",
"##S",
",",
"or",
"R",
"##ip",
"##ple",
".",
"B",
".",
"Advances",
"consensus",
"algorithms",
"A",
"successful",
"consensus",
"algorithm",
"suggests",
"performance",
",",
"security",
",",
"and",
"convenience",
".",
"Recently",
",",
"a",
"good",
"deal",
"of",
"effort",
"has",
"been",
"put",
"into",
"improving",
"consensus",
"algorithms",
"in",
"the",
"block",
"##cha",
"##in",
".",
"New",
"consensus",
"algorithms",
"have",
"been",
"developed",
"with",
"the",
"aim",
"of",
"solving",
"some",
"specific",
"di",
"##lemma",
"##s",
"found",
"with",
"regard",
"to",
"the",
"block",
"##cha",
"##in",
".",
"The",
"primary",
"approach",
"of",
"P",
"##eer",
"##C",
"##ens",
"##us",
"is",
"to",
"de",
"##co",
"##up",
"##le",
"block",
"production",
"and",
"transaction"
] | State of the art and challenges facing consensus p | 123 |
urations because
they take authenticated nodes. In the middle, all opposites we
find mixed consensus protocols that intend to increase the
efficiency of PBFT and PoW. As an example, Proof of
Elapsed Time removes the need for costly mining at PoW with
the use of profiting reliable devices. The other illustration is
957978-1-5386-2290-2/18/$31.00 Β©2018 IEEE ICOIN 2018
Proof of Authority [4] which helps PBFT by pre-finding
trusted nodes in which users vote on their own in order to
achieve | [
15468,
117,
1106,
11865,
1134,
10923,
8096,
1169,
1129,
12235,
2569,
119,
146,
11604,
16776,
1104,
1142,
117,
1103,
2351,
1144,
3228,
170,
1207,
10923,
3136,
1106,
4989,
1115,
170,
3510,
6570,
170,
3860,
8080,
2420,
119,
5322,
1115,
1344,
3510,
3964,
3001,
13018,
27400,
2528,
1394,
112,
188,
2699,
119,
13615,
1103,
144,
15825,
1183,
1124,
21704,
2556,
152,
4832,
22552,
1181,
12859,
1942,
8871,
113,
144,
3048,
9025,
1942,
114,
4129,
4557,
6708,
1144,
1151,
3000,
1106,
9474,
1142,
2486,
119,
1130,
5014,
1106,
1103,
1211,
16639,
3392,
5471,
117,
144,
3048,
9025,
1942,
17981,
1103,
5020,
117,
1105,
13418,
1336,
4835,
1106,
2812,
1103,
1436,
1141,
119,
144,
3048,
9025,
1942,
2234,
170,
1207,
10923,
9932,
1111,
8536,
118,
1106,
118,
8536,
3510,
7147,
1394,
2344,
1107,
1134,
11183,
1150,
3272,
1664,
118,
12196,
6777,
1116,
1104,
1231,
19091,
12853,
5474,
1111,
1103,
1763,
1352,
22675,
12217,
1116,
1110,
1549,
9635,
1106,
9509,
1103,
3510,
119,
1507,
1292,
170,
11309,
117,
13418,
1138,
1106,
8422,
1385,
3510,
23103,
1116,
1939,
1104,
1554,
5511,
7097,
119,
159,
119,
18732,
15517,
2162,
13329,
24805,
8093,
7147,
1394,
1144,
2602,
1157,
3209,
1111,
20892,
1103,
2361,
2380,
1114,
1157,
6818,
4625,
1107,
1103,
1532,
1104,
5306,
1475,
11858,
4412,
2734,
117,
1679,
22398,
9517,
117,
1126,
10031,
15455,
117,
1105,
23097,
6328,
119,
1130,
1142,
1844,
117,
1195,
2906,
170,
2335,
24431,
1104,
1103,
3510,
7147,
1394,
119,
1284,
1148,
1660,
1126,
24431,
1104,
3510,
7147,
1394,
7951,
1259,
3510,
7147,
1394,
4220,
117,
1105,
1103,
3607,
5924,
1104,
1103,
3510,
7147,
1394,
119,
1284,
1173,
6265,
1103,
2530,
10923,
14975,
1215,
1107,
1103,
3510,
7147,
1394,
119,
1284,
19774,
1105,
14133,
1292,
19755,
1107,
1472,
18788,
119,
7282,
117,
1195,
2190,
1199,
7806,
1105,
2645,
1115,
1156,
24856,
1200,
3510,
7147,
1394,
1718,
117,
1105,
7584,
7317,
3708,
1199,
1104,
1103,
3685,
8015,
1111,
15097,
1292,
2492,
119,
1789,
1936,
2174,
7768,
1132,
1145,
3000,
119,
25883,
3510,
7147,
1394,
118,
1359,
4683,
1132,
3450,
1158,
1146,
117,
1105,
1195,
2197,
1106,
5880,
1126,
1107,
118,
5415,
4449,
1104,
3510,
7147,
1394,
118,
1359,
4683,
1107,
1103,
2174,
119,
7118,
119,
155,
9919,
12420,
10036,
3048,
141,
18172,
8231,
21669,
11414,
1708,
7549,
1250,
1209,
19832,
1129,
18397,
1105,
3869,
21053,
119,
21325,
117,
4518,
1242,
19755,
1107,
1103,
5806,
3205,
1606,
1103,
2860,
1106,
1147,
8096,
1222,
1147,
2440,
1106,
118,
14372,
188,
7867,
6328,
117,
14372,
2699,
117,
1105,
14372,
9909,
117,
6808,
170,
9483,
1634,
1104,
1844,
119,
8094,
117,
1142,
5149,
1126,
5670,
1501,
4506,
1134,
5315,
6962,
1106,
4607,
1147,
3254,
1643,
17121,
1106,
11000,
2174,
3510,
7147,
1394,
188,
7867,
6328,
1105,
2699,
11778,
4385,
119,
5533,
117,
1175,
1132,
7722,
1104,
19916,
6305,
5336,
188,
10941,
10805,
1905,
1206,
10923,
117,
5336,
14239,
11309,
10700,
7747,
1122,
2502,
1106,
9248,
1103,
8050,
10704,
11315,
1233,
1105,
2443,
3584,
119,
155,
14663,
9637,
11680,
10954,
1708,
164,
122,
166,
107,
19585,
12298,
118,
2698,
117,
1609,
117,
1105,
17351,
142,
8420,
14136,
7230
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
6,
6,
6,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0
] | [
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
6,
6,
6,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0
] | [
"confirmation",
",",
"to",
"guarantee",
"which",
"consensus",
"efficiency",
"can",
"be",
"dramatically",
"increased",
".",
"I",
"##rre",
"##spective",
"of",
"this",
",",
"the",
"author",
"has",
"suggested",
"a",
"new",
"consensus",
"approach",
"to",
"ensure",
"that",
"a",
"block",
"produces",
"a",
"relatively",
"consistent",
"speed",
".",
"Note",
"that",
"high",
"block",
"generation",
"levels",
"compromise",
"Bit",
"##co",
"##in",
"'",
"s",
"security",
".",
"Hence",
"the",
"G",
"##reed",
"##y",
"He",
"##avi",
"##est",
"O",
"##bs",
"##erve",
"##d",
"Sub",
"##T",
"##ree",
"(",
"G",
"##H",
"##OS",
"##T",
")",
"chain",
"selection",
"principle",
"has",
"been",
"proposed",
"to",
"solve",
"this",
"issue",
".",
"In",
"contrast",
"to",
"the",
"most",
"prolonged",
"branch",
"scheme",
",",
"G",
"##H",
"##OS",
"##T",
"weights",
"the",
"branches",
",",
"and",
"miners",
"may",
"choose",
"to",
"follow",
"the",
"best",
"one",
".",
"G",
"##H",
"##OS",
"##T",
"introduced",
"a",
"new",
"consensus",
"algorithm",
"for",
"peer",
"-",
"to",
"-",
"peer",
"block",
"##cha",
"##in",
"systems",
"in",
"which",
"anybody",
"who",
"offers",
"non",
"-",
"interactive",
"proof",
"##s",
"of",
"re",
"##tri",
"##eva",
"##bility",
"for",
"the",
"past",
"state",
"snaps",
"##hot",
"##s",
"is",
"given",
"consent",
"to",
"generate",
"the",
"block",
".",
"During",
"these",
"a",
"protocol",
",",
"miners",
"have",
"to",
"gather",
"old",
"block",
"header",
"##s",
"instead",
"of",
"full",
"blocks",
"exclusively",
".",
"V",
".",
"CO",
"##NC",
"##L",
"##US",
"##ION",
"Block",
"##cha",
"##in",
"has",
"shown",
"its",
"potential",
"for",
"transforming",
"the",
"traditional",
"industry",
"with",
"its",
"essential",
"properties",
"in",
"the",
"form",
"of",
"96",
"##1",
"decent",
"##ral",
"##ization",
",",
"per",
"##sist",
"##ency",
",",
"an",
"##ony",
"##mity",
",",
"and",
"audit",
"##ability",
".",
"In",
"this",
"research",
",",
"we",
"offer",
"a",
"complete",
"overview",
"of",
"the",
"block",
"##cha",
"##in",
".",
"We",
"first",
"give",
"an",
"overview",
"of",
"block",
"##cha",
"##in",
"technologies",
"including",
"block",
"##cha",
"##in",
"architecture",
",",
"and",
"the",
"critical",
"characteristics",
"of",
"the",
"block",
"##cha",
"##in",
".",
"We",
"then",
"discuss",
"the",
"standard",
"consensus",
"algorithms",
"used",
"in",
"the",
"block",
"##cha",
"##in",
".",
"We",
"analyze",
"and",
"compare",
"these",
"protocols",
"in",
"different",
"respects",
".",
"Furthermore",
",",
"we",
"list",
"some",
"challenges",
"and",
"problems",
"that",
"would",
"hind",
"##er",
"block",
"##cha",
"##in",
"development",
",",
"and",
"sum",
"##mar",
"##ize",
"some",
"of",
"the",
"existing",
"approaches",
"for",
"solving",
"these",
"issues",
".",
"Some",
"possible",
"future",
"directions",
"are",
"also",
"proposed",
".",
"Nowadays",
"block",
"##cha",
"##in",
"-",
"based",
"applications",
"are",
"spring",
"##ing",
"up",
",",
"and",
"we",
"plan",
"to",
"conduct",
"an",
"in",
"-",
"depth",
"investigation",
"of",
"block",
"##cha",
"##in",
"-",
"based",
"applications",
"in",
"the",
"future",
".",
"VI",
".",
"R",
"##ES",
"##EA",
"##RC",
"##H",
"D",
"##IR",
"##EC",
"##TI",
"##ON",
"##S",
"Future",
"work",
"will",
"undoubtedly",
"be",
"compelling",
"and",
"worth",
"##while",
".",
"Specifically",
",",
"putting",
"many",
"protocols",
"in",
"the",
"appropriate",
"spot",
"using",
"the",
"value",
"to",
"their",
"efficiency",
"against",
"their",
"particular",
"to",
"-",
"node",
"s",
"##cal",
"##ability",
",",
"node",
"security",
",",
"and",
"node",
"privacy",
",",
"involves",
"a",
"reasonable",
"level",
"of",
"research",
".",
"Nevertheless",
",",
"this",
"represents",
"an",
"immediate",
"open",
"challenge",
"which",
"requires",
"researchers",
"to",
"improve",
"their",
"com",
"##p",
"##rehension",
"to",
"facilitate",
"future",
"block",
"##cha",
"##in",
"s",
"##cal",
"##ability",
"and",
"security",
"enhance",
"##ments",
".",
"Additionally",
",",
"there",
"are",
"plenty",
"of",
"prospective",
"opportunities",
"involving",
"s",
"##yne",
"##rg",
"##ies",
"between",
"consensus",
",",
"involving",
"incorporating",
"protocol",
"strategies",
"whenever",
"it",
"comes",
"to",
"improving",
"the",
"ad",
"##vers",
"##aria",
"##l",
"and",
"network",
"models",
".",
"R",
"##EF",
"##ER",
"##EN",
"##CE",
"##S",
"[",
"1",
"]",
"\"",
"Pa",
"##rity",
"-",
"fast",
",",
"light",
",",
"and",
"robust",
"E",
"##ther",
"##eum",
"client"
] | State of the art and challenges facing consensus p | 124 |
consensus. Likewise, Stellar [5] and Ripple [6]
augment PBFT by achieving consensus in smaller networks.
In the next section, we provide related work associated
with consensus protocol. Part III explains consensus protocol
comparisons which are used in Section IV for analysis
purposes. Section V offers a conclusion with regard to the
survey of consensus protocols, and section VI deals with
future research directions.
II. RELATED WORK
A. CAP Theorem
CAP Theorem [7] is a system that di | [
117,
107,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
14247,
1785,
22218,
120,
14247,
1785,
117,
1446,
164,
123,
166,
150,
119,
159,
7563,
14987,
117,
107,
1109,
12485,
1111,
188,
7867,
1895,
3510,
7147,
1394,
8113,
131,
6777,
118,
1104,
1250,
5016,
119,
1133,
25544,
117,
107,
1107,
3353,
23855,
1107,
3998,
4354,
118,
178,
25264,
1708,
10294,
117,
1410,
119,
164,
124,
166,
150,
119,
11919,
1105,
139,
119,
5255,
20428,
1964,
117,
107,
153,
18890,
8377,
6088,
15745,
117,
107,
1107,
20661,
1104,
1103,
2973,
1646,
11680,
19678,
26520,
1113,
20961,
6475,
4800,
1105,
146,
26318,
18415,
113,
11570,
17243,
114,
117,
1203,
5705,
117,
5060,
117,
3066,
117,
1729,
117,
4329,
119,
21121,
782,
21331,
119,
164,
125,
166,
107,
5096,
10008,
1104,
3748,
9236,
117,
107,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
14247,
1785,
22218,
120,
14247,
1785,
120,
192,
12635,
120,
5096,
10008,
118,
1104,
118,
5987,
118,
19589,
1116,
119,
117,
1446,
164,
126,
166,
1681,
7085,
22815,
1279,
117,
107,
1109,
12126,
1197,
16752,
3792,
14410,
17580,
131,
138,
26356,
20725,
6747,
1111,
4639,
118,
1634,
16752,
3792,
14410,
117,
107,
1428,
1512,
117,
1446,
119,
164,
127,
166,
24446,
1377,
1673,
9817,
143,
119,
117,
14069,
3263,
144,
119,
152,
119,
117,
2268,
6919,
138,
119,
117,
1192,
11553,
2087,
143,
119,
117,
18933,
2511,
142,
119,
107,
155,
9717,
7136,
131,
3278,
7334,
1105,
3929,
21163,
117,
107,
4623,
1105,
4623,
13849,
20463,
119,
4623,
1410,
117,
22842,
8797,
1107,
6701,
2444,
117,
10857,
5556,
26752,
119,
18919,
164,
128,
166,
1302,
14535,
2713,
2024,
117,
107,
8157,
1113,
8093,
7147,
1394,
14164,
1105,
11336,
6951,
4326,
143,
3663,
10973,
16337,
7178,
107,
117,
1188,
2592,
1110,
1103,
1871,
1104,
1103,
5980,
11058,
1118,
1999,
112,
188,
3424,
1104,
14592,
117,
5820,
117,
1105,
7358,
113,
22157,
21669,
114,
117,
1345,
1446,
164,
129,
166,
149,
119,
21372,
4342,
117,
155,
119,
156,
15342,
1777,
1377,
117,
1105,
150,
119,
153,
23860,
117,
107,
1109,
8377,
14729,
2463,
117,
107,
9690,
2107,
13809,
22946,
1113,
21076,
18388,
1105,
6475,
113,
16972,
27258,
10719,
114,
117,
10857,
119,
125,
117,
1185,
119,
124,
117,
2294,
119,
164,
130,
166,
151,
119,
156,
3293,
4043,
117,
107,
25308,
1107,
4901,
2699,
117,
107,
1581,
119,
164,
1275,
166,
150,
119,
11919,
1105,
139,
119,
5255,
20428,
1964,
117,
107,
153,
18890,
8377,
6088,
15745,
117,
107,
1107,
20661,
1104,
1103,
2973,
1646,
11680,
19678,
26520,
1113,
20961,
6475,
4800,
1105,
146,
26318,
18415,
113,
11570,
17243,
114,
117,
1203,
5705,
117,
5060,
117,
3066,
117,
1729,
117,
4329,
119,
21121,
782,
21331,
119,
164,
1429,
166,
26824,
5933,
11896,
1968,
12610,
117,
107,
27400,
2528,
1394,
131,
138,
153,
8284,
118,
1106,
118,
153,
8284,
10952,
10511,
3910,
117,
107,
1369,
164,
1367,
166,
151,
119,
157,
119,
2031,
8586,
117,
107,
1212,
1103,
6119,
4129,
3013,
1105,
18693,
2191,
118,
5915,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
117,
107,
20463,
2713,
20777,
2155
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0
] | [
",",
"\"",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"par",
"##ity",
"##tech",
"/",
"par",
"##ity",
",",
"2016",
"[",
"2",
"]",
"M",
".",
"V",
"##uk",
"##olic",
",",
"\"",
"The",
"quest",
"for",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"fabric",
":",
"proof",
"-",
"of",
"work",
"vs",
".",
"but",
"replication",
",",
"\"",
"in",
"Open",
"Problems",
"in",
"Network",
"Security",
"-",
"i",
"##Net",
"##S",
"##ec",
",",
"2015",
".",
"[",
"3",
"]",
"M",
".",
"Castro",
"and",
"B",
".",
"Li",
"##sko",
"##v",
",",
"\"",
"P",
"##ractical",
"Byzantine",
"fault",
"tolerance",
",",
"\"",
"in",
"Proceedings",
"of",
"the",
"3rd",
"US",
"##EN",
"##IX",
"Symposium",
"on",
"Operating",
"Systems",
"Design",
"and",
"I",
"##mple",
"##mentation",
"(",
"OS",
"##DI",
")",
",",
"New",
"Orleans",
",",
"Louisiana",
",",
"USA",
",",
"1999",
",",
"pp",
".",
"173",
"β",
"186",
".",
"[",
"4",
"]",
"\"",
"Pro",
"##of",
"of",
"authority",
"chains",
",",
"\"",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"par",
"##ity",
"##tech",
"/",
"par",
"##ity",
"/",
"w",
"##iki",
"/",
"Pro",
"##of",
"-",
"of",
"-",
"Authority",
"-",
"Chain",
"##s",
".",
",",
"2016",
"[",
"5",
"]",
"David",
"Ma",
"##zier",
"##es",
",",
"\"",
"The",
"Stella",
"##r",
"Con",
"##sen",
"##sus",
"Protocol",
":",
"A",
"Fed",
"##erated",
"Model",
"for",
"Internet",
"-",
"level",
"Con",
"##sen",
"##sus",
",",
"\"",
"February",
"25",
",",
"2016",
".",
"[",
"6",
"]",
"Arm",
"##k",
"##ne",
"##cht",
"F",
".",
",",
"Kara",
"##me",
"G",
".",
"O",
".",
",",
"Man",
"##dal",
"A",
".",
",",
"You",
"##sse",
"##f",
"F",
".",
",",
"Zen",
"##ner",
"E",
".",
"\"",
"R",
"##ip",
"##ple",
":",
"Over",
"##view",
"and",
"Out",
"##look",
",",
"\"",
"Trust",
"and",
"Trust",
"##worthy",
"Computing",
".",
"Trust",
"2015",
",",
"Lecture",
"Notes",
"in",
"Computer",
"Science",
",",
"vol",
"92",
"##29",
".",
"Springer",
"[",
"7",
"]",
"No",
"##mura",
"Research",
"Institute",
",",
"\"",
"Survey",
"on",
"Block",
"##cha",
"##in",
"Technologies",
"and",
"Re",
"##lated",
"Services",
"F",
"##Y",
"##20",
"##15",
"Report",
"\"",
",",
"This",
"report",
"is",
"the",
"result",
"of",
"the",
"survey",
"contracted",
"by",
"Japan",
"'",
"s",
"Ministry",
"of",
"Economy",
",",
"Trade",
",",
"and",
"Industry",
"(",
"ME",
"##TI",
")",
",",
"March",
"2016",
"[",
"8",
"]",
"L",
".",
"Lam",
"##port",
",",
"R",
".",
"S",
"##hos",
"##ta",
"##k",
",",
"and",
"M",
".",
"P",
"##ease",
",",
"\"",
"The",
"Byzantine",
"generals",
"problem",
",",
"\"",
"AC",
"##M",
"Trans",
"##actions",
"on",
"Programming",
"Languages",
"and",
"Systems",
"(",
"TO",
"##PL",
"##AS",
")",
",",
"vol",
".",
"4",
",",
"no",
".",
"3",
",",
"1982",
".",
"[",
"9",
"]",
"N",
".",
"S",
"##za",
"##bo",
",",
"\"",
"Advances",
"in",
"distributed",
"security",
",",
"\"",
"2003",
".",
"[",
"10",
"]",
"M",
".",
"Castro",
"and",
"B",
".",
"Li",
"##sko",
"##v",
",",
"\"",
"P",
"##ractical",
"Byzantine",
"fault",
"tolerance",
",",
"\"",
"in",
"Proceedings",
"of",
"the",
"3rd",
"US",
"##EN",
"##IX",
"Symposium",
"on",
"Operating",
"Systems",
"Design",
"and",
"I",
"##mple",
"##mentation",
"(",
"OS",
"##DI",
")",
",",
"New",
"Orleans",
",",
"Louisiana",
",",
"USA",
",",
"1999",
",",
"pp",
".",
"173",
"β",
"186",
".",
"[",
"11",
"]",
"Sato",
"##shi",
"Na",
"##ka",
"##moto",
",",
"\"",
"Bit",
"##co",
"##in",
":",
"A",
"P",
"##eer",
"-",
"to",
"-",
"P",
"##eer",
"Electronic",
"Cash",
"System",
",",
"\"",
"2008",
"[",
"12",
"]",
"N",
".",
"T",
".",
"Court",
"##ois",
",",
"\"",
"On",
"the",
"longest",
"chain",
"rule",
"and",
"programmed",
"self",
"-",
"destruction",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"\"",
"Computing",
"Research",
"Rep",
"##os"
] | State of the art and challenges facing consensus p | 125 |
consensus. Likewise, Stellar [5] and Ripple [6]
augment PBFT by achieving consensus in smaller networks.
In the next section, we provide related work associated
with consensus protocol. Part III explains consensus protocol
comparisons which are used in Section IV for analysis
purposes. Section V offers a conclusion with regard to the
survey of consensus protocols, and section VI deals with
future research directions.
II. RELATED WORK
A. CAP Theorem
CAP Theorem [7] is a system that di | [
117,
107,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
14247,
1785,
22218,
120,
14247,
1785,
117,
1446,
164,
123,
166,
150,
119,
159,
7563,
14987,
117,
107,
1109,
12485,
1111,
188,
7867,
1895,
3510,
7147,
1394,
8113,
131,
6777,
118,
1104,
1250,
5016,
119,
1133,
25544,
117,
107,
1107,
3353,
23855,
1107,
3998,
4354,
118,
178,
25264,
1708,
10294,
117,
1410,
119,
164,
124,
166,
150,
119,
11919,
1105,
139,
119,
5255,
20428,
1964,
117,
107,
153,
18890,
8377,
6088,
15745,
117,
107,
1107,
20661,
1104,
1103,
2973,
1646,
11680,
19678,
26520,
1113,
20961,
6475,
4800,
1105,
146,
26318,
18415,
113,
11570,
17243,
114,
117,
1203,
5705,
117,
5060,
117,
3066,
117,
1729,
117,
4329,
119,
21121,
782,
21331,
119,
164,
125,
166,
107,
5096,
10008,
1104,
3748,
9236,
117,
107,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
14247,
1785,
22218,
120,
14247,
1785,
120,
192,
12635,
120,
5096,
10008,
118,
1104,
118,
5987,
118,
19589,
1116,
119,
117,
1446,
164,
126,
166,
1681,
7085,
22815,
1279,
117,
107,
1109,
12126,
1197,
16752,
3792,
14410,
17580,
131,
138,
26356,
20725,
6747,
1111,
4639,
118,
1634,
16752,
3792,
14410,
117,
107,
1428,
1512,
117,
1446,
119,
164,
127,
166,
24446,
1377,
1673,
9817,
143,
119,
117,
14069,
3263,
144,
119,
152,
119,
117,
2268,
6919,
138,
119,
117,
1192,
11553,
2087,
143,
119,
117,
18933,
2511,
142,
119,
107,
155,
9717,
7136,
131,
3278,
7334,
1105,
3929,
21163,
117,
107,
4623,
1105,
4623,
13849,
20463,
119,
4623,
1410,
117,
22842,
8797,
1107,
6701,
2444,
117,
10857,
5556,
26752,
119,
18919,
164,
128,
166,
1302,
14535,
2713,
2024,
117,
107,
8157,
1113,
8093,
7147,
1394,
14164,
1105,
11336,
6951,
4326,
143,
3663,
10973,
16337,
7178,
107,
117,
1188,
2592,
1110,
1103,
1871,
1104,
1103,
5980,
11058,
1118,
1999,
112,
188,
3424,
1104,
14592,
117,
5820,
117,
1105,
7358,
113,
22157,
21669,
114,
117,
1345,
1446,
164,
129,
166,
149,
119,
21372,
4342,
117,
155,
119,
156,
15342,
1777,
1377,
117,
1105,
150,
119,
153,
23860,
117,
107,
1109,
8377,
14729,
2463,
117,
107,
9690,
2107,
13809,
22946,
1113,
21076,
18388,
1105,
6475,
113,
16972,
27258,
10719,
114,
117,
10857,
119,
125,
117,
1185,
119,
124,
117,
2294,
119,
164,
130,
166,
151,
119,
156,
3293,
4043,
117,
107,
25308,
1107,
4901,
2699,
117,
107,
1581,
119,
164,
1275,
166,
150,
119,
11919,
1105,
139,
119,
5255,
20428,
1964,
117,
107,
153,
18890,
8377,
6088,
15745,
117,
107,
1107,
20661,
1104,
1103,
2973,
1646,
11680,
19678,
26520,
1113,
20961,
6475,
4800,
1105,
146,
26318,
18415,
113,
11570,
17243,
114,
117,
1203,
5705,
117,
5060,
117,
3066,
117,
1729,
117,
4329,
119,
21121,
782,
21331,
119,
164,
1429,
166,
26824,
5933,
11896,
1968,
12610,
117,
107,
27400,
2528,
1394,
131,
138,
153,
8284,
118,
1106,
118,
153,
8284,
10952,
10511,
3910,
117,
107,
1369,
164,
1367,
166,
151,
119,
157,
119,
2031,
8586,
117,
107,
1212,
1103,
6119,
4129,
3013,
1105,
18693,
2191,
118,
5915,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
117,
107,
20463,
2713,
20777,
2155
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
",",
"\"",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"par",
"##ity",
"##tech",
"/",
"par",
"##ity",
",",
"2016",
"[",
"2",
"]",
"M",
".",
"V",
"##uk",
"##olic",
",",
"\"",
"The",
"quest",
"for",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"fabric",
":",
"proof",
"-",
"of",
"work",
"vs",
".",
"but",
"replication",
",",
"\"",
"in",
"Open",
"Problems",
"in",
"Network",
"Security",
"-",
"i",
"##Net",
"##S",
"##ec",
",",
"2015",
".",
"[",
"3",
"]",
"M",
".",
"Castro",
"and",
"B",
".",
"Li",
"##sko",
"##v",
",",
"\"",
"P",
"##ractical",
"Byzantine",
"fault",
"tolerance",
",",
"\"",
"in",
"Proceedings",
"of",
"the",
"3rd",
"US",
"##EN",
"##IX",
"Symposium",
"on",
"Operating",
"Systems",
"Design",
"and",
"I",
"##mple",
"##mentation",
"(",
"OS",
"##DI",
")",
",",
"New",
"Orleans",
",",
"Louisiana",
",",
"USA",
",",
"1999",
",",
"pp",
".",
"173",
"β",
"186",
".",
"[",
"4",
"]",
"\"",
"Pro",
"##of",
"of",
"authority",
"chains",
",",
"\"",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"par",
"##ity",
"##tech",
"/",
"par",
"##ity",
"/",
"w",
"##iki",
"/",
"Pro",
"##of",
"-",
"of",
"-",
"Authority",
"-",
"Chain",
"##s",
".",
",",
"2016",
"[",
"5",
"]",
"David",
"Ma",
"##zier",
"##es",
",",
"\"",
"The",
"Stella",
"##r",
"Con",
"##sen",
"##sus",
"Protocol",
":",
"A",
"Fed",
"##erated",
"Model",
"for",
"Internet",
"-",
"level",
"Con",
"##sen",
"##sus",
",",
"\"",
"February",
"25",
",",
"2016",
".",
"[",
"6",
"]",
"Arm",
"##k",
"##ne",
"##cht",
"F",
".",
",",
"Kara",
"##me",
"G",
".",
"O",
".",
",",
"Man",
"##dal",
"A",
".",
",",
"You",
"##sse",
"##f",
"F",
".",
",",
"Zen",
"##ner",
"E",
".",
"\"",
"R",
"##ip",
"##ple",
":",
"Over",
"##view",
"and",
"Out",
"##look",
",",
"\"",
"Trust",
"and",
"Trust",
"##worthy",
"Computing",
".",
"Trust",
"2015",
",",
"Lecture",
"Notes",
"in",
"Computer",
"Science",
",",
"vol",
"92",
"##29",
".",
"Springer",
"[",
"7",
"]",
"No",
"##mura",
"Research",
"Institute",
",",
"\"",
"Survey",
"on",
"Block",
"##cha",
"##in",
"Technologies",
"and",
"Re",
"##lated",
"Services",
"F",
"##Y",
"##20",
"##15",
"Report",
"\"",
",",
"This",
"report",
"is",
"the",
"result",
"of",
"the",
"survey",
"contracted",
"by",
"Japan",
"'",
"s",
"Ministry",
"of",
"Economy",
",",
"Trade",
",",
"and",
"Industry",
"(",
"ME",
"##TI",
")",
",",
"March",
"2016",
"[",
"8",
"]",
"L",
".",
"Lam",
"##port",
",",
"R",
".",
"S",
"##hos",
"##ta",
"##k",
",",
"and",
"M",
".",
"P",
"##ease",
",",
"\"",
"The",
"Byzantine",
"generals",
"problem",
",",
"\"",
"AC",
"##M",
"Trans",
"##actions",
"on",
"Programming",
"Languages",
"and",
"Systems",
"(",
"TO",
"##PL",
"##AS",
")",
",",
"vol",
".",
"4",
",",
"no",
".",
"3",
",",
"1982",
".",
"[",
"9",
"]",
"N",
".",
"S",
"##za",
"##bo",
",",
"\"",
"Advances",
"in",
"distributed",
"security",
",",
"\"",
"2003",
".",
"[",
"10",
"]",
"M",
".",
"Castro",
"and",
"B",
".",
"Li",
"##sko",
"##v",
",",
"\"",
"P",
"##ractical",
"Byzantine",
"fault",
"tolerance",
",",
"\"",
"in",
"Proceedings",
"of",
"the",
"3rd",
"US",
"##EN",
"##IX",
"Symposium",
"on",
"Operating",
"Systems",
"Design",
"and",
"I",
"##mple",
"##mentation",
"(",
"OS",
"##DI",
")",
",",
"New",
"Orleans",
",",
"Louisiana",
",",
"USA",
",",
"1999",
",",
"pp",
".",
"173",
"β",
"186",
".",
"[",
"11",
"]",
"Sato",
"##shi",
"Na",
"##ka",
"##moto",
",",
"\"",
"Bit",
"##co",
"##in",
":",
"A",
"P",
"##eer",
"-",
"to",
"-",
"P",
"##eer",
"Electronic",
"Cash",
"System",
",",
"\"",
"2008",
"[",
"12",
"]",
"N",
".",
"T",
".",
"Court",
"##ois",
",",
"\"",
"On",
"the",
"longest",
"chain",
"rule",
"and",
"programmed",
"self",
"-",
"destruction",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"\"",
"Computing",
"Research",
"Rep",
"##os"
] | State of the art and challenges facing consensus p | 126 |
stributes multiple
nodes that handle common data, and shows which distributed
systems can completely satisfy the following three properties:
Consistency (C) is a status by which each node has the latest
data at the same time. Availability (A) is the status where any
failure of a specific node does not affect other nodes. Partition
tolerance (P) is the status by which nodes can continue
operations, even with a failure in the network.ο
The blockchain is one of the distributed systems which can
sa | [
15419,
1183,
117,
7882,
119,
20777,
119,
170,
4832,
120,
8183,
1571,
119,
4991,
23124,
117,
1387,
119,
164,
1492,
166,
147,
119,
138,
119,
148,
10747,
117,
146,
119,
140,
119,
22618,
117,
1105,
142,
119,
160,
119,
11907,
26929,
117,
107,
1109,
8142,
1104,
2113,
2528,
1394,
5463,
117,
1137,
2113,
2528,
1394,
1107,
1103,
2915,
1104,
8050,
10704,
5927,
117,
107,
1107,
160,
27514,
1708,
112,
1492,
131,
20661,
1104,
1103,
5247,
16350,
1113,
1103,
7525,
1104,
4219,
4354,
117,
1340,
1381,
119,
164,
1489,
166,
146,
119,
3096,
25918,
117,
140,
119,
2499,
117,
138,
119,
12107,
1584,
10659,
1182,
117,
1105,
150,
119,
24580,
7355,
117,
107,
5096,
10008,
1104,
3246,
131,
16409,
22835,
2113,
2528,
1394,
112,
188,
6777,
1104,
1250,
2258,
6777,
1104,
8219,
117,
107,
1107,
20820,
2036,
7235,
112,
1489,
131,
20661,
1104,
1103,
5612,
16350,
1113,
1103,
7525,
1104,
16942,
117,
6475,
117,
1105,
3291,
8223,
15012,
2116,
117,
1340,
1387,
119,
164,
1405,
166,
147,
119,
4425,
1105,
138,
119,
8493,
117,
107,
2827,
131,
23603,
4676,
19716,
1114,
2113,
2528,
1394,
117,
107,
1107,
3604,
112,
1367,
131,
20661,
1104,
1103,
5050,
1570,
3047,
1113,
7748,
15586,
6451,
9543,
1105,
7154,
4354,
117,
9751,
119,
1368,
119,
164,
1479,
166,
138,
119,
4388,
117,
150,
119,
20385,
2858,
117,
149,
119,
23460,
3361,
1197,
117,
150,
119,
13359,
4830,
23091,
117,
144,
119,
10593,
117,
138,
119,
3902,
117,
138,
119,
21377,
3447,
4487,
117,
147,
119,
4446,
28169,
1320,
117,
1105,
153,
119,
8769,
8683,
117,
107,
13832,
6639,
1979,
3510,
7147,
1394,
18168,
1114,
185,
12606,
3660,
1334,
7147,
4935,
117,
107,
7882,
119,
20777,
119,
117,
14125,
119,
1387,
119,
164,
1542,
166,
138,
119,
3902,
117,
138,
119,
23915,
5999,
117,
142,
119,
14104,
117,
139,
119,
19585,
11791,
117,
1105,
147,
119,
22795,
117,
107,
14286,
1918,
2528,
1394,
131,
20777,
2149,
5674,
4253,
2113,
2528,
1394,
1250,
1111,
2233,
10149,
117,
107,
1107,
16625,
112,
1489,
131,
20661,
1104,
1103,
22031,
16206,
26520,
1113,
4354,
1105,
153,
2047,
2497,
3457,
117,
1318,
1387,
119,
164,
1407,
166,
107,
20318,
21590,
3521,
117,
107,
15397,
3436,
117,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
177,
24312,
19693,
1197,
120,
1486,
21590,
118,
4160,
117,
1446,
164,
1627,
166,
107,
5096,
10008,
1104,
8468,
11478,
5591,
1159,
113,
4225,
114,
117,
107,
18630,
131,
120,
120,
1107,
7854,
19693,
1197,
119,
176,
7088,
10354,
119,
178,
1186,
120,
4784,
119,
28066,
108,
6777,
118,
1104,
118,
8468,
11478,
5591,
118,
1159,
118,
4225,
119,
117,
1387,
164,
1406,
166,
1135,
1777,
1183,
142,
18543,
117,
24930,
5521,
142,
8124,
9198,
14840,
117,
18653,
1394,
11274,
2203,
1200,
117,
1105,
6284,
7488,
3498,
26978,
11553,
117,
107,
27400,
2528,
1394,
118,
21174,
131,
138,
188,
7867,
1895,
3510,
7147,
1394,
11309,
117,
107,
170,
1197,
3190,
11083,
3073,
10988,
170,
1197,
3190,
11083,
131,
17576,
1568,
119,
5507,
1568,
26303,
117,
1410,
119,
164,
1626,
166,
2392,
1186,
159,
7563,
14987,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##itor",
"##y",
",",
"Tech",
".",
"Rep",
".",
"a",
"##bs",
"/",
"140",
"##5",
".",
"05",
"##34",
",",
"2014",
".",
"[",
"13",
"]",
"J",
".",
"A",
".",
"K",
"##roll",
",",
"I",
".",
"C",
".",
"Davey",
",",
"and",
"E",
".",
"W",
".",
"Fe",
"##lten",
",",
"\"",
"The",
"economics",
"of",
"bit",
"##co",
"##in",
"mining",
",",
"or",
"bit",
"##co",
"##in",
"in",
"the",
"presence",
"of",
"ad",
"##vers",
"##aries",
",",
"\"",
"in",
"W",
"##EI",
"##S",
"'",
"13",
":",
"Proceedings",
"of",
"the",
"12th",
"Workshop",
"on",
"the",
"Economics",
"of",
"Information",
"Security",
",",
"June",
"2013",
".",
"[",
"14",
"]",
"I",
".",
"Ben",
"##tov",
",",
"C",
".",
"Lee",
",",
"A",
".",
"Mi",
"##z",
"##rah",
"##i",
",",
"and",
"M",
".",
"Rosen",
"##feld",
",",
"\"",
"Pro",
"##of",
"of",
"activity",
":",
"Ex",
"##tending",
"bit",
"##co",
"##in",
"'",
"s",
"proof",
"of",
"work",
"via",
"proof",
"of",
"stake",
",",
"\"",
"in",
"Net",
"##E",
"##con",
"'",
"14",
":",
"Proceedings",
"of",
"the",
"9th",
"Workshop",
"on",
"the",
"Economics",
"of",
"Networks",
",",
"Systems",
",",
"and",
"Co",
"##mp",
"##uta",
"##tion",
",",
"June",
"2014",
".",
"[",
"15",
"]",
"J",
".",
"Clark",
"and",
"A",
".",
"Essex",
",",
"\"",
"Commission",
":",
"Carbon",
"dating",
"commitments",
"with",
"bit",
"##co",
"##in",
",",
"\"",
"in",
"FC",
"'",
"12",
":",
"Proceedings",
"of",
"the",
"16th",
"International",
"Conference",
"on",
"Financial",
"Cry",
"##pt",
"##ography",
"and",
"Data",
"Security",
",",
"Mar",
".",
"2012",
".",
"[",
"16",
"]",
"A",
".",
"Back",
",",
"M",
".",
"Coral",
"##lo",
",",
"L",
".",
"Dash",
"##j",
"##r",
",",
"M",
".",
"Fr",
"##ied",
"##enbach",
",",
"G",
".",
"Maxwell",
",",
"A",
".",
"Miller",
",",
"A",
".",
"Poe",
"##ls",
"##tra",
",",
"J",
".",
"Tim",
"##Β΄",
"##on",
",",
"and",
"P",
".",
"Wu",
"##ille",
",",
"\"",
"En",
"##ab",
"##ling",
"block",
"##cha",
"##in",
"innovations",
"with",
"p",
"##eg",
"##ged",
"side",
"##cha",
"##ins",
",",
"\"",
"Tech",
".",
"Rep",
".",
",",
"Oct",
".",
"2014",
".",
"[",
"17",
"]",
"A",
".",
"Miller",
",",
"A",
".",
"Ju",
"##els",
",",
"E",
".",
"Shi",
",",
"B",
".",
"Pa",
"##rno",
",",
"and",
"J",
".",
"Katz",
",",
"\"",
"Per",
"##ma",
"##co",
"##in",
":",
"Rep",
"##ur",
"##po",
"##sing",
"bit",
"##co",
"##in",
"work",
"for",
"data",
"preservation",
",",
"\"",
"in",
"SP",
"'",
"14",
":",
"Proceedings",
"of",
"the",
"35th",
"IEEE",
"Symposium",
"on",
"Security",
"and",
"P",
"##ri",
"##va",
"##cy",
",",
"May",
"2014",
".",
"[",
"18",
"]",
"\"",
"Saw",
"##tooth",
"lake",
",",
"\"",
"Intel",
"Corporation",
",",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"h",
"##yper",
"##ledge",
"##r",
"/",
"saw",
"##tooth",
"-",
"core",
",",
"2016",
"[",
"19",
"]",
"\"",
"Pro",
"##of",
"of",
"el",
"##ap",
"##sed",
"time",
"(",
"poet",
")",
",",
"\"",
"https",
":",
"/",
"/",
"in",
"##tel",
"##ledge",
"##r",
".",
"g",
"##ith",
"##ub",
".",
"i",
"##o",
"/",
"introduction",
".",
"html",
"#",
"proof",
"-",
"of",
"-",
"el",
"##ap",
"##sed",
"-",
"time",
"-",
"poet",
".",
",",
"2014",
"[",
"20",
"]",
"It",
"##ta",
"##y",
"E",
"##yal",
",",
"Ad",
"##em",
"E",
"##fe",
"Gen",
"##cer",
",",
"Em",
"##in",
"Gun",
"Sir",
"##er",
",",
"and",
"Rob",
"##bert",
"van",
"Rene",
"##sse",
",",
"\"",
"Bit",
"##co",
"##in",
"-",
"ng",
":",
"A",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"protocol",
",",
"\"",
"a",
"##r",
"##X",
"##iv",
"pre",
"##print",
"a",
"##r",
"##X",
"##iv",
":",
"151",
"##0",
".",
"02",
"##0",
"##37",
",",
"2015",
".",
"[",
"21",
"]",
"Mark",
"##o",
"V",
"##uk",
"##olic",
","
] | State of the art and challenges facing consensus p | 127 |
tisfy both availability (A) and partition tolerance (P) but
cannot satisfy the condition of consistency (C). Instead, as long
as the separation of the network is time-limited, the system is
regarded as maintaining the ultimate consistency. Ultimate
consistency is | [
107,
1109,
12485,
1111,
188,
7867,
1895,
3510,
7147,
1394,
8113,
131,
5096,
10008,
118,
1104,
118,
1250,
5016,
119,
171,
4964,
25544,
117,
107,
1130,
20661,
1104,
1103,
13729,
11410,
160,
2349,
1429,
119,
125,
16350,
178,
25264,
1708,
10294,
1410,
119,
1410,
119,
164,
1659,
166,
9132,
162,
117,
23158,
147,
119,
107,
1760,
146,
1186,
1942,
3651,
1671,
2235,
1359,
1113,
1103,
11309,
1104,
2113,
2528,
1394,
117,
107,
4186,
1570,
3511,
1113,
4810,
1107,
1397,
118,
3964,
6379,
113,
146,
19747,
2249,
114,
132,
1410,
119,
185,
119,
21421,
782,
5539,
119,
9465,
131,
8413,
131,
120,
120,
173,
1775,
119,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
146,
19747,
2249,
119,
1410,
119,
3102,
1559,
23249,
13144,
119,
164,
1695,
166,
156,
119,
1670,
117,
148,
119,
26424,
18062,
24996,
117,
138,
119,
148,
16732,
117,
147,
119,
2586,
10781,
117,
144,
119,
14763,
17704,
2822,
10232,
117,
1105,
153,
119,
144,
19888,
117,
107,
4525,
8715,
131,
138,
5354,
6451,
13335,
2149,
5123,
3457,
1359,
1113,
6777,
1116,
1104,
2000,
117,
107,
146,
8101,
2069,
15586,
6451,
4807,
174,
2101,
4854,
1204,
15041,
117,
10857,
119,
1410,
117,
185,
119,
3882,
1604,
117,
1410,
119,
164,
1572,
166,
141,
2001,
10205,
1200,
117,
107,
9352,
12606,
2913,
5096,
10008,
118,
1104,
118,
1457,
9899,
113,
141,
23329,
1708,
114,
117,
107,
27400,
5480,
1874,
1653,
26311,
117,
1387,
164,
1512,
166,
142,
139,
9827,
1399,
117,
107,
5157,
2692,
7937,
1204,
131,
8377,
143,
14045,
1706,
2879,
3923,
1107,
1103,
4936,
1104,
8093,
7147,
4935,
117,
107,
1446,
5306,
1477
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0
] | [
"\"",
"The",
"quest",
"for",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"fabric",
":",
"Pro",
"##of",
"-",
"of",
"-",
"work",
"vs",
".",
"b",
"##ft",
"replication",
",",
"\"",
"In",
"Proceedings",
"of",
"the",
"IF",
"##IP",
"W",
"##G",
"11",
".",
"4",
"Workshop",
"i",
"##Net",
"##S",
"##ec",
"2015",
".",
"2015",
".",
"[",
"22",
"]",
"Zhang",
"Y",
",",
"Wen",
"J",
".",
"\"",
"An",
"I",
"##o",
"##T",
"electric",
"business",
"model",
"based",
"on",
"the",
"protocol",
"of",
"bit",
"##co",
"##in",
",",
"\"",
"18th",
"International",
"conference",
"on",
"intelligence",
"in",
"next",
"-",
"generation",
"networks",
"(",
"I",
"##CI",
"##N",
")",
";",
"2015",
".",
"p",
".",
"184",
"β",
"91",
".",
"doi",
":",
"http",
":",
"/",
"/",
"d",
"##x",
".",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"I",
"##CI",
"##N",
".",
"2015",
".",
"70",
"##7",
"##38",
"##30",
".",
"[",
"23",
"]",
"S",
".",
"Park",
",",
"K",
".",
"Pie",
"##tr",
"##zak",
",",
"A",
".",
"K",
"##won",
",",
"J",
".",
"Al",
"##wen",
",",
"G",
".",
"Fu",
"##chs",
"##ba",
"##uer",
",",
"and",
"P",
".",
"G",
"##azi",
",",
"\"",
"Space",
"mini",
":",
"A",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"based",
"on",
"proof",
"##s",
"of",
"space",
",",
"\"",
"I",
"##AC",
"##R",
"Cry",
"##pt",
"##ology",
"e",
"##P",
"##rin",
"##t",
"Archive",
",",
"vol",
".",
"2015",
",",
"p",
".",
"52",
"##8",
",",
"2015",
".",
"[",
"24",
"]",
"D",
"La",
"##rim",
"##er",
",",
"\"",
"Del",
"##eg",
"##ated",
"Pro",
"##of",
"-",
"of",
"-",
"St",
"##ake",
"(",
"D",
"##PO",
"##S",
")",
",",
"\"",
"Bit",
"##sha",
"##re",
"white",
"##paper",
",",
"2014",
"[",
"25",
"]",
"E",
"B",
"##uch",
"##man",
",",
"\"",
"Ten",
"##der",
"##min",
"##t",
":",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"in",
"the",
"Age",
"of",
"Block",
"##cha",
"##ins",
",",
"\"",
"2016",
"96",
"##2"
] | State of the art and challenges facing consensus p | 128 |
tisfy both availability (A) and partition tolerance (P) but
cannot satisfy the condition of consistency (C). Instead, as long
as the separation of the network is time-limited, the system is
regarded as maintaining the ultimate consistency. Ultimate
consistency is | [
107,
1109,
12485,
1111,
188,
7867,
1895,
3510,
7147,
1394,
8113,
131,
5096,
10008,
118,
1104,
118,
1250,
5016,
119,
171,
4964,
25544,
117,
107,
1130,
20661,
1104,
1103,
13729,
11410,
160,
2349,
1429,
119,
125,
16350,
178,
25264,
1708,
10294,
1410,
119,
1410,
119,
164,
1659,
166,
9132,
162,
117,
23158,
147,
119,
107,
1760,
146,
1186,
1942,
3651,
1671,
2235,
1359,
1113,
1103,
11309,
1104,
2113,
2528,
1394,
117,
107,
4186,
1570,
3511,
1113,
4810,
1107,
1397,
118,
3964,
6379,
113,
146,
19747,
2249,
114,
132,
1410,
119,
185,
119,
21421,
782,
5539,
119,
9465,
131,
8413,
131,
120,
120,
173,
1775,
119,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
146,
19747,
2249,
119,
1410,
119,
3102,
1559,
23249,
13144,
119,
164,
1695,
166,
156,
119,
1670,
117,
148,
119,
26424,
18062,
24996,
117,
138,
119,
148,
16732,
117,
147,
119,
2586,
10781,
117,
144,
119,
14763,
17704,
2822,
10232,
117,
1105,
153,
119,
144,
19888,
117,
107,
4525,
8715,
131,
138,
5354,
6451,
13335,
2149,
5123,
3457,
1359,
1113,
6777,
1116,
1104,
2000,
117,
107,
146,
8101,
2069,
15586,
6451,
4807,
174,
2101,
4854,
1204,
15041,
117,
10857,
119,
1410,
117,
185,
119,
3882,
1604,
117,
1410,
119,
164,
1572,
166,
141,
2001,
10205,
1200,
117,
107,
9352,
12606,
2913,
5096,
10008,
118,
1104,
118,
1457,
9899,
113,
141,
23329,
1708,
114,
117,
107,
27400,
5480,
1874,
1653,
26311,
117,
1387,
164,
1512,
166,
142,
139,
9827,
1399,
117,
107,
5157,
2692,
7937,
1204,
131,
8377,
143,
14045,
1706,
2879,
3923,
1107,
1103,
4936,
1104,
8093,
7147,
4935,
117,
107,
1446,
5306,
1477
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"\"",
"The",
"quest",
"for",
"s",
"##cal",
"##able",
"block",
"##cha",
"##in",
"fabric",
":",
"Pro",
"##of",
"-",
"of",
"-",
"work",
"vs",
".",
"b",
"##ft",
"replication",
",",
"\"",
"In",
"Proceedings",
"of",
"the",
"IF",
"##IP",
"W",
"##G",
"11",
".",
"4",
"Workshop",
"i",
"##Net",
"##S",
"##ec",
"2015",
".",
"2015",
".",
"[",
"22",
"]",
"Zhang",
"Y",
",",
"Wen",
"J",
".",
"\"",
"An",
"I",
"##o",
"##T",
"electric",
"business",
"model",
"based",
"on",
"the",
"protocol",
"of",
"bit",
"##co",
"##in",
",",
"\"",
"18th",
"International",
"conference",
"on",
"intelligence",
"in",
"next",
"-",
"generation",
"networks",
"(",
"I",
"##CI",
"##N",
")",
";",
"2015",
".",
"p",
".",
"184",
"β",
"91",
".",
"doi",
":",
"http",
":",
"/",
"/",
"d",
"##x",
".",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"I",
"##CI",
"##N",
".",
"2015",
".",
"70",
"##7",
"##38",
"##30",
".",
"[",
"23",
"]",
"S",
".",
"Park",
",",
"K",
".",
"Pie",
"##tr",
"##zak",
",",
"A",
".",
"K",
"##won",
",",
"J",
".",
"Al",
"##wen",
",",
"G",
".",
"Fu",
"##chs",
"##ba",
"##uer",
",",
"and",
"P",
".",
"G",
"##azi",
",",
"\"",
"Space",
"mini",
":",
"A",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"based",
"on",
"proof",
"##s",
"of",
"space",
",",
"\"",
"I",
"##AC",
"##R",
"Cry",
"##pt",
"##ology",
"e",
"##P",
"##rin",
"##t",
"Archive",
",",
"vol",
".",
"2015",
",",
"p",
".",
"52",
"##8",
",",
"2015",
".",
"[",
"24",
"]",
"D",
"La",
"##rim",
"##er",
",",
"\"",
"Del",
"##eg",
"##ated",
"Pro",
"##of",
"-",
"of",
"-",
"St",
"##ake",
"(",
"D",
"##PO",
"##S",
")",
",",
"\"",
"Bit",
"##sha",
"##re",
"white",
"##paper",
",",
"2014",
"[",
"25",
"]",
"E",
"B",
"##uch",
"##man",
",",
"\"",
"Ten",
"##der",
"##min",
"##t",
":",
"Byzantine",
"F",
"##ault",
"To",
"##ler",
"##ance",
"in",
"the",
"Age",
"of",
"Block",
"##cha",
"##ins",
",",
"\"",
"2016",
"96",
"##2"
] | State of the art and challenges facing consensus p | 129 |
Attack Incentive and Security of Exchanging Tokens on Proof-of-Work Blockchain
AUTHORS
ABSTRACT
In a consensus algorithm based on Proof-of-Work, miners are motivated by crypto rewards. Furthermore, security is guaranteed because a cost of a 50% attack chance is higher than the potential rewards. However, because of the sudden price jump of cryptocurrencies and cheap prices of mining machines like ASICs, the cost and profit were on equilibrium for Bitcoin in 2017.
In this situation, attackers are motiv | [
13704,
3561,
3452,
2109,
1105,
4354,
1104,
16409,
23286,
1706,
6378,
1116,
1113,
5096,
10008,
118,
1104,
118,
6955,
8093,
7147,
1394,
21646,
24162,
9565,
1708,
20066,
23313,
8101,
1942,
1130,
170,
10923,
9932,
1359,
1113,
5096,
10008,
118,
1104,
118,
6955,
117,
13418,
1132,
13241,
1118,
5354,
6451,
1186,
22278,
119,
7282,
117,
2699,
1110,
13008,
1272,
170,
2616,
1104,
170,
1851,
110,
2035,
2640,
1110,
2299,
1190,
1103,
3209,
22278,
119,
1438,
117,
1272,
1104,
1103,
4962,
3945,
5152,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
10928,
7352,
1104,
5463,
6555,
1176,
15278,
9741,
1116,
117,
1103,
2616,
1105,
5022,
1127,
1113,
15784,
1111,
27400,
2528,
1394,
1107,
1504,
119,
1130,
1142,
2820,
117,
19450,
1132,
13241,
1118,
1103,
5233,
1206,
1144,
1324,
1540,
1105,
11709,
119,
1130,
1142,
2526,
117,
1195,
5594,
1115,
1175,
1110,
25319,
1206,
5463,
1540,
1113,
1103,
2443,
1105,
3945,
1104,
18290,
5026,
1115,
1169,
1129,
1678,
5343,
1193,
1113,
170,
3510,
7147,
1394,
119,
24222,
1150,
3670,
22559,
1116,
1113,
1103,
18959,
2924,
3510,
7147,
1394,
1431,
8804,
5463,
1540,
1105,
3670,
22559,
1116,
17780,
1190,
1103,
2035,
2616,
1177,
1115,
5022,
1105,
2616,
1104,
1103,
19114,
1132,
1136,
1107,
15784,
119,
21362,
1708,
18732,
15517,
16668,
11365,
4354,
1105,
9909,
117,
12120,
2050,
2047,
24595,
2344,
2699,
117,
20463,
3442,
20941,
117,
6747,
1158,
1105,
14314,
148,
2036,
3663,
2924,
9565,
13675,
8093,
7147,
1394,
117,
5096,
10008,
118,
1104,
118,
6955,
117,
1706,
6378,
3670,
9690,
2107,
15374,
21669,
11414,
131,
15969,
23313,
15609,
21986,
21669,
11414,
27400,
2528,
1394,
1110,
170,
8536,
118,
1106,
118,
8536,
4828,
7727,
1449,
164,
1406,
166,
119,
2994,
14372,
1647,
13618,
2233,
113,
21514,
1116,
114,
1113,
170,
21340,
1197,
7905,
1107,
1172,
1105,
23073,
21514,
1116,
1132,
1136,
21776,
1118,
5991,
15856,
1103,
21340,
1197,
119,
1109,
21340,
1197,
1110,
1270,
789,
8093,
7147,
1394,
790,
1105,
15029,
1294,
10923,
1177,
1115,
1103,
21340,
1197,
1296,
14372,
3486,
7634,
20904,
119,
1706,
1294,
170,
10923,
117,
27400,
2528,
1394,
2745,
5096,
10008,
118,
1104,
118,
6955,
113,
18959,
2924,
114,
1107,
1103,
1532,
1104,
170,
9988,
13544,
1115,
170,
4795,
1169,
9474,
1118,
5369,
19903,
1540,
119,
2279,
170,
14372,
1115,
4090,
1103,
2590,
1169,
1243,
5354,
6451,
13335,
2149,
5123,
9805,
1112,
22278,
117,
1606,
1103,
21927,
1104,
2284,
5463,
117,
1103,
1965,
1104,
15097,
18959,
2924,
1110,
1270,
789,
5463,
119,
790,
1109,
10923,
6978,
1359,
1113,
18959,
2924,
1548,
5343,
4895,
1126,
19114,
6268,
1116,
1166,
1851,
110,
1104,
8178,
19675,
1348,
1540,
1107,
1103,
2443,
119,
5533,
117,
2699,
13008,
1118,
1103,
2616,
1104,
1851,
110,
2035,
1110,
1136,
1107,
15784,
1114,
11709,
119,
1438,
117,
1118,
1103,
4962,
3945,
5152,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
10928,
1193,
1104,
5463,
6555,
1176,
15278,
9741,
1116,
117,
1103,
2616,
1108,
1107,
15784,
1111,
27400,
2528,
1394,
1107,
1504,
119,
1130,
1142,
2820,
117,
1103,
5463,
2616,
1110,
1136,
170,
4267,
10606,
8298,
2109,
1111,
19450,
1272,
1115,
1152,
1169,
1243,
22278,
15122,
1106,
1103,
2616
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
8,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
8,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"Attack",
"Inc",
"##ent",
"##ive",
"and",
"Security",
"of",
"Ex",
"##changing",
"To",
"##ken",
"##s",
"on",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"Block",
"##cha",
"##in",
"AU",
"##TH",
"##OR",
"##S",
"ABS",
"##TR",
"##AC",
"##T",
"In",
"a",
"consensus",
"algorithm",
"based",
"on",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
",",
"miners",
"are",
"motivated",
"by",
"cry",
"##pt",
"##o",
"rewards",
".",
"Furthermore",
",",
"security",
"is",
"guaranteed",
"because",
"a",
"cost",
"of",
"a",
"50",
"%",
"attack",
"chance",
"is",
"higher",
"than",
"the",
"potential",
"rewards",
".",
"However",
",",
"because",
"of",
"the",
"sudden",
"price",
"jump",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"cheap",
"prices",
"of",
"mining",
"machines",
"like",
"AS",
"##IC",
"##s",
",",
"the",
"cost",
"and",
"profit",
"were",
"on",
"equilibrium",
"for",
"Bit",
"##co",
"##in",
"in",
"2017",
".",
"In",
"this",
"situation",
",",
"attackers",
"are",
"motivated",
"by",
"the",
"balance",
"between",
"has",
"##h",
"power",
"and",
"profits",
".",
"In",
"this",
"paper",
",",
"we",
"describe",
"that",
"there",
"is",
"relevance",
"between",
"mining",
"power",
"on",
"the",
"network",
"and",
"price",
"of",
"##tok",
"##ens",
"that",
"can",
"be",
"taken",
"secure",
"##ly",
"on",
"a",
"block",
"##cha",
"##in",
".",
"Users",
"who",
"exchange",
"token",
"##s",
"on",
"the",
"Po",
"##W",
"block",
"##cha",
"##in",
"should",
"monitor",
"mining",
"power",
"and",
"exchange",
"token",
"##s",
"cheaper",
"than",
"the",
"attack",
"cost",
"so",
"that",
"profit",
"and",
"cost",
"of",
"the",
"attacker",
"are",
"not",
"in",
"equilibrium",
".",
"CC",
"##S",
"CO",
"##NC",
"##EP",
"##TS",
"Security",
"and",
"privacy",
",",
"Di",
"##st",
"##ri",
"##buted",
"systems",
"security",
",",
"Computing",
"method",
"##ologies",
",",
"Model",
"##ing",
"and",
"simulation",
"K",
"##E",
"##Y",
"##W",
"##OR",
"##DS",
"Block",
"##cha",
"##in",
",",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
",",
"To",
"##ken",
"exchange",
"AC",
"##M",
"SEC",
"##TI",
"##ON",
":",
"IN",
"##TR",
"##OD",
"##UC",
"##TI",
"##ON",
"Bit",
"##co",
"##in",
"is",
"a",
"peer",
"-",
"to",
"-",
"peer",
"electronic",
"payment",
"system",
"[",
"20",
"]",
".",
"Each",
"node",
"record",
"transaction",
"data",
"(",
"TX",
"##s",
")",
"on",
"a",
"ledge",
"##r",
"stored",
"in",
"them",
"and",
"verify",
"TX",
"##s",
"are",
"not",
"conflicting",
"by",
"refer",
"##encing",
"the",
"ledge",
"##r",
".",
"The",
"ledge",
"##r",
"is",
"called",
"β",
"Block",
"##cha",
"##in",
"β",
"and",
"nodes",
"make",
"consensus",
"so",
"that",
"the",
"ledge",
"##r",
"each",
"node",
"holds",
"keeps",
"consistency",
".",
"To",
"make",
"a",
"consensus",
",",
"Bit",
"##co",
"##in",
"uses",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"(",
"Po",
"##W",
")",
"in",
"the",
"form",
"of",
"a",
"mathematical",
"puzzle",
"that",
"a",
"user",
"can",
"solve",
"by",
"spending",
"computational",
"power",
".",
"Because",
"a",
"node",
"that",
"finds",
"the",
"answer",
"can",
"get",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"as",
"rewards",
",",
"using",
"the",
"metaphor",
"of",
"gold",
"mining",
",",
"the",
"process",
"of",
"solving",
"Po",
"##W",
"is",
"called",
"β",
"mining",
".",
"β",
"The",
"consensus",
"mechanism",
"based",
"on",
"Po",
"##W",
"##is",
"secure",
"unless",
"an",
"attacker",
"obtain",
"##s",
"over",
"50",
"%",
"of",
"##com",
"##putation",
"##al",
"power",
"in",
"the",
"network",
".",
"Additionally",
",",
"security",
"guaranteed",
"by",
"the",
"cost",
"of",
"50",
"%",
"attack",
"is",
"not",
"in",
"equilibrium",
"with",
"profits",
".",
"However",
",",
"by",
"the",
"sudden",
"price",
"jump",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"cheap",
"##ly",
"of",
"mining",
"machines",
"like",
"AS",
"##IC",
"##s",
",",
"the",
"cost",
"was",
"in",
"equilibrium",
"for",
"Bit",
"##co",
"##in",
"in",
"2017",
".",
"In",
"this",
"situation",
",",
"the",
"mining",
"cost",
"is",
"not",
"a",
"di",
"##sin",
"##cent",
"##ive",
"for",
"attackers",
"because",
"that",
"they",
"can",
"get",
"rewards",
"proportional",
"to",
"the",
"cost"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 130 |
ated by the balance between hash power and profits. In this paper, we describe that there is relevance between mining power on the network and price oftokens that can be taken securely on a blockchain. Users who exchange tokens on the PoW blockchain should monitor mining power and exchange tokens cheaper than the attack cost so that profit and cost of the attacker are not in equilibrium.
CCS CONCEPTS
Security and privacy, Distributed systems security, Computing methodologies, Modeling and simulation
KE | [
1104,
1103,
2035,
119,
1130,
170,
1851,
110,
2035,
117,
1103,
19114,
1169,
1243,
5354,
6451,
13335,
2149,
5123,
3457,
1112,
1103,
10703,
1105,
5022,
1104,
2035,
1105,
1169,
10301,
1103,
2616,
1121,
1103,
2443,
787,
188,
1144,
1324,
1540,
119,
1130,
27400,
2528,
1394,
117,
1191,
170,
1851,
110,
2035,
1110,
11168,
117,
1103,
3945,
1104,
2064,
2875,
2528,
4935,
1209,
2303,
1177,
1122,
3411,
1112,
170,
4267,
10606,
8298,
2109,
1111,
19450,
119,
1130,
142,
8420,
14136,
164,
1765,
166,
117,
1103,
3945,
1104,
22559,
1116,
113,
174,
119,
176,
119,
117,
4508,
1758,
1118,
23580,
1658,
118,
1406,
164,
1367,
166,
114,
1110,
2121,
1136,
4634,
1118,
2443,
2699,
119,
6589,
117,
19450,
1132,
13241,
1118,
1103,
5233,
1206,
1144,
1324,
1540,
1105,
11709,
119,
1284,
1758,
1115,
1175,
1110,
7503,
1206,
5463,
1540,
1113,
1103,
2443,
1105,
3945,
1104,
22559,
1116,
1115,
170,
4795,
1169,
1321,
1113,
170,
3510,
7147,
1394,
119,
24222,
1150,
3670,
22559,
1116,
1113,
1103,
18959,
2924,
3510,
7147,
1394,
1431,
8804,
5463,
1540,
1105,
3670,
22559,
1116,
17780,
1190,
2035,
2616,
1177,
1115,
11709,
1105,
4692,
1104,
1103,
19114,
1110,
1136,
15784,
119,
15374,
21669,
11414,
131,
139,
2162,
9244,
2428,
23258,
1592,
11607,
8093,
7147,
1394,
1110,
170,
1449,
1107,
1134,
1296,
14372,
7634,
1126,
12647,
6696,
118,
1178,
21340,
1197,
117,
1105,
1118,
1103,
12647,
16264,
3013,
1103,
21340,
1197,
7634,
20904,
1256,
1463,
1296,
14372,
5049,
8942,
119,
143,
2346,
14697,
2249,
14697,
2036,
131,
1130,
1142,
2526,
117,
8093,
7147,
1394,
2086,
1103,
1449,
117,
170,
3510,
7147,
1394,
2086,
1103,
21340,
1197,
1115,
1296,
14372,
7634,
119,
1130,
27400,
2528,
1394,
117,
1296,
14372,
1169,
23073,
14409,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
1118,
7455,
1106,
170,
3510,
7147,
1394,
1115,
1110,
7905,
6889,
119,
13615,
117,
15029,
1169,
11552,
789,
2702,
118,
5369,
790,
1107,
1134,
1126,
19114,
15539,
1103,
1269,
5354,
6451,
13335,
2149,
5123,
3457,
1106,
1472,
4713,
119,
2994,
14372,
4822,
170,
1383,
1104,
22480,
14409,
1112,
789,
8093,
790,
1107,
170,
3510,
7147,
1394,
119,
138,
3510,
2075,
1103,
5354,
6451,
9597,
1144,
1324,
1295,
1104,
1103,
1314,
1141,
1107,
1103,
3510,
7147,
1394,
119,
1650,
1142,
2401,
117,
1191,
1126,
19114,
1231,
2246,
23202,
170,
2166,
13618,
117,
1103,
1144,
1324,
1295,
1104,
170,
3510,
1115,
2075,
1122,
1110,
2014,
117,
1105,
1103,
1144,
1324,
1104,
1103,
1397,
1141,
1110,
2014,
1315,
119,
13615,
117,
1126,
19114,
2993,
1106,
11984,
1155,
5511,
2547,
1121,
1103,
1231,
16674,
1141,
1106,
1103,
1314,
1141,
119,
1706,
1712,
20904,
1105,
7262,
1104,
1231,
17729,
117,
3510,
11166,
2993,
1106,
9474,
170,
9988,
13544,
1270,
789,
5096,
10008,
118,
1104,
118,
6955,
113,
18959,
2924,
114,
790,
1105,
1511,
1103,
2590,
1107,
1103,
1207,
3510,
119,
18959,
2924,
1144,
1103,
5924,
1115,
15097,
2993,
1277,
19903,
1540,
1133,
23073,
1158,
1103,
2590,
1110,
3014,
119,
1409,
1199,
3510,
11166,
2228,
5511,
1115,
1511,
21776,
14409,
1118,
1231,
17729,
1103,
1763,
117,
15029,
11552,
1103,
4139,
1112,
170,
789,
13097,
790,
119,
1332,
170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"of",
"the",
"attack",
".",
"In",
"a",
"50",
"%",
"attack",
",",
"the",
"attacker",
"can",
"get",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"as",
"the",
"reward",
"and",
"profit",
"of",
"attack",
"and",
"can",
"estimate",
"the",
"cost",
"from",
"the",
"network",
"β",
"s",
"has",
"##h",
"power",
".",
"In",
"Bit",
"##co",
"##in",
",",
"if",
"a",
"50",
"%",
"attack",
"is",
"detected",
",",
"the",
"price",
"of",
"##B",
"##it",
"##co",
"##ins",
"will",
"fall",
"so",
"it",
"serves",
"as",
"a",
"di",
"##sin",
"##cent",
"##ive",
"for",
"attackers",
".",
"In",
"E",
"##ther",
"##eum",
"[",
"27",
"]",
",",
"the",
"price",
"of",
"token",
"##s",
"(",
"e",
".",
"g",
".",
",",
"lands",
"described",
"by",
"ER",
"##C",
"-",
"20",
"[",
"12",
"]",
")",
"is",
"sometimes",
"not",
"affected",
"by",
"network",
"security",
".",
"Therefore",
",",
"attackers",
"are",
"motivated",
"by",
"the",
"balance",
"between",
"has",
"##h",
"power",
"and",
"profits",
".",
"We",
"described",
"that",
"there",
"is",
"relevant",
"between",
"mining",
"power",
"on",
"the",
"network",
"and",
"price",
"of",
"token",
"##s",
"that",
"a",
"user",
"can",
"take",
"on",
"a",
"block",
"##cha",
"##in",
".",
"Users",
"who",
"exchange",
"token",
"##s",
"on",
"the",
"Po",
"##W",
"block",
"##cha",
"##in",
"should",
"monitor",
"mining",
"power",
"and",
"exchange",
"token",
"##s",
"cheaper",
"than",
"attack",
"cost",
"so",
"that",
"profits",
"and",
"costs",
"of",
"the",
"attacker",
"is",
"not",
"equilibrium",
".",
"SEC",
"##TI",
"##ON",
":",
"B",
"##L",
"##OC",
"##K",
"##CH",
"##A",
"##IN",
"Block",
"##cha",
"##in",
"is",
"a",
"system",
"in",
"which",
"each",
"node",
"keeps",
"an",
"app",
"##end",
"-",
"only",
"ledge",
"##r",
",",
"and",
"by",
"the",
"app",
"##ending",
"rule",
"the",
"ledge",
"##r",
"keeps",
"consistency",
"even",
"though",
"each",
"node",
"operates",
"independently",
".",
"F",
"##O",
"##OT",
"##N",
"##OT",
"##E",
":",
"In",
"this",
"paper",
",",
"Block",
"##cha",
"##in",
"means",
"the",
"system",
",",
"a",
"block",
"##cha",
"##in",
"means",
"the",
"ledge",
"##r",
"that",
"each",
"node",
"keeps",
".",
"In",
"Bit",
"##co",
"##in",
",",
"each",
"node",
"can",
"verify",
"transactions",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"by",
"referring",
"to",
"a",
"block",
"##cha",
"##in",
"that",
"is",
"stored",
"locally",
".",
"Hence",
",",
"nodes",
"can",
"detect",
"β",
"double",
"-",
"spending",
"β",
"in",
"which",
"an",
"attacker",
"pays",
"the",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"to",
"different",
"users",
".",
"Each",
"node",
"stores",
"a",
"set",
"of",
"verified",
"transactions",
"as",
"β",
"Block",
"β",
"in",
"a",
"block",
"##cha",
"##in",
".",
"A",
"block",
"includes",
"the",
"cry",
"##pt",
"##ographic",
"has",
"##h",
"number",
"of",
"the",
"last",
"one",
"in",
"the",
"block",
"##cha",
"##in",
".",
"By",
"this",
"structure",
",",
"if",
"an",
"attacker",
"re",
"##w",
"##rites",
"a",
"previous",
"transaction",
",",
"the",
"has",
"##h",
"number",
"of",
"a",
"block",
"that",
"includes",
"it",
"is",
"changed",
",",
"and",
"the",
"has",
"##h",
"of",
"the",
"next",
"one",
"is",
"changed",
"too",
".",
"Hence",
",",
"an",
"attacker",
"needs",
"to",
"update",
"all",
"blocks",
"starting",
"from",
"the",
"re",
"##written",
"one",
"to",
"the",
"last",
"one",
".",
"To",
"keep",
"consistency",
"and",
"difficulty",
"of",
"re",
"##writing",
",",
"block",
"maker",
"needs",
"to",
"solve",
"a",
"mathematical",
"puzzle",
"called",
"β",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"(",
"Po",
"##W",
")",
"β",
"and",
"include",
"the",
"answer",
"in",
"the",
"new",
"block",
".",
"Po",
"##W",
"has",
"the",
"characteristics",
"that",
"solving",
"needs",
"much",
"computational",
"power",
"but",
"verify",
"##ing",
"the",
"answer",
"is",
"simple",
".",
"If",
"some",
"block",
"maker",
"makes",
"blocks",
"that",
"include",
"conflicting",
"transactions",
"by",
"re",
"##writing",
"the",
"past",
",",
"nodes",
"detect",
"the",
"conflict",
"as",
"a",
"β",
"fork",
"β",
".",
"When",
"a"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 131 |
ated by the balance between hash power and profits. In this paper, we describe that there is relevance between mining power on the network and price oftokens that can be taken securely on a blockchain. Users who exchange tokens on the PoW blockchain should monitor mining power and exchange tokens cheaper than the attack cost so that profit and cost of the attacker are not in equilibrium.
CCS CONCEPTS
Security and privacy, Distributed systems security, Computing methodologies, Modeling and simulation
KE | [
1104,
1103,
2035,
119,
1130,
170,
1851,
110,
2035,
117,
1103,
19114,
1169,
1243,
5354,
6451,
13335,
2149,
5123,
3457,
1112,
1103,
10703,
1105,
5022,
1104,
2035,
1105,
1169,
10301,
1103,
2616,
1121,
1103,
2443,
787,
188,
1144,
1324,
1540,
119,
1130,
27400,
2528,
1394,
117,
1191,
170,
1851,
110,
2035,
1110,
11168,
117,
1103,
3945,
1104,
2064,
2875,
2528,
4935,
1209,
2303,
1177,
1122,
3411,
1112,
170,
4267,
10606,
8298,
2109,
1111,
19450,
119,
1130,
142,
8420,
14136,
164,
1765,
166,
117,
1103,
3945,
1104,
22559,
1116,
113,
174,
119,
176,
119,
117,
4508,
1758,
1118,
23580,
1658,
118,
1406,
164,
1367,
166,
114,
1110,
2121,
1136,
4634,
1118,
2443,
2699,
119,
6589,
117,
19450,
1132,
13241,
1118,
1103,
5233,
1206,
1144,
1324,
1540,
1105,
11709,
119,
1284,
1758,
1115,
1175,
1110,
7503,
1206,
5463,
1540,
1113,
1103,
2443,
1105,
3945,
1104,
22559,
1116,
1115,
170,
4795,
1169,
1321,
1113,
170,
3510,
7147,
1394,
119,
24222,
1150,
3670,
22559,
1116,
1113,
1103,
18959,
2924,
3510,
7147,
1394,
1431,
8804,
5463,
1540,
1105,
3670,
22559,
1116,
17780,
1190,
2035,
2616,
1177,
1115,
11709,
1105,
4692,
1104,
1103,
19114,
1110,
1136,
15784,
119,
15374,
21669,
11414,
131,
139,
2162,
9244,
2428,
23258,
1592,
11607,
8093,
7147,
1394,
1110,
170,
1449,
1107,
1134,
1296,
14372,
7634,
1126,
12647,
6696,
118,
1178,
21340,
1197,
117,
1105,
1118,
1103,
12647,
16264,
3013,
1103,
21340,
1197,
7634,
20904,
1256,
1463,
1296,
14372,
5049,
8942,
119,
143,
2346,
14697,
2249,
14697,
2036,
131,
1130,
1142,
2526,
117,
8093,
7147,
1394,
2086,
1103,
1449,
117,
170,
3510,
7147,
1394,
2086,
1103,
21340,
1197,
1115,
1296,
14372,
7634,
119,
1130,
27400,
2528,
1394,
117,
1296,
14372,
1169,
23073,
14409,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
1118,
7455,
1106,
170,
3510,
7147,
1394,
1115,
1110,
7905,
6889,
119,
13615,
117,
15029,
1169,
11552,
789,
2702,
118,
5369,
790,
1107,
1134,
1126,
19114,
15539,
1103,
1269,
5354,
6451,
13335,
2149,
5123,
3457,
1106,
1472,
4713,
119,
2994,
14372,
4822,
170,
1383,
1104,
22480,
14409,
1112,
789,
8093,
790,
1107,
170,
3510,
7147,
1394,
119,
138,
3510,
2075,
1103,
5354,
6451,
9597,
1144,
1324,
1295,
1104,
1103,
1314,
1141,
1107,
1103,
3510,
7147,
1394,
119,
1650,
1142,
2401,
117,
1191,
1126,
19114,
1231,
2246,
23202,
170,
2166,
13618,
117,
1103,
1144,
1324,
1295,
1104,
170,
3510,
1115,
2075,
1122,
1110,
2014,
117,
1105,
1103,
1144,
1324,
1104,
1103,
1397,
1141,
1110,
2014,
1315,
119,
13615,
117,
1126,
19114,
2993,
1106,
11984,
1155,
5511,
2547,
1121,
1103,
1231,
16674,
1141,
1106,
1103,
1314,
1141,
119,
1706,
1712,
20904,
1105,
7262,
1104,
1231,
17729,
117,
3510,
11166,
2993,
1106,
9474,
170,
9988,
13544,
1270,
789,
5096,
10008,
118,
1104,
118,
6955,
113,
18959,
2924,
114,
790,
1105,
1511,
1103,
2590,
1107,
1103,
1207,
3510,
119,
18959,
2924,
1144,
1103,
5924,
1115,
15097,
2993,
1277,
19903,
1540,
1133,
23073,
1158,
1103,
2590,
1110,
3014,
119,
1409,
1199,
3510,
11166,
2228,
5511,
1115,
1511,
21776,
14409,
1118,
1231,
17729,
1103,
1763,
117,
15029,
11552,
1103,
4139,
1112,
170,
789,
13097,
790,
119,
1332,
170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"of",
"the",
"attack",
".",
"In",
"a",
"50",
"%",
"attack",
",",
"the",
"attacker",
"can",
"get",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"as",
"the",
"reward",
"and",
"profit",
"of",
"attack",
"and",
"can",
"estimate",
"the",
"cost",
"from",
"the",
"network",
"β",
"s",
"has",
"##h",
"power",
".",
"In",
"Bit",
"##co",
"##in",
",",
"if",
"a",
"50",
"%",
"attack",
"is",
"detected",
",",
"the",
"price",
"of",
"##B",
"##it",
"##co",
"##ins",
"will",
"fall",
"so",
"it",
"serves",
"as",
"a",
"di",
"##sin",
"##cent",
"##ive",
"for",
"attackers",
".",
"In",
"E",
"##ther",
"##eum",
"[",
"27",
"]",
",",
"the",
"price",
"of",
"token",
"##s",
"(",
"e",
".",
"g",
".",
",",
"lands",
"described",
"by",
"ER",
"##C",
"-",
"20",
"[",
"12",
"]",
")",
"is",
"sometimes",
"not",
"affected",
"by",
"network",
"security",
".",
"Therefore",
",",
"attackers",
"are",
"motivated",
"by",
"the",
"balance",
"between",
"has",
"##h",
"power",
"and",
"profits",
".",
"We",
"described",
"that",
"there",
"is",
"relevant",
"between",
"mining",
"power",
"on",
"the",
"network",
"and",
"price",
"of",
"token",
"##s",
"that",
"a",
"user",
"can",
"take",
"on",
"a",
"block",
"##cha",
"##in",
".",
"Users",
"who",
"exchange",
"token",
"##s",
"on",
"the",
"Po",
"##W",
"block",
"##cha",
"##in",
"should",
"monitor",
"mining",
"power",
"and",
"exchange",
"token",
"##s",
"cheaper",
"than",
"attack",
"cost",
"so",
"that",
"profits",
"and",
"costs",
"of",
"the",
"attacker",
"is",
"not",
"equilibrium",
".",
"SEC",
"##TI",
"##ON",
":",
"B",
"##L",
"##OC",
"##K",
"##CH",
"##A",
"##IN",
"Block",
"##cha",
"##in",
"is",
"a",
"system",
"in",
"which",
"each",
"node",
"keeps",
"an",
"app",
"##end",
"-",
"only",
"ledge",
"##r",
",",
"and",
"by",
"the",
"app",
"##ending",
"rule",
"the",
"ledge",
"##r",
"keeps",
"consistency",
"even",
"though",
"each",
"node",
"operates",
"independently",
".",
"F",
"##O",
"##OT",
"##N",
"##OT",
"##E",
":",
"In",
"this",
"paper",
",",
"Block",
"##cha",
"##in",
"means",
"the",
"system",
",",
"a",
"block",
"##cha",
"##in",
"means",
"the",
"ledge",
"##r",
"that",
"each",
"node",
"keeps",
".",
"In",
"Bit",
"##co",
"##in",
",",
"each",
"node",
"can",
"verify",
"transactions",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"by",
"referring",
"to",
"a",
"block",
"##cha",
"##in",
"that",
"is",
"stored",
"locally",
".",
"Hence",
",",
"nodes",
"can",
"detect",
"β",
"double",
"-",
"spending",
"β",
"in",
"which",
"an",
"attacker",
"pays",
"the",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"to",
"different",
"users",
".",
"Each",
"node",
"stores",
"a",
"set",
"of",
"verified",
"transactions",
"as",
"β",
"Block",
"β",
"in",
"a",
"block",
"##cha",
"##in",
".",
"A",
"block",
"includes",
"the",
"cry",
"##pt",
"##ographic",
"has",
"##h",
"number",
"of",
"the",
"last",
"one",
"in",
"the",
"block",
"##cha",
"##in",
".",
"By",
"this",
"structure",
",",
"if",
"an",
"attacker",
"re",
"##w",
"##rites",
"a",
"previous",
"transaction",
",",
"the",
"has",
"##h",
"number",
"of",
"a",
"block",
"that",
"includes",
"it",
"is",
"changed",
",",
"and",
"the",
"has",
"##h",
"of",
"the",
"next",
"one",
"is",
"changed",
"too",
".",
"Hence",
",",
"an",
"attacker",
"needs",
"to",
"update",
"all",
"blocks",
"starting",
"from",
"the",
"re",
"##written",
"one",
"to",
"the",
"last",
"one",
".",
"To",
"keep",
"consistency",
"and",
"difficulty",
"of",
"re",
"##writing",
",",
"block",
"maker",
"needs",
"to",
"solve",
"a",
"mathematical",
"puzzle",
"called",
"β",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"(",
"Po",
"##W",
")",
"β",
"and",
"include",
"the",
"answer",
"in",
"the",
"new",
"block",
".",
"Po",
"##W",
"has",
"the",
"characteristics",
"that",
"solving",
"needs",
"much",
"computational",
"power",
"but",
"verify",
"##ing",
"the",
"answer",
"is",
"simple",
".",
"If",
"some",
"block",
"maker",
"makes",
"blocks",
"that",
"include",
"conflicting",
"transactions",
"by",
"re",
"##writing",
"the",
"past",
",",
"nodes",
"detect",
"the",
"conflict",
"as",
"a",
"β",
"fork",
"β",
".",
"When",
"a"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 132 |
YWORDS
Blockchain, Proof-of-Work, Token exchange ACM
SECTION: INTRODUCTION
Bitcoin is a peer-to-peer electronic payment system [20]. Each node record transaction data (TXs) on a ledger stored in them and verify TXs are not conflicting by referencing the ledger. The ledger is called βBlockchainβ and nodes make consensus so that the ledger each node holds keeps consistency.
To make a consensus, Bitcoin uses Proof-of-Work (PoW) in the form of a mathematical puzzle that a user can solve by spending comput | [
13097,
5940,
117,
1296,
14372,
12747,
1103,
4129,
1515,
1103,
2439,
7584,
1104,
1103,
18959,
2924,
6615,
7262,
1112,
5663,
119,
13615,
117,
1296,
14372,
7634,
1103,
3510,
7147,
1394,
1115,
2097,
1103,
2026,
19903,
1540,
1107,
1103,
2443,
119,
5533,
117,
1165,
1126,
19114,
1231,
2246,
23202,
170,
2166,
13618,
1105,
4642,
1106,
13226,
5511,
1235,
1103,
1314,
1141,
117,
1120,
1103,
1269,
1159,
7345,
15029,
1132,
1543,
1207,
5511,
1115,
7543,
1103,
1314,
1141,
119,
13615,
117,
7345,
15029,
3417,
4835,
5511,
1115,
1127,
1189,
1118,
7345,
13418,
119,
1706,
9381,
1107,
1126,
2035,
117,
19450,
1444,
1106,
1294,
5511,
1103,
7901,
1107,
1103,
2443,
1118,
5369,
19903,
1540,
2610,
1190,
7345,
3200,
119,
1130,
1168,
1734,
117,
1103,
19114,
2993,
1166,
1851,
110,
1104,
19903,
1540,
1107,
1103,
2443,
1111,
1612,
1106,
9381,
119,
1109,
2035,
1104,
2033,
1167,
1190,
1851,
110,
19903,
1540,
1110,
1270,
1103,
789,
1851,
110,
2035,
119,
790,
1109,
13457,
1115,
170,
3510,
7147,
1394,
1110,
5343,
1272,
2702,
118,
5369,
1118,
1231,
17729,
1674,
1136,
3333,
1110,
13008,
1118,
1103,
7262,
1104,
2033,
1851,
110,
19903,
1540,
1105,
1103,
3719,
1206,
1103,
2035,
2616,
1105,
1103,
5022,
119,
1706,
182,
3329,
18851,
15029,
1106,
1294,
5511,
117,
1103,
1449,
22278,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
1106,
1103,
11166,
1150,
24219,
1107,
1543,
170,
3510,
119,
1130,
27400,
2528,
1394,
117,
1103,
1449,
3643,
3510,
11166,
1106,
22884,
170,
789,
9584,
14017,
13618,
790,
1115,
15539,
11166,
1199,
2113,
2528,
4935,
1107,
1103,
3510,
119,
1188,
6978,
2736,
1176,
5463,
2284,
1118,
5369,
4692,
117,
1177,
1543,
170,
3510,
1118,
15097,
18959,
2924,
1110,
1270,
789,
5463,
790,
117,
1105,
3510,
11166,
1110,
1270,
789,
2317,
1197,
119,
790,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
16972,
22441,
2249,
142,
3190,
23258,
14962,
16523,
21748,
139,
2162,
9244,
2428,
23258,
1592,
11607,
3743,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
117,
1247,
1132,
1317,
10698,
1115,
5494,
1103,
2266,
1104,
22559,
1116,
1654,
113,
174,
119,
176,
119,
117,
170,
2952,
13274,
1176,
4508,
117,
3539,
1141,
164,
1492,
117,
1542,
117,
1572,
166,
114,
1113,
8093,
7147,
1394,
119,
142,
8420,
14136,
164,
1765,
166,
1110,
1141,
1104,
1788,
23019,
8093,
7147,
1394,
1115,
4795,
1169,
9410,
22559,
1118,
1560,
3483,
1176,
20375,
1785,
164,
130,
166,
119,
1706,
1576,
170,
1788,
1113,
142,
1582,
1874,
1818,
117,
170,
4795,
2228,
170,
13618,
1511,
1103,
1788,
117,
1105,
1103,
2443,
5669,
1122,
1165,
1296,
14372,
22884,
1116,
3510,
2075,
1103,
13618,
1154,
170,
3510,
7147,
1394,
119,
21076,
3483,
1113,
142,
8420,
14136,
1132,
14283,
1403,
118,
2335,
1177,
1115,
170,
4795,
1169,
3593,
1126,
13157,
7812,
1105,
1177,
1113,
119,
1706,
3843,
1142,
117,
1119,
2993,
1106,
2653,
5354,
6451,
13335,
2149,
5123,
9805,
117,
142,
8420,
117,
2452,
1106,
170,
1295,
1104,
1103,
1788,
1965,
2585,
119,
1409,
1119,
6474,
1126,
13157,
7812,
117,
1119,
2993,
1106,
2653,
13157,
5354,
6451,
13335,
2149,
5123,
9805,
1106,
1576,
1122,
119,
1124,
1169,
1243,
142,
8420,
1116,
1118
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0
] | [
"fork",
"happens",
",",
"each",
"node",
"regards",
"the",
"chain",
"having",
"the",
"highest",
"sum",
"of",
"the",
"Po",
"##W",
"answers",
"difficulty",
"as",
"correct",
".",
"Hence",
",",
"each",
"node",
"keeps",
"the",
"block",
"##cha",
"##in",
"that",
"spent",
"the",
"largest",
"computational",
"power",
"in",
"the",
"network",
".",
"Additionally",
",",
"when",
"an",
"attacker",
"re",
"##w",
"##rites",
"a",
"previous",
"transaction",
"and",
"tries",
"to",
"remake",
"blocks",
"until",
"the",
"last",
"one",
",",
"at",
"the",
"same",
"time",
"honest",
"nodes",
"are",
"making",
"new",
"blocks",
"that",
"connect",
"the",
"last",
"one",
".",
"Hence",
",",
"honest",
"nodes",
"typically",
"choose",
"blocks",
"that",
"were",
"made",
"by",
"honest",
"miners",
".",
"To",
"succeed",
"in",
"an",
"attack",
",",
"attackers",
"need",
"to",
"make",
"blocks",
"the",
"fastest",
"in",
"the",
"network",
"by",
"spending",
"computational",
"power",
"larger",
"than",
"honest",
"ones",
".",
"In",
"other",
"words",
",",
"the",
"attacker",
"needs",
"over",
"50",
"%",
"of",
"computational",
"power",
"in",
"the",
"network",
"for",
"sure",
"to",
"succeed",
".",
"The",
"attack",
"of",
"getting",
"more",
"than",
"50",
"%",
"computational",
"power",
"is",
"called",
"the",
"β",
"50",
"%",
"attack",
".",
"β",
"The",
"assumption",
"that",
"a",
"block",
"##cha",
"##in",
"is",
"secure",
"because",
"double",
"-",
"spending",
"by",
"re",
"##writing",
"does",
"not",
"happen",
"is",
"guaranteed",
"by",
"the",
"difficulty",
"of",
"getting",
"50",
"%",
"computational",
"power",
"and",
"the",
"difference",
"between",
"the",
"attack",
"cost",
"and",
"the",
"profit",
".",
"To",
"m",
"##ot",
"##ivate",
"nodes",
"to",
"make",
"blocks",
",",
"the",
"system",
"rewards",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"to",
"the",
"maker",
"who",
"succeeds",
"in",
"making",
"a",
"block",
".",
"In",
"Bit",
"##co",
"##in",
",",
"the",
"system",
"allows",
"block",
"maker",
"to",
"insert",
"a",
"β",
"coin",
"##base",
"transaction",
"β",
"that",
"pays",
"maker",
"some",
"bit",
"##co",
"##ins",
"in",
"the",
"block",
".",
"This",
"mechanism",
"looks",
"like",
"mining",
"gold",
"by",
"spending",
"costs",
",",
"so",
"making",
"a",
"block",
"by",
"solving",
"Po",
"##W",
"is",
"called",
"β",
"mining",
"β",
",",
"and",
"block",
"maker",
"is",
"called",
"β",
"mine",
"##r",
".",
"β",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"TO",
"##KE",
"##N",
"E",
"##X",
"##CH",
"##AN",
"##GE",
"ON",
"B",
"##L",
"##OC",
"##K",
"##CH",
"##A",
"##IN",
"Instead",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"There",
"are",
"several",
"proposals",
"that",
"manage",
"the",
"rights",
"of",
"token",
"##s",
"control",
"(",
"e",
".",
"g",
".",
",",
"a",
"physical",
"asset",
"like",
"lands",
",",
"digital",
"one",
"[",
"13",
",",
"17",
",",
"24",
"]",
")",
"on",
"Block",
"##cha",
"##in",
".",
"E",
"##ther",
"##eum",
"[",
"27",
"]",
"is",
"one",
"of",
"program",
"##mable",
"Block",
"##cha",
"##in",
"that",
"user",
"can",
"define",
"token",
"by",
"original",
"languages",
"like",
"Solid",
"##ity",
"[",
"9",
"]",
".",
"To",
"run",
"a",
"program",
"on",
"E",
"##th",
"##re",
"##um",
",",
"a",
"user",
"makes",
"a",
"transaction",
"include",
"the",
"program",
",",
"and",
"the",
"network",
"processes",
"it",
"when",
"each",
"node",
"insert",
"##s",
"block",
"includes",
"the",
"transaction",
"into",
"a",
"block",
"##cha",
"##in",
".",
"Programming",
"languages",
"on",
"E",
"##ther",
"##eum",
"are",
"Turin",
"##g",
"-",
"complete",
"so",
"that",
"a",
"user",
"can",
"write",
"an",
"infinite",
"loop",
"and",
"so",
"on",
".",
"To",
"prevent",
"this",
",",
"he",
"needs",
"to",
"pay",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"E",
"##ther",
",",
"according",
"to",
"a",
"number",
"of",
"the",
"program",
"process",
"step",
".",
"If",
"he",
"writes",
"an",
"infinite",
"loop",
",",
"he",
"needs",
"to",
"pay",
"infinite",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"to",
"run",
"it",
".",
"He",
"can",
"get",
"E",
"##ther",
"##s",
"by"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 133 |
YWORDS
Blockchain, Proof-of-Work, Token exchange ACM
SECTION: INTRODUCTION
Bitcoin is a peer-to-peer electronic payment system [20]. Each node record transaction data (TXs) on a ledger stored in them and verify TXs are not conflicting by referencing the ledger. The ledger is called βBlockchainβ and nodes make consensus so that the ledger each node holds keeps consistency.
To make a consensus, Bitcoin uses Proof-of-Work (PoW) in the form of a mathematical puzzle that a user can solve by spending comput | [
13097,
5940,
117,
1296,
14372,
12747,
1103,
4129,
1515,
1103,
2439,
7584,
1104,
1103,
18959,
2924,
6615,
7262,
1112,
5663,
119,
13615,
117,
1296,
14372,
7634,
1103,
3510,
7147,
1394,
1115,
2097,
1103,
2026,
19903,
1540,
1107,
1103,
2443,
119,
5533,
117,
1165,
1126,
19114,
1231,
2246,
23202,
170,
2166,
13618,
1105,
4642,
1106,
13226,
5511,
1235,
1103,
1314,
1141,
117,
1120,
1103,
1269,
1159,
7345,
15029,
1132,
1543,
1207,
5511,
1115,
7543,
1103,
1314,
1141,
119,
13615,
117,
7345,
15029,
3417,
4835,
5511,
1115,
1127,
1189,
1118,
7345,
13418,
119,
1706,
9381,
1107,
1126,
2035,
117,
19450,
1444,
1106,
1294,
5511,
1103,
7901,
1107,
1103,
2443,
1118,
5369,
19903,
1540,
2610,
1190,
7345,
3200,
119,
1130,
1168,
1734,
117,
1103,
19114,
2993,
1166,
1851,
110,
1104,
19903,
1540,
1107,
1103,
2443,
1111,
1612,
1106,
9381,
119,
1109,
2035,
1104,
2033,
1167,
1190,
1851,
110,
19903,
1540,
1110,
1270,
1103,
789,
1851,
110,
2035,
119,
790,
1109,
13457,
1115,
170,
3510,
7147,
1394,
1110,
5343,
1272,
2702,
118,
5369,
1118,
1231,
17729,
1674,
1136,
3333,
1110,
13008,
1118,
1103,
7262,
1104,
2033,
1851,
110,
19903,
1540,
1105,
1103,
3719,
1206,
1103,
2035,
2616,
1105,
1103,
5022,
119,
1706,
182,
3329,
18851,
15029,
1106,
1294,
5511,
117,
1103,
1449,
22278,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
1106,
1103,
11166,
1150,
24219,
1107,
1543,
170,
3510,
119,
1130,
27400,
2528,
1394,
117,
1103,
1449,
3643,
3510,
11166,
1106,
22884,
170,
789,
9584,
14017,
13618,
790,
1115,
15539,
11166,
1199,
2113,
2528,
4935,
1107,
1103,
3510,
119,
1188,
6978,
2736,
1176,
5463,
2284,
1118,
5369,
4692,
117,
1177,
1543,
170,
3510,
1118,
15097,
18959,
2924,
1110,
1270,
789,
5463,
790,
117,
1105,
3510,
11166,
1110,
1270,
789,
2317,
1197,
119,
790,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
16972,
22441,
2249,
142,
3190,
23258,
14962,
16523,
21748,
139,
2162,
9244,
2428,
23258,
1592,
11607,
3743,
1104,
5354,
6451,
13335,
2149,
5123,
9805,
117,
1247,
1132,
1317,
10698,
1115,
5494,
1103,
2266,
1104,
22559,
1116,
1654,
113,
174,
119,
176,
119,
117,
170,
2952,
13274,
1176,
4508,
117,
3539,
1141,
164,
1492,
117,
1542,
117,
1572,
166,
114,
1113,
8093,
7147,
1394,
119,
142,
8420,
14136,
164,
1765,
166,
1110,
1141,
1104,
1788,
23019,
8093,
7147,
1394,
1115,
4795,
1169,
9410,
22559,
1118,
1560,
3483,
1176,
20375,
1785,
164,
130,
166,
119,
1706,
1576,
170,
1788,
1113,
142,
1582,
1874,
1818,
117,
170,
4795,
2228,
170,
13618,
1511,
1103,
1788,
117,
1105,
1103,
2443,
5669,
1122,
1165,
1296,
14372,
22884,
1116,
3510,
2075,
1103,
13618,
1154,
170,
3510,
7147,
1394,
119,
21076,
3483,
1113,
142,
8420,
14136,
1132,
14283,
1403,
118,
2335,
1177,
1115,
170,
4795,
1169,
3593,
1126,
13157,
7812,
1105,
1177,
1113,
119,
1706,
3843,
1142,
117,
1119,
2993,
1106,
2653,
5354,
6451,
13335,
2149,
5123,
9805,
117,
142,
8420,
117,
2452,
1106,
170,
1295,
1104,
1103,
1788,
1965,
2585,
119,
1409,
1119,
6474,
1126,
13157,
7812,
117,
1119,
2993,
1106,
2653,
13157,
5354,
6451,
13335,
2149,
5123,
9805,
1106,
1576,
1122,
119,
1124,
1169,
1243,
142,
8420,
1116,
1118
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"fork",
"happens",
",",
"each",
"node",
"regards",
"the",
"chain",
"having",
"the",
"highest",
"sum",
"of",
"the",
"Po",
"##W",
"answers",
"difficulty",
"as",
"correct",
".",
"Hence",
",",
"each",
"node",
"keeps",
"the",
"block",
"##cha",
"##in",
"that",
"spent",
"the",
"largest",
"computational",
"power",
"in",
"the",
"network",
".",
"Additionally",
",",
"when",
"an",
"attacker",
"re",
"##w",
"##rites",
"a",
"previous",
"transaction",
"and",
"tries",
"to",
"remake",
"blocks",
"until",
"the",
"last",
"one",
",",
"at",
"the",
"same",
"time",
"honest",
"nodes",
"are",
"making",
"new",
"blocks",
"that",
"connect",
"the",
"last",
"one",
".",
"Hence",
",",
"honest",
"nodes",
"typically",
"choose",
"blocks",
"that",
"were",
"made",
"by",
"honest",
"miners",
".",
"To",
"succeed",
"in",
"an",
"attack",
",",
"attackers",
"need",
"to",
"make",
"blocks",
"the",
"fastest",
"in",
"the",
"network",
"by",
"spending",
"computational",
"power",
"larger",
"than",
"honest",
"ones",
".",
"In",
"other",
"words",
",",
"the",
"attacker",
"needs",
"over",
"50",
"%",
"of",
"computational",
"power",
"in",
"the",
"network",
"for",
"sure",
"to",
"succeed",
".",
"The",
"attack",
"of",
"getting",
"more",
"than",
"50",
"%",
"computational",
"power",
"is",
"called",
"the",
"β",
"50",
"%",
"attack",
".",
"β",
"The",
"assumption",
"that",
"a",
"block",
"##cha",
"##in",
"is",
"secure",
"because",
"double",
"-",
"spending",
"by",
"re",
"##writing",
"does",
"not",
"happen",
"is",
"guaranteed",
"by",
"the",
"difficulty",
"of",
"getting",
"50",
"%",
"computational",
"power",
"and",
"the",
"difference",
"between",
"the",
"attack",
"cost",
"and",
"the",
"profit",
".",
"To",
"m",
"##ot",
"##ivate",
"nodes",
"to",
"make",
"blocks",
",",
"the",
"system",
"rewards",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"to",
"the",
"maker",
"who",
"succeeds",
"in",
"making",
"a",
"block",
".",
"In",
"Bit",
"##co",
"##in",
",",
"the",
"system",
"allows",
"block",
"maker",
"to",
"insert",
"a",
"β",
"coin",
"##base",
"transaction",
"β",
"that",
"pays",
"maker",
"some",
"bit",
"##co",
"##ins",
"in",
"the",
"block",
".",
"This",
"mechanism",
"looks",
"like",
"mining",
"gold",
"by",
"spending",
"costs",
",",
"so",
"making",
"a",
"block",
"by",
"solving",
"Po",
"##W",
"is",
"called",
"β",
"mining",
"β",
",",
"and",
"block",
"maker",
"is",
"called",
"β",
"mine",
"##r",
".",
"β",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"TO",
"##KE",
"##N",
"E",
"##X",
"##CH",
"##AN",
"##GE",
"ON",
"B",
"##L",
"##OC",
"##K",
"##CH",
"##A",
"##IN",
"Instead",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"There",
"are",
"several",
"proposals",
"that",
"manage",
"the",
"rights",
"of",
"token",
"##s",
"control",
"(",
"e",
".",
"g",
".",
",",
"a",
"physical",
"asset",
"like",
"lands",
",",
"digital",
"one",
"[",
"13",
",",
"17",
",",
"24",
"]",
")",
"on",
"Block",
"##cha",
"##in",
".",
"E",
"##ther",
"##eum",
"[",
"27",
"]",
"is",
"one",
"of",
"program",
"##mable",
"Block",
"##cha",
"##in",
"that",
"user",
"can",
"define",
"token",
"by",
"original",
"languages",
"like",
"Solid",
"##ity",
"[",
"9",
"]",
".",
"To",
"run",
"a",
"program",
"on",
"E",
"##th",
"##re",
"##um",
",",
"a",
"user",
"makes",
"a",
"transaction",
"include",
"the",
"program",
",",
"and",
"the",
"network",
"processes",
"it",
"when",
"each",
"node",
"insert",
"##s",
"block",
"includes",
"the",
"transaction",
"into",
"a",
"block",
"##cha",
"##in",
".",
"Programming",
"languages",
"on",
"E",
"##ther",
"##eum",
"are",
"Turin",
"##g",
"-",
"complete",
"so",
"that",
"a",
"user",
"can",
"write",
"an",
"infinite",
"loop",
"and",
"so",
"on",
".",
"To",
"prevent",
"this",
",",
"he",
"needs",
"to",
"pay",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"E",
"##ther",
",",
"according",
"to",
"a",
"number",
"of",
"the",
"program",
"process",
"step",
".",
"If",
"he",
"writes",
"an",
"infinite",
"loop",
",",
"he",
"needs",
"to",
"pay",
"infinite",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"to",
"run",
"it",
".",
"He",
"can",
"get",
"E",
"##ther",
"##s",
"by"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 134 |
ational power. Because a node that finds the answer can get cryptocurrencies as rewards, using the metaphor of gold mining, the process of solving PoW is called βmining.β The consensus mechanism based on PoWis secure unless an attacker obtains over 50% ofcomputational power in the network. Additionally, security guaranteed by the cost of 50% attack is not in equilibrium with profits.
However, by the sudden price jump of cryptocurrencies and cheaply of mining machines like ASICs, the cost was in equilibri | [
1103,
1269,
5463,
10703,
1965,
1114,
27400,
2528,
1394,
119,
1212,
142,
8420,
14136,
117,
1175,
1132,
1317,
10698,
1106,
9410,
22559,
1116,
1105,
4036,
1115,
5582,
164,
129,
117,
1367,
117,
1744,
166,
119,
1650,
4612,
1114,
1168,
2648,
117,
4713,
1169,
3670,
22559,
7743,
119,
1650,
1142,
5471,
117,
4713,
1169,
1965,
8216,
117,
1176,
9241,
1105,
4147,
1842,
10015,
119,
1135,
1110,
1270,
789,
13015,
16752,
26193,
119,
790,
15374,
21669,
11414,
131,
1851,
110,
13020,
9159,
1658,
2428,
150,
15609,
2036,
1284,
17794,
1103,
2235,
1104,
1851,
110,
2035,
119,
11389,
122,
2196,
13117,
11934,
119,
157,
19985,
17516,
122,
3446,
117,
1195,
10301,
1126,
19114,
3370,
1851,
110,
19903,
1540,
119,
13615,
117,
1170,
1119,
15539,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
117,
1119,
1169,
9509,
170,
13618,
1115,
15539,
1269,
5354,
6451,
13335,
2149,
5123,
9805,
1114,
24749,
1103,
1148,
1141,
119,
15982,
122,
2196,
1293,
1103,
19114,
24219,
1103,
2702,
118,
5369,
2035,
119,
143,
23413,
19556,
2036,
122,
131,
8543,
156,
11741,
3408,
1113,
13097,
1158,
2035,
132,
113,
170,
114,
1760,
19114,
2653,
2113,
2528,
4935,
1268,
1334,
6800,
117,
1105,
1142,
13618,
1802,
1107,
170,
2221,
3510,
119,
1109,
6800,
15008,
2221,
3510,
1105,
10130,
18349,
119,
113,
171,
114,
1599,
117,
1103,
19114,
15539,
1103,
1269,
2113,
2528,
4935,
1106,
1103,
1286,
1334,
117,
1105,
1122,
1802,
170,
1894,
3510,
119,
1109,
13704,
1200,
16994,
19903,
1540,
1106,
1103,
1499,
1104,
1103,
1894,
3510,
119,
113,
172,
114,
1967,
1167,
19903,
1540,
16994,
1106,
1103,
1894,
1141,
117,
1103,
2443,
2274,
4129,
1511,
1103,
1894,
3510,
1112,
5663,
117,
1114,
24749,
2221,
3510,
117,
1268,
1334,
6800,
12667,
18349,
119,
1130,
1142,
2820,
117,
1119,
1169,
1142,
2035,
132,
122,
114,
1119,
15539,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
170,
6800,
1396,
2047,
16847,
7727,
1118,
9444,
1122,
1110,
13137,
1107,
170,
3510,
7147,
1394,
119,
123,
114,
1103,
6800,
3952,
170,
18349,
1106,
1140,
119,
124,
114,
1258,
1119,
3370,
1103,
18349,
117,
1119,
15539,
1330,
6800,
1118,
1543,
170,
13618,
1115,
1119,
15539,
1103,
1269,
5354,
6451,
13335,
2149,
5123,
9805,
1107,
4065,
122,
1105,
3370,
1330,
18349,
119,
125,
114,
1124,
7785,
1207,
3510,
2075,
1103,
1248,
13618,
1105,
2228,
170,
13097,
1107,
1103,
2443,
119,
126,
114,
1124,
3430,
5463,
1177,
1115,
12647,
6696,
5511,
1170,
13097,
1174,
3510,
119,
127,
114,
23670,
1104,
1103,
2443,
4392,
13097,
1174,
5511,
1105,
10570,
1103,
1148,
13618,
117,
1105,
1173,
1103,
1148,
6800,
12667,
1103,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
1103,
18349,
119,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
18732,
9272,
11345,
13020,
9159,
1658,
2428,
5893,
117,
1195,
10301,
1126,
2670,
2616,
1104,
1103,
2035,
119,
138,
8172,
3945,
1105,
1126,
3651,
3945,
1532,
1103,
2616,
1106,
1243,
1851,
110,
19903,
1540,
119,
1130,
8093,
7147,
1394,
117,
19903,
1540,
1110,
2602,
1118,
1293,
1242,
1551,
170,
3395,
1169,
20446,
1103,
1144,
1324,
3053,
1679,
1141,
1248,
132,
157,
3048,
120,
188,
2196,
12008,
1611,
10664,
1104,
23172,
1144
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
7,
8,
0,
0,
1,
2,
2,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
9,
10,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
7,
8,
0,
0,
1,
2,
2,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
4,
4,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
9,
10,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"same",
"mining",
"reward",
"process",
"with",
"Bit",
"##co",
"##in",
".",
"On",
"E",
"##ther",
"##eum",
",",
"there",
"are",
"several",
"proposals",
"to",
"define",
"token",
"##s",
"and",
"transfer",
"that",
"ownership",
"[",
"8",
",",
"12",
",",
"26",
"]",
".",
"By",
"combination",
"with",
"other",
"programs",
",",
"users",
"can",
"exchange",
"token",
"automatically",
".",
"By",
"this",
"scheme",
",",
"users",
"can",
"process",
"contracts",
",",
"like",
"buying",
"and",
"selling",
"real",
"estates",
".",
"It",
"is",
"called",
"β",
"Smart",
"Con",
"##tracts",
".",
"β",
"SEC",
"##TI",
"##ON",
":",
"50",
"%",
"AT",
"##TA",
"##C",
"##K",
"M",
"##OD",
"##E",
"We",
"propose",
"the",
"model",
"of",
"50",
"%",
"attack",
".",
"Table",
"1",
"shows",
"modeling",
"parameters",
".",
"T",
"##AB",
"##LE",
"1",
"Here",
",",
"we",
"estimate",
"an",
"attacker",
"gets",
"50",
"%",
"computational",
"power",
".",
"Hence",
",",
"after",
"he",
"pays",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"he",
"can",
"generate",
"a",
"transaction",
"that",
"pays",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"with",
"withdrawing",
"the",
"first",
"one",
".",
"Figure",
"1",
"shows",
"how",
"the",
"attacker",
"succeeds",
"the",
"double",
"-",
"spending",
"attack",
".",
"F",
"##IG",
"##UR",
"##E",
"1",
":",
"Double",
"S",
"##pen",
"##ding",
"on",
"fork",
"##ing",
"attack",
";",
"(",
"a",
")",
"An",
"attacker",
"pay",
"bit",
"##co",
"##ins",
"right",
"side",
"merchant",
",",
"and",
"this",
"transaction",
"recorded",
"in",
"a",
"blue",
"block",
".",
"The",
"merchant",
"checks",
"blue",
"block",
"and",
"sends",
"merchandise",
".",
"(",
"b",
")",
"Then",
",",
"the",
"attacker",
"pays",
"the",
"same",
"bit",
"##co",
"##ins",
"to",
"the",
"left",
"side",
",",
"and",
"it",
"recorded",
"a",
"red",
"block",
".",
"The",
"Attack",
"##er",
"spends",
"computational",
"power",
"to",
"the",
"top",
"of",
"the",
"red",
"block",
".",
"(",
"c",
")",
"Since",
"more",
"computational",
"power",
"spends",
"to",
"the",
"red",
"one",
",",
"the",
"network",
"takes",
"chain",
"include",
"the",
"red",
"block",
"as",
"correct",
",",
"with",
"withdrawing",
"blue",
"block",
",",
"right",
"side",
"merchant",
"loses",
"merchandise",
".",
"In",
"this",
"situation",
",",
"he",
"can",
"this",
"attack",
";",
"1",
")",
"he",
"pays",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"a",
"merchant",
"ve",
"##ri",
"##fies",
"payment",
"by",
"checking",
"it",
"is",
"inserted",
"in",
"a",
"block",
"##cha",
"##in",
".",
"2",
")",
"the",
"merchant",
"send",
"a",
"merchandise",
"to",
"him",
".",
"3",
")",
"After",
"he",
"gets",
"the",
"merchandise",
",",
"he",
"pays",
"another",
"merchant",
"by",
"making",
"a",
"transaction",
"that",
"he",
"pays",
"the",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"in",
"phase",
"1",
"and",
"gets",
"another",
"merchandise",
".",
"4",
")",
"He",
"mines",
"new",
"block",
"includes",
"the",
"second",
"transaction",
"and",
"makes",
"a",
"fork",
"in",
"the",
"network",
".",
"5",
")",
"He",
"continues",
"mining",
"so",
"that",
"app",
"##end",
"blocks",
"after",
"fork",
"##ed",
"block",
".",
"6",
")",
"Majority",
"of",
"the",
"network",
"accept",
"fork",
"##ed",
"blocks",
"and",
"withdraw",
"the",
"first",
"transaction",
",",
"and",
"then",
"the",
"first",
"merchant",
"loses",
"the",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"the",
"merchandise",
".",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"CO",
"##ST",
"OF",
"AT",
"##TA",
"##C",
"##K",
"Next",
",",
"we",
"estimate",
"an",
"economic",
"cost",
"of",
"the",
"attack",
".",
"A",
"hardware",
"price",
"and",
"an",
"electric",
"price",
"form",
"the",
"cost",
"to",
"get",
"50",
"%",
"computational",
"power",
".",
"In",
"Block",
"##cha",
"##in",
",",
"computational",
"power",
"is",
"shown",
"by",
"how",
"many",
"times",
"a",
"machine",
"can",
"calculate",
"the",
"has",
"##h",
"function",
"per",
"one",
"second",
";",
"T",
"##H",
"/",
"s",
"shows",
"Te",
"##ra",
"counts",
"of",
"calculating",
"has"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 135 |
ational power. Because a node that finds the answer can get cryptocurrencies as rewards, using the metaphor of gold mining, the process of solving PoW is called βmining.β The consensus mechanism based on PoWis secure unless an attacker obtains over 50% ofcomputational power in the network. Additionally, security guaranteed by the cost of 50% attack is not in equilibrium with profits.
However, by the sudden price jump of cryptocurrencies and cheaply of mining machines like ASICs, the cost was in equilibri | [
1103,
1269,
5463,
10703,
1965,
1114,
27400,
2528,
1394,
119,
1212,
142,
8420,
14136,
117,
1175,
1132,
1317,
10698,
1106,
9410,
22559,
1116,
1105,
4036,
1115,
5582,
164,
129,
117,
1367,
117,
1744,
166,
119,
1650,
4612,
1114,
1168,
2648,
117,
4713,
1169,
3670,
22559,
7743,
119,
1650,
1142,
5471,
117,
4713,
1169,
1965,
8216,
117,
1176,
9241,
1105,
4147,
1842,
10015,
119,
1135,
1110,
1270,
789,
13015,
16752,
26193,
119,
790,
15374,
21669,
11414,
131,
1851,
110,
13020,
9159,
1658,
2428,
150,
15609,
2036,
1284,
17794,
1103,
2235,
1104,
1851,
110,
2035,
119,
11389,
122,
2196,
13117,
11934,
119,
157,
19985,
17516,
122,
3446,
117,
1195,
10301,
1126,
19114,
3370,
1851,
110,
19903,
1540,
119,
13615,
117,
1170,
1119,
15539,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
117,
1119,
1169,
9509,
170,
13618,
1115,
15539,
1269,
5354,
6451,
13335,
2149,
5123,
9805,
1114,
24749,
1103,
1148,
1141,
119,
15982,
122,
2196,
1293,
1103,
19114,
24219,
1103,
2702,
118,
5369,
2035,
119,
143,
23413,
19556,
2036,
122,
131,
8543,
156,
11741,
3408,
1113,
13097,
1158,
2035,
132,
113,
170,
114,
1760,
19114,
2653,
2113,
2528,
4935,
1268,
1334,
6800,
117,
1105,
1142,
13618,
1802,
1107,
170,
2221,
3510,
119,
1109,
6800,
15008,
2221,
3510,
1105,
10130,
18349,
119,
113,
171,
114,
1599,
117,
1103,
19114,
15539,
1103,
1269,
2113,
2528,
4935,
1106,
1103,
1286,
1334,
117,
1105,
1122,
1802,
170,
1894,
3510,
119,
1109,
13704,
1200,
16994,
19903,
1540,
1106,
1103,
1499,
1104,
1103,
1894,
3510,
119,
113,
172,
114,
1967,
1167,
19903,
1540,
16994,
1106,
1103,
1894,
1141,
117,
1103,
2443,
2274,
4129,
1511,
1103,
1894,
3510,
1112,
5663,
117,
1114,
24749,
2221,
3510,
117,
1268,
1334,
6800,
12667,
18349,
119,
1130,
1142,
2820,
117,
1119,
1169,
1142,
2035,
132,
122,
114,
1119,
15539,
1199,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
170,
6800,
1396,
2047,
16847,
7727,
1118,
9444,
1122,
1110,
13137,
1107,
170,
3510,
7147,
1394,
119,
123,
114,
1103,
6800,
3952,
170,
18349,
1106,
1140,
119,
124,
114,
1258,
1119,
3370,
1103,
18349,
117,
1119,
15539,
1330,
6800,
1118,
1543,
170,
13618,
1115,
1119,
15539,
1103,
1269,
5354,
6451,
13335,
2149,
5123,
9805,
1107,
4065,
122,
1105,
3370,
1330,
18349,
119,
125,
114,
1124,
7785,
1207,
3510,
2075,
1103,
1248,
13618,
1105,
2228,
170,
13097,
1107,
1103,
2443,
119,
126,
114,
1124,
3430,
5463,
1177,
1115,
12647,
6696,
5511,
1170,
13097,
1174,
3510,
119,
127,
114,
23670,
1104,
1103,
2443,
4392,
13097,
1174,
5511,
1105,
10570,
1103,
1148,
13618,
117,
1105,
1173,
1103,
1148,
6800,
12667,
1103,
5354,
6451,
13335,
2149,
5123,
9805,
1105,
1103,
18349,
119,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
18732,
9272,
11345,
13020,
9159,
1658,
2428,
5893,
117,
1195,
10301,
1126,
2670,
2616,
1104,
1103,
2035,
119,
138,
8172,
3945,
1105,
1126,
3651,
3945,
1532,
1103,
2616,
1106,
1243,
1851,
110,
19903,
1540,
119,
1130,
8093,
7147,
1394,
117,
19903,
1540,
1110,
2602,
1118,
1293,
1242,
1551,
170,
3395,
1169,
20446,
1103,
1144,
1324,
3053,
1679,
1141,
1248,
132,
157,
3048,
120,
188,
2196,
12008,
1611,
10664,
1104,
23172,
1144
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"same",
"mining",
"reward",
"process",
"with",
"Bit",
"##co",
"##in",
".",
"On",
"E",
"##ther",
"##eum",
",",
"there",
"are",
"several",
"proposals",
"to",
"define",
"token",
"##s",
"and",
"transfer",
"that",
"ownership",
"[",
"8",
",",
"12",
",",
"26",
"]",
".",
"By",
"combination",
"with",
"other",
"programs",
",",
"users",
"can",
"exchange",
"token",
"automatically",
".",
"By",
"this",
"scheme",
",",
"users",
"can",
"process",
"contracts",
",",
"like",
"buying",
"and",
"selling",
"real",
"estates",
".",
"It",
"is",
"called",
"β",
"Smart",
"Con",
"##tracts",
".",
"β",
"SEC",
"##TI",
"##ON",
":",
"50",
"%",
"AT",
"##TA",
"##C",
"##K",
"M",
"##OD",
"##E",
"We",
"propose",
"the",
"model",
"of",
"50",
"%",
"attack",
".",
"Table",
"1",
"shows",
"modeling",
"parameters",
".",
"T",
"##AB",
"##LE",
"1",
"Here",
",",
"we",
"estimate",
"an",
"attacker",
"gets",
"50",
"%",
"computational",
"power",
".",
"Hence",
",",
"after",
"he",
"pays",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
",",
"he",
"can",
"generate",
"a",
"transaction",
"that",
"pays",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"with",
"withdrawing",
"the",
"first",
"one",
".",
"Figure",
"1",
"shows",
"how",
"the",
"attacker",
"succeeds",
"the",
"double",
"-",
"spending",
"attack",
".",
"F",
"##IG",
"##UR",
"##E",
"1",
":",
"Double",
"S",
"##pen",
"##ding",
"on",
"fork",
"##ing",
"attack",
";",
"(",
"a",
")",
"An",
"attacker",
"pay",
"bit",
"##co",
"##ins",
"right",
"side",
"merchant",
",",
"and",
"this",
"transaction",
"recorded",
"in",
"a",
"blue",
"block",
".",
"The",
"merchant",
"checks",
"blue",
"block",
"and",
"sends",
"merchandise",
".",
"(",
"b",
")",
"Then",
",",
"the",
"attacker",
"pays",
"the",
"same",
"bit",
"##co",
"##ins",
"to",
"the",
"left",
"side",
",",
"and",
"it",
"recorded",
"a",
"red",
"block",
".",
"The",
"Attack",
"##er",
"spends",
"computational",
"power",
"to",
"the",
"top",
"of",
"the",
"red",
"block",
".",
"(",
"c",
")",
"Since",
"more",
"computational",
"power",
"spends",
"to",
"the",
"red",
"one",
",",
"the",
"network",
"takes",
"chain",
"include",
"the",
"red",
"block",
"as",
"correct",
",",
"with",
"withdrawing",
"blue",
"block",
",",
"right",
"side",
"merchant",
"loses",
"merchandise",
".",
"In",
"this",
"situation",
",",
"he",
"can",
"this",
"attack",
";",
"1",
")",
"he",
"pays",
"some",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"a",
"merchant",
"ve",
"##ri",
"##fies",
"payment",
"by",
"checking",
"it",
"is",
"inserted",
"in",
"a",
"block",
"##cha",
"##in",
".",
"2",
")",
"the",
"merchant",
"send",
"a",
"merchandise",
"to",
"him",
".",
"3",
")",
"After",
"he",
"gets",
"the",
"merchandise",
",",
"he",
"pays",
"another",
"merchant",
"by",
"making",
"a",
"transaction",
"that",
"he",
"pays",
"the",
"same",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"in",
"phase",
"1",
"and",
"gets",
"another",
"merchandise",
".",
"4",
")",
"He",
"mines",
"new",
"block",
"includes",
"the",
"second",
"transaction",
"and",
"makes",
"a",
"fork",
"in",
"the",
"network",
".",
"5",
")",
"He",
"continues",
"mining",
"so",
"that",
"app",
"##end",
"blocks",
"after",
"fork",
"##ed",
"block",
".",
"6",
")",
"Majority",
"of",
"the",
"network",
"accept",
"fork",
"##ed",
"blocks",
"and",
"withdraw",
"the",
"first",
"transaction",
",",
"and",
"then",
"the",
"first",
"merchant",
"loses",
"the",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"and",
"the",
"merchandise",
".",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"CO",
"##ST",
"OF",
"AT",
"##TA",
"##C",
"##K",
"Next",
",",
"we",
"estimate",
"an",
"economic",
"cost",
"of",
"the",
"attack",
".",
"A",
"hardware",
"price",
"and",
"an",
"electric",
"price",
"form",
"the",
"cost",
"to",
"get",
"50",
"%",
"computational",
"power",
".",
"In",
"Block",
"##cha",
"##in",
",",
"computational",
"power",
"is",
"shown",
"by",
"how",
"many",
"times",
"a",
"machine",
"can",
"calculate",
"the",
"has",
"##h",
"function",
"per",
"one",
"second",
";",
"T",
"##H",
"/",
"s",
"shows",
"Te",
"##ra",
"counts",
"of",
"calculating",
"has"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 136 |
um for Bitcoin in 2017. In this situation, the mining cost is not a disincentive for attackers because that they can get rewards proportional to the cost of the attack.
In a 50% attack, the attacker can get cryptocurrency as the reward and profit of attack and can estimate the cost from the networkβs hash power. In Bitcoin, if a 50% attack is detected, the price ofBitcoins will fall so it serves as a disincentive for attackers. In Ethereum [27], the price of tokens (e.g., lands described by ERC-20 [12]) | [
1324,
3053,
1679,
1141,
1248,
119,
138,
6022,
1106,
1103,
1703,
1295,
1104,
1144,
1324,
19218,
1551,
1104,
1155,
15029,
1110,
1270,
789,
1144,
20955,
1566,
119,
790,
1706,
1243,
1166,
1851,
110,
19903,
1540,
1118,
5321,
15029,
1106,
170,
2443,
117,
1165,
10736,
1324,
168,
2443,
24162,
120,
188,
4061,
170,
2006,
19903,
1540,
117,
1126,
19114,
2993,
10736,
1324,
168,
2443,
168,
157,
3048,
120,
188,
119,
1284,
10301,
19450,
1329,
15278,
9741,
1116,
11769,
3121,
26740,
1111,
5463,
119,
1284,
9410,
1126,
15278,
9741,
1169,
20446,
10736,
1324,
168,
1112,
1596,
168,
157,
3048,
120,
188,
117,
1157,
1540,
8160,
20862,
168,
1112,
1596,
168,
160,
117,
1157,
3945,
1110,
7510,
168,
1112,
1596,
1237,
8876,
119,
1599,
117,
1195,
2484,
1111,
1126,
3651,
3945,
1111,
1141,
2396,
113,
180,
2246,
1324,
114,
1112,
4493,
1237,
8876,
119,
13615,
117,
11577,
1126,
19114,
5049,
15278,
9741,
1107,
13704,
1942,
10453,
2005,
117,
1175,
2196,
1103,
8172,
3945,
9322,
1105,
3651,
3945,
2896,
10294,
1204,
117,
1105,
1103,
2035,
2616,
117,
3291,
2050,
1110,
1103,
7584,
1104,
1172,
119,
142,
4880,
2591,
13821,
24805,
122,
142,
4880,
2591,
13821,
24805,
123,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
11629,
2346,
17675,
1942,
11345,
7462,
13020,
9159,
1658,
2428,
1284,
1758,
1120,
1103,
1499,
1104,
1142,
2237,
19114,
12535,
1103,
1148,
18349,
1112,
11709,
119,
5533,
117,
1119,
1169,
1243,
22278,
1111,
5463,
5511,
119,
1335,
1103,
1159,
1155,
13418,
1107,
1103,
2443,
2317,
170,
3510,
1170,
170,
2440,
1141,
117,
1103,
6022,
1115,
170,
2317,
1197,
1169,
1525,
18959,
2924,
2590,
1105,
2228,
170,
3510,
1110,
1103,
1269,
1112,
1144,
20955,
1566,
1103,
2317,
1197,
1144,
119,
1332,
170,
2317,
1197,
2834,
1525,
1103,
2590,
117,
1119,
1674,
1136,
1243,
22278,
1105,
15445,
19903,
1540,
119,
1284,
9410,
1115,
138,
5463,
10703,
1111,
1141,
3510,
1110,
11336,
5984,
1105,
170,
1144,
20955,
1566,
1115,
170,
2317,
1197,
1144,
1110,
10736,
1324,
2069,
2193,
119,
1599,
117,
1126,
2637,
2860,
1104,
5463,
22278,
1110,
142,
4880,
2591,
13821,
24805,
124,
2994,
5463,
1965,
1110,
1126,
2457,
3443,
119,
13615,
117,
5463,
1126,
2637,
2860,
1104,
183,
5463,
22278,
117,
11336,
5984,
183,
1110,
142,
4880,
2591,
13821,
24805,
125,
138,
3945,
1104,
1103,
18349,
1115,
1126,
19114,
3370,
1118,
1103,
2035,
1110,
149,
119,
1130,
27400,
2528,
1394,
1653,
2526,
117,
170,
2244,
9750,
1104,
1126,
2035,
1115,
1231,
2246,
23202,
195,
3510,
1114,
10736,
1324,
2069,
2193,
110,
19903,
1540,
117,
140,
1584,
117,
1110,
2602,
1118,
142,
4880,
2591,
13821,
24805,
126,
142,
4880,
2591,
13821,
24805,
127,
13615,
117,
1126,
2637,
2860,
1104,
5022,
1118,
1126,
2035,
1115,
1231,
2246,
23202,
195,
3510,
1114,
10736,
1324,
2069,
2193,
110,
19903,
1540,
1110,
142,
4880,
2591,
13821,
24805,
128,
15374,
21669,
11414,
131,
23096,
12507,
3663,
13882,
1708,
11345,
15969,
10954,
15681,
26140,
15969,
139,
12150,
15678,
11607,
26546,
1942,
2924,
9565,
2428,
1109,
7262,
1104,
2033,
1851,
110,
19903,
1540,
1105,
1136,
15784,
1206,
1103,
2035,
2616,
1105,
1103,
5022,
24512,
1103,
2699,
1222,
2702
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##h",
"function",
"per",
"one",
"second",
".",
"A",
"ratio",
"to",
"the",
"total",
"number",
"of",
"has",
"##h",
"calculation",
"times",
"of",
"all",
"nodes",
"is",
"called",
"β",
"has",
"##hra",
"##te",
".",
"β",
"To",
"get",
"over",
"50",
"%",
"computational",
"power",
"by",
"adding",
"nodes",
"to",
"a",
"network",
",",
"when",
"Has",
"##h",
"_",
"network",
"##TH",
"/",
"s",
"stands",
"a",
"whole",
"computational",
"power",
",",
"an",
"attacker",
"needs",
"Has",
"##h",
"_",
"network",
"_",
"T",
"##H",
"/",
"s",
".",
"We",
"estimate",
"attackers",
"use",
"AS",
"##IC",
"##s",
"op",
"##ti",
"##mized",
"for",
"mining",
".",
"We",
"define",
"an",
"AS",
"##IC",
"can",
"calculate",
"Has",
"##h",
"_",
"as",
"##ic",
"_",
"T",
"##H",
"/",
"s",
",",
"its",
"power",
"consumption",
"Watt",
"_",
"as",
"##ic",
"_",
"W",
",",
"its",
"price",
"is",
"Price",
"_",
"as",
"##ic",
"American",
"dollar",
".",
"Then",
",",
"we",
"stand",
"for",
"an",
"electric",
"price",
"for",
"one",
"hour",
"(",
"k",
"##w",
"##h",
")",
"as",
"EP",
"American",
"dollar",
".",
"Hence",
",",
"assuming",
"an",
"attacker",
"operates",
"AS",
"##IC",
"in",
"Attack",
"##T",
"##ime",
"hours",
",",
"there",
"shows",
"the",
"hardware",
"price",
"Hard",
"and",
"electric",
"price",
"El",
"##ec",
"##t",
",",
"and",
"the",
"attack",
"cost",
",",
"Co",
"##st",
"is",
"the",
"sum",
"of",
"them",
".",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"1",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"2",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"PR",
"##O",
"##FI",
"##T",
"OF",
"THE",
"AT",
"##TA",
"##C",
"##K",
"We",
"described",
"at",
"the",
"top",
"of",
"this",
"section",
"attacker",
"gains",
"the",
"first",
"merchandise",
"as",
"profits",
".",
"Additionally",
",",
"he",
"can",
"get",
"rewards",
"for",
"mining",
"blocks",
".",
"At",
"the",
"time",
"all",
"miners",
"in",
"the",
"network",
"mine",
"a",
"block",
"after",
"a",
"particular",
"one",
",",
"the",
"ratio",
"that",
"a",
"mine",
"##r",
"can",
"find",
"Po",
"##W",
"answer",
"and",
"makes",
"a",
"block",
"is",
"the",
"same",
"as",
"has",
"##hra",
"##te",
"the",
"mine",
"##r",
"has",
".",
"When",
"a",
"mine",
"##r",
"cannot",
"find",
"the",
"answer",
",",
"he",
"does",
"not",
"get",
"rewards",
"and",
"wasted",
"computational",
"power",
".",
"We",
"define",
"that",
"A",
"mining",
"reward",
"for",
"one",
"block",
"is",
"Re",
"##ward",
"and",
"a",
"has",
"##hra",
"##te",
"that",
"a",
"mine",
"##r",
"has",
"is",
"Has",
"##h",
"##R",
"##ate",
".",
"Then",
",",
"an",
"expected",
"value",
"of",
"mining",
"rewards",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"3",
"Each",
"mining",
"process",
"is",
"an",
"independent",
"trial",
".",
"Hence",
",",
"mining",
"an",
"expected",
"value",
"of",
"n",
"mining",
"rewards",
",",
"Re",
"##ward",
"n",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"4",
"A",
"price",
"of",
"the",
"merchandise",
"that",
"an",
"attacker",
"gets",
"by",
"the",
"attack",
"is",
"L",
".",
"In",
"Bit",
"##co",
"##in",
"white",
"paper",
",",
"a",
"success",
"probability",
"of",
"an",
"attack",
"that",
"re",
"##w",
"##rites",
"z",
"block",
"with",
"Has",
"##h",
"##R",
"##ate",
"%",
"computational",
"power",
",",
"C",
"##z",
",",
"is",
"shown",
"by",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"5",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"6",
"Hence",
",",
"an",
"expected",
"value",
"of",
"profit",
"by",
"an",
"attack",
"that",
"re",
"##w",
"##rites",
"z",
"block",
"with",
"Has",
"##h",
"##R",
"##ate",
"%",
"computational",
"power",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"7",
"SEC",
"##TI",
"##ON",
":",
"AN",
"##AL",
"##Y",
"##SI",
"##S",
"OF",
"IN",
"##CE",
"##NT",
"##IVE",
"IN",
"B",
"##IT",
"##CO",
"##IN",
"NE",
"##T",
"##W",
"##OR",
"##K",
"The",
"difficulty",
"of",
"getting",
"50",
"%",
"computational",
"power",
"and",
"not",
"equilibrium",
"between",
"the",
"attack",
"cost",
"and",
"the",
"profit",
"guarantees",
"the",
"security",
"against",
"double"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 137 |
um for Bitcoin in 2017. In this situation, the mining cost is not a disincentive for attackers because that they can get rewards proportional to the cost of the attack.
In a 50% attack, the attacker can get cryptocurrency as the reward and profit of attack and can estimate the cost from the networkβs hash power. In Bitcoin, if a 50% attack is detected, the price ofBitcoins will fall so it serves as a disincentive for attackers. In Ethereum [27], the price of tokens (e.g., lands described by ERC-20 [12]) | [
1324,
3053,
1679,
1141,
1248,
119,
138,
6022,
1106,
1103,
1703,
1295,
1104,
1144,
1324,
19218,
1551,
1104,
1155,
15029,
1110,
1270,
789,
1144,
20955,
1566,
119,
790,
1706,
1243,
1166,
1851,
110,
19903,
1540,
1118,
5321,
15029,
1106,
170,
2443,
117,
1165,
10736,
1324,
168,
2443,
24162,
120,
188,
4061,
170,
2006,
19903,
1540,
117,
1126,
19114,
2993,
10736,
1324,
168,
2443,
168,
157,
3048,
120,
188,
119,
1284,
10301,
19450,
1329,
15278,
9741,
1116,
11769,
3121,
26740,
1111,
5463,
119,
1284,
9410,
1126,
15278,
9741,
1169,
20446,
10736,
1324,
168,
1112,
1596,
168,
157,
3048,
120,
188,
117,
1157,
1540,
8160,
20862,
168,
1112,
1596,
168,
160,
117,
1157,
3945,
1110,
7510,
168,
1112,
1596,
1237,
8876,
119,
1599,
117,
1195,
2484,
1111,
1126,
3651,
3945,
1111,
1141,
2396,
113,
180,
2246,
1324,
114,
1112,
4493,
1237,
8876,
119,
13615,
117,
11577,
1126,
19114,
5049,
15278,
9741,
1107,
13704,
1942,
10453,
2005,
117,
1175,
2196,
1103,
8172,
3945,
9322,
1105,
3651,
3945,
2896,
10294,
1204,
117,
1105,
1103,
2035,
2616,
117,
3291,
2050,
1110,
1103,
7584,
1104,
1172,
119,
142,
4880,
2591,
13821,
24805,
122,
142,
4880,
2591,
13821,
24805,
123,
156,
2591,
2064,
118,
15374,
21669,
11414,
131,
11629,
2346,
17675,
1942,
11345,
7462,
13020,
9159,
1658,
2428,
1284,
1758,
1120,
1103,
1499,
1104,
1142,
2237,
19114,
12535,
1103,
1148,
18349,
1112,
11709,
119,
5533,
117,
1119,
1169,
1243,
22278,
1111,
5463,
5511,
119,
1335,
1103,
1159,
1155,
13418,
1107,
1103,
2443,
2317,
170,
3510,
1170,
170,
2440,
1141,
117,
1103,
6022,
1115,
170,
2317,
1197,
1169,
1525,
18959,
2924,
2590,
1105,
2228,
170,
3510,
1110,
1103,
1269,
1112,
1144,
20955,
1566,
1103,
2317,
1197,
1144,
119,
1332,
170,
2317,
1197,
2834,
1525,
1103,
2590,
117,
1119,
1674,
1136,
1243,
22278,
1105,
15445,
19903,
1540,
119,
1284,
9410,
1115,
138,
5463,
10703,
1111,
1141,
3510,
1110,
11336,
5984,
1105,
170,
1144,
20955,
1566,
1115,
170,
2317,
1197,
1144,
1110,
10736,
1324,
2069,
2193,
119,
1599,
117,
1126,
2637,
2860,
1104,
5463,
22278,
1110,
142,
4880,
2591,
13821,
24805,
124,
2994,
5463,
1965,
1110,
1126,
2457,
3443,
119,
13615,
117,
5463,
1126,
2637,
2860,
1104,
183,
5463,
22278,
117,
11336,
5984,
183,
1110,
142,
4880,
2591,
13821,
24805,
125,
138,
3945,
1104,
1103,
18349,
1115,
1126,
19114,
3370,
1118,
1103,
2035,
1110,
149,
119,
1130,
27400,
2528,
1394,
1653,
2526,
117,
170,
2244,
9750,
1104,
1126,
2035,
1115,
1231,
2246,
23202,
195,
3510,
1114,
10736,
1324,
2069,
2193,
110,
19903,
1540,
117,
140,
1584,
117,
1110,
2602,
1118,
142,
4880,
2591,
13821,
24805,
126,
142,
4880,
2591,
13821,
24805,
127,
13615,
117,
1126,
2637,
2860,
1104,
5022,
1118,
1126,
2035,
1115,
1231,
2246,
23202,
195,
3510,
1114,
10736,
1324,
2069,
2193,
110,
19903,
1540,
1110,
142,
4880,
2591,
13821,
24805,
128,
15374,
21669,
11414,
131,
23096,
12507,
3663,
13882,
1708,
11345,
15969,
10954,
15681,
26140,
15969,
139,
12150,
15678,
11607,
26546,
1942,
2924,
9565,
2428,
1109,
7262,
1104,
2033,
1851,
110,
19903,
1540,
1105,
1136,
15784,
1206,
1103,
2035,
2616,
1105,
1103,
5022,
24512,
1103,
2699,
1222,
2702
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##h",
"function",
"per",
"one",
"second",
".",
"A",
"ratio",
"to",
"the",
"total",
"number",
"of",
"has",
"##h",
"calculation",
"times",
"of",
"all",
"nodes",
"is",
"called",
"β",
"has",
"##hra",
"##te",
".",
"β",
"To",
"get",
"over",
"50",
"%",
"computational",
"power",
"by",
"adding",
"nodes",
"to",
"a",
"network",
",",
"when",
"Has",
"##h",
"_",
"network",
"##TH",
"/",
"s",
"stands",
"a",
"whole",
"computational",
"power",
",",
"an",
"attacker",
"needs",
"Has",
"##h",
"_",
"network",
"_",
"T",
"##H",
"/",
"s",
".",
"We",
"estimate",
"attackers",
"use",
"AS",
"##IC",
"##s",
"op",
"##ti",
"##mized",
"for",
"mining",
".",
"We",
"define",
"an",
"AS",
"##IC",
"can",
"calculate",
"Has",
"##h",
"_",
"as",
"##ic",
"_",
"T",
"##H",
"/",
"s",
",",
"its",
"power",
"consumption",
"Watt",
"_",
"as",
"##ic",
"_",
"W",
",",
"its",
"price",
"is",
"Price",
"_",
"as",
"##ic",
"American",
"dollar",
".",
"Then",
",",
"we",
"stand",
"for",
"an",
"electric",
"price",
"for",
"one",
"hour",
"(",
"k",
"##w",
"##h",
")",
"as",
"EP",
"American",
"dollar",
".",
"Hence",
",",
"assuming",
"an",
"attacker",
"operates",
"AS",
"##IC",
"in",
"Attack",
"##T",
"##ime",
"hours",
",",
"there",
"shows",
"the",
"hardware",
"price",
"Hard",
"and",
"electric",
"price",
"El",
"##ec",
"##t",
",",
"and",
"the",
"attack",
"cost",
",",
"Co",
"##st",
"is",
"the",
"sum",
"of",
"them",
".",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"1",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"2",
"S",
"##U",
"##B",
"-",
"SEC",
"##TI",
"##ON",
":",
"PR",
"##O",
"##FI",
"##T",
"OF",
"THE",
"AT",
"##TA",
"##C",
"##K",
"We",
"described",
"at",
"the",
"top",
"of",
"this",
"section",
"attacker",
"gains",
"the",
"first",
"merchandise",
"as",
"profits",
".",
"Additionally",
",",
"he",
"can",
"get",
"rewards",
"for",
"mining",
"blocks",
".",
"At",
"the",
"time",
"all",
"miners",
"in",
"the",
"network",
"mine",
"a",
"block",
"after",
"a",
"particular",
"one",
",",
"the",
"ratio",
"that",
"a",
"mine",
"##r",
"can",
"find",
"Po",
"##W",
"answer",
"and",
"makes",
"a",
"block",
"is",
"the",
"same",
"as",
"has",
"##hra",
"##te",
"the",
"mine",
"##r",
"has",
".",
"When",
"a",
"mine",
"##r",
"cannot",
"find",
"the",
"answer",
",",
"he",
"does",
"not",
"get",
"rewards",
"and",
"wasted",
"computational",
"power",
".",
"We",
"define",
"that",
"A",
"mining",
"reward",
"for",
"one",
"block",
"is",
"Re",
"##ward",
"and",
"a",
"has",
"##hra",
"##te",
"that",
"a",
"mine",
"##r",
"has",
"is",
"Has",
"##h",
"##R",
"##ate",
".",
"Then",
",",
"an",
"expected",
"value",
"of",
"mining",
"rewards",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"3",
"Each",
"mining",
"process",
"is",
"an",
"independent",
"trial",
".",
"Hence",
",",
"mining",
"an",
"expected",
"value",
"of",
"n",
"mining",
"rewards",
",",
"Re",
"##ward",
"n",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"4",
"A",
"price",
"of",
"the",
"merchandise",
"that",
"an",
"attacker",
"gets",
"by",
"the",
"attack",
"is",
"L",
".",
"In",
"Bit",
"##co",
"##in",
"white",
"paper",
",",
"a",
"success",
"probability",
"of",
"an",
"attack",
"that",
"re",
"##w",
"##rites",
"z",
"block",
"with",
"Has",
"##h",
"##R",
"##ate",
"%",
"computational",
"power",
",",
"C",
"##z",
",",
"is",
"shown",
"by",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"5",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"6",
"Hence",
",",
"an",
"expected",
"value",
"of",
"profit",
"by",
"an",
"attack",
"that",
"re",
"##w",
"##rites",
"z",
"block",
"with",
"Has",
"##h",
"##R",
"##ate",
"%",
"computational",
"power",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"7",
"SEC",
"##TI",
"##ON",
":",
"AN",
"##AL",
"##Y",
"##SI",
"##S",
"OF",
"IN",
"##CE",
"##NT",
"##IVE",
"IN",
"B",
"##IT",
"##CO",
"##IN",
"NE",
"##T",
"##W",
"##OR",
"##K",
"The",
"difficulty",
"of",
"getting",
"50",
"%",
"computational",
"power",
"and",
"not",
"equilibrium",
"between",
"the",
"attack",
"cost",
"and",
"the",
"profit",
"guarantees",
"the",
"security",
"against",
"double"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 138 |
is sometimes not affected by network security. Therefore, attackers are motivated by the balance between hash power and profits.
We described that there is relevant between mining power
on the network and price of tokens that a user can take on a blockchain. Users who exchange tokens on the PoW blockchain should monitor mining power and exchange tokens cheaper than attack cost so that profits and costs of the attacker is not equilibrium.
SECTION: BLOCKCHAIN
Blockchain is a system in which each node kee | [
118,
5369,
2035,
1118,
1851,
110,
2035,
119,
13615,
117,
170,
2820,
1115,
1103,
2699,
1110,
13008,
1110,
142,
4880,
2591,
13821,
24805,
129,
1599,
117,
1195,
19774,
1103,
3879,
1104,
2699,
1107,
27400,
2528,
1394,
1121,
12182,
1348,
1869,
2103,
1118,
8093,
7147,
1394,
119,
23992,
164,
126,
166,
119,
1130,
1142,
19774,
117,
1195,
10301,
13418,
1329,
1760,
1204,
9685,
1197,
156,
1580,
1182,
164,
125,
166,
117,
1141,
1104,
1918,
1394,
1193,
1215,
15278,
9741,
1111,
5463,
119,
11389,
123,
2196,
1103,
188,
25392,
1104,
1708,
1580,
1182,
119,
157,
19985,
17516,
123,
131,
156,
1580,
1182,
188,
25392,
1284,
3393,
1103,
3651,
3945,
1112,
1126,
1903,
1237,
3945,
164,
122,
166,
117,
121,
119,
122,
1237,
5860,
119,
1130,
27400,
2528,
1394,
117,
1103,
5463,
7262,
1110,
10491,
1177,
1115,
1126,
1903,
5463,
14235,
1110,
1275,
1904,
119,
13615,
117,
5463,
1110,
2244,
1572,
113,
177,
114,
240,
16480,
113,
182,
114,
134,
15373,
1551,
1107,
1275,
113,
182,
114,
1141,
1285,
119,
1284,
10301,
1851,
110,
2035,
117,
1173,
1126,
19114,
787,
188,
1144,
20955,
1566,
1110,
1851,
110,
119,
15982,
123,
2196,
1103,
2637,
2860,
1104,
5463,
22278,
1105,
2035,
2616,
1107,
1141,
1285,
119,
143,
23413,
19556,
2036,
123,
131,
16409,
26426,
1174,
2860,
1104,
22278,
1105,
2035,
2616,
1556,
6103,
1115,
5463,
3395,
1199,
1201,
2403,
1110,
2211,
188,
25392,
1190,
156,
1580,
1182,
117,
1103,
2616,
1110,
2299,
1190,
1142,
2482,
119,
1599,
117,
2589,
1103,
1344,
5152,
1104,
5354,
6451,
13335,
2149,
5123,
3457,
3945,
1107,
1504,
117,
1103,
6796,
1104,
1658,
15540,
1105,
11336,
5984,
1116,
17175,
1527,
1110,
2871,
3291,
2050,
135,
11336,
5984,
1116,
17175,
1527,
119,
1130,
1103,
1344,
5152,
1104,
3945,
1107,
1504,
117,
19450,
1132,
13241,
1118,
1251,
11709,
1104,
2702,
118,
5369,
149,
119,
1130,
1168,
1734,
117,
170,
6800,
1431,
6699,
1115,
170,
20315,
1336,
4732,
170,
2702,
118,
5369,
2035,
119,
1731,
1242,
5511,
19114,
2222,
1106,
1231,
2246,
10587,
9113,
1113,
8468,
11478,
5591,
1551,
1121,
1103,
1148,
13618,
6455,
1235,
19114,
1243,
18349,
119,
1124,
3816,
1103,
2035,
1165,
1119,
3370,
18349,
119,
13615,
117,
8093,
2249,
1818,
1119,
4642,
1106,
1231,
2246,
10587,
1110,
142,
4880,
2591,
13821,
24805,
130,
2857,
1126,
19114,
12535,
1851,
110,
19903,
1540,
117,
1290,
3651,
2616,
1110,
1315,
2211,
1190,
1103,
8172,
2616,
117,
1122,
1110,
3123,
1115,
1119,
2326,
2035,
1263,
1159,
119,
9841,
117,
1119,
1231,
2246,
23202,
1167,
5511,
117,
12535,
1167,
22278,
119,
13615,
117,
1167,
1159,
1121,
1103,
1148,
13618,
1104,
2702,
118,
5369,
182,
3329,
18851,
1116,
1140,
119,
15982,
124,
2196,
1293,
1263,
1159,
1106,
15784,
1206,
1851,
110,
2035,
2616,
1105,
22278,
119,
1130,
1504,
117,
2211,
1190,
1275,
118,
2396,
2035,
1108,
15784,
119,
143,
23413,
19556,
2036,
124,
131,
13704,
1159,
1106,
15784,
1206,
2616,
1105,
10703,
15374,
21669,
11414,
131,
13219,
23413,
13821,
24805,
11345,
13020,
9159,
1658,
2428,
15969,
10954,
15681,
26140,
1370,
10878,
182,
3329,
18851,
2702,
118,
5369,
117,
170,
6800,
7634,
170,
3945,
1104,
22559,
1116,
1113
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0
] | [
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0
] | [
"-",
"spending",
"attack",
"by",
"50",
"%",
"attack",
".",
"Hence",
",",
"a",
"situation",
"that",
"the",
"security",
"is",
"guaranteed",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"8",
"Then",
",",
"we",
"analyze",
"the",
"condition",
"of",
"security",
"in",
"Bit",
"##co",
"##in",
"from",
"static",
"##al",
"information",
"reported",
"by",
"Block",
"##cha",
"##in",
".",
"info",
"[",
"5",
"]",
".",
"In",
"this",
"analyze",
",",
"we",
"estimate",
"miners",
"use",
"An",
"##t",
"##mine",
"##r",
"S",
"##9",
"##i",
"[",
"4",
"]",
",",
"one",
"of",
"##ma",
"##in",
"##ly",
"used",
"AS",
"##IC",
"for",
"mining",
".",
"Table",
"2",
"shows",
"the",
"s",
"##pec",
"of",
"##S",
"##9",
"##i",
".",
"T",
"##AB",
"##LE",
"2",
":",
"S",
"##9",
"##i",
"s",
"##pec",
"We",
"defined",
"the",
"electric",
"price",
"as",
"an",
"average",
"American",
"price",
"[",
"1",
"]",
",",
"0",
".",
"1",
"American",
"dollars",
".",
"In",
"Bit",
"##co",
"##in",
",",
"the",
"mining",
"difficulty",
"is",
"adjusted",
"so",
"that",
"an",
"average",
"mining",
"interval",
"is",
"10",
"minutes",
".",
"Hence",
",",
"mining",
"is",
"success",
"24",
"(",
"h",
")",
"Γ",
"##60",
"(",
"m",
")",
"=",
"144",
"times",
"in",
"10",
"(",
"m",
")",
"one",
"day",
".",
"We",
"estimate",
"50",
"%",
"attack",
",",
"then",
"an",
"attacker",
"β",
"s",
"has",
"##hra",
"##te",
"is",
"50",
"%",
".",
"Figure",
"2",
"shows",
"the",
"expected",
"value",
"of",
"mining",
"rewards",
"and",
"attack",
"cost",
"in",
"one",
"day",
".",
"F",
"##IG",
"##UR",
"##E",
"2",
":",
"Ex",
"##pect",
"##ed",
"value",
"of",
"rewards",
"and",
"attack",
"cost",
"With",
"considering",
"that",
"mining",
"machine",
"some",
"years",
"ago",
"is",
"lower",
"s",
"##pec",
"than",
"S",
"##9",
"##i",
",",
"the",
"cost",
"is",
"higher",
"than",
"this",
"figure",
".",
"Then",
",",
"except",
"the",
"high",
"jump",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"price",
"in",
"2017",
",",
"the",
"relation",
"of",
"##C",
"##ost",
"and",
"Re",
"##ward",
"##s",
"##14",
"##4",
"is",
"mainly",
"Co",
"##st",
">",
"Re",
"##ward",
"##s",
"##14",
"##4",
".",
"In",
"the",
"high",
"jump",
"of",
"price",
"in",
"2017",
",",
"attackers",
"are",
"motivated",
"by",
"any",
"profits",
"of",
"double",
"-",
"spending",
"L",
".",
"In",
"other",
"words",
",",
"a",
"merchant",
"should",
"suppose",
"that",
"a",
"buyer",
"may",
"operate",
"a",
"double",
"-",
"spending",
"attack",
".",
"How",
"many",
"blocks",
"attacker",
"try",
"to",
"re",
"##w",
"##rite",
"depends",
"on",
"el",
"##ap",
"##sed",
"times",
"from",
"the",
"first",
"transaction",
"generated",
"until",
"attacker",
"get",
"merchandise",
".",
"He",
"starts",
"the",
"attack",
"when",
"he",
"gets",
"merchandise",
".",
"Hence",
",",
"Block",
"##N",
"##um",
"he",
"tries",
"to",
"re",
"##w",
"##rite",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"9",
"Once",
"an",
"attacker",
"gains",
"50",
"%",
"computational",
"power",
",",
"since",
"electric",
"cost",
"is",
"too",
"lower",
"than",
"the",
"hardware",
"cost",
",",
"it",
"is",
"easy",
"that",
"he",
"runs",
"attack",
"long",
"time",
".",
"Moreover",
",",
"he",
"re",
"##w",
"##rites",
"more",
"blocks",
",",
"gains",
"more",
"rewards",
".",
"Hence",
",",
"more",
"time",
"from",
"the",
"first",
"transaction",
"of",
"double",
"-",
"spending",
"m",
"##ot",
"##ivate",
"##s",
"him",
".",
"Figure",
"3",
"shows",
"how",
"long",
"time",
"to",
"equilibrium",
"between",
"50",
"%",
"attack",
"cost",
"and",
"rewards",
".",
"In",
"2017",
",",
"lower",
"than",
"10",
"-",
"hour",
"attack",
"was",
"equilibrium",
".",
"F",
"##IG",
"##UR",
"##E",
"3",
":",
"Attack",
"time",
"to",
"equilibrium",
"between",
"cost",
"and",
"reward",
"SEC",
"##TI",
"##ON",
":",
"MIT",
"##IG",
"##AT",
"##ION",
"OF",
"AT",
"##TA",
"##C",
"##K",
"IN",
"##CE",
"##NT",
"##IVE",
"For",
"preventing",
"m",
"##ot",
"##ivate",
"double",
"-",
"spending",
",",
"a",
"merchant",
"keeps",
"a",
"price",
"of",
"token",
"##s",
"on"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 139 |
is sometimes not affected by network security. Therefore, attackers are motivated by the balance between hash power and profits.
We described that there is relevant between mining power
on the network and price of tokens that a user can take on a blockchain. Users who exchange tokens on the PoW blockchain should monitor mining power and exchange tokens cheaper than attack cost so that profits and costs of the attacker is not equilibrium.
SECTION: BLOCKCHAIN
Blockchain is a system in which each node kee | [
118,
5369,
2035,
1118,
1851,
110,
2035,
119,
13615,
117,
170,
2820,
1115,
1103,
2699,
1110,
13008,
1110,
142,
4880,
2591,
13821,
24805,
129,
1599,
117,
1195,
19774,
1103,
3879,
1104,
2699,
1107,
27400,
2528,
1394,
1121,
12182,
1348,
1869,
2103,
1118,
8093,
7147,
1394,
119,
23992,
164,
126,
166,
119,
1130,
1142,
19774,
117,
1195,
10301,
13418,
1329,
1760,
1204,
9685,
1197,
156,
1580,
1182,
164,
125,
166,
117,
1141,
1104,
1918,
1394,
1193,
1215,
15278,
9741,
1111,
5463,
119,
11389,
123,
2196,
1103,
188,
25392,
1104,
1708,
1580,
1182,
119,
157,
19985,
17516,
123,
131,
156,
1580,
1182,
188,
25392,
1284,
3393,
1103,
3651,
3945,
1112,
1126,
1903,
1237,
3945,
164,
122,
166,
117,
121,
119,
122,
1237,
5860,
119,
1130,
27400,
2528,
1394,
117,
1103,
5463,
7262,
1110,
10491,
1177,
1115,
1126,
1903,
5463,
14235,
1110,
1275,
1904,
119,
13615,
117,
5463,
1110,
2244,
1572,
113,
177,
114,
240,
16480,
113,
182,
114,
134,
15373,
1551,
1107,
1275,
113,
182,
114,
1141,
1285,
119,
1284,
10301,
1851,
110,
2035,
117,
1173,
1126,
19114,
787,
188,
1144,
20955,
1566,
1110,
1851,
110,
119,
15982,
123,
2196,
1103,
2637,
2860,
1104,
5463,
22278,
1105,
2035,
2616,
1107,
1141,
1285,
119,
143,
23413,
19556,
2036,
123,
131,
16409,
26426,
1174,
2860,
1104,
22278,
1105,
2035,
2616,
1556,
6103,
1115,
5463,
3395,
1199,
1201,
2403,
1110,
2211,
188,
25392,
1190,
156,
1580,
1182,
117,
1103,
2616,
1110,
2299,
1190,
1142,
2482,
119,
1599,
117,
2589,
1103,
1344,
5152,
1104,
5354,
6451,
13335,
2149,
5123,
3457,
3945,
1107,
1504,
117,
1103,
6796,
1104,
1658,
15540,
1105,
11336,
5984,
1116,
17175,
1527,
1110,
2871,
3291,
2050,
135,
11336,
5984,
1116,
17175,
1527,
119,
1130,
1103,
1344,
5152,
1104,
3945,
1107,
1504,
117,
19450,
1132,
13241,
1118,
1251,
11709,
1104,
2702,
118,
5369,
149,
119,
1130,
1168,
1734,
117,
170,
6800,
1431,
6699,
1115,
170,
20315,
1336,
4732,
170,
2702,
118,
5369,
2035,
119,
1731,
1242,
5511,
19114,
2222,
1106,
1231,
2246,
10587,
9113,
1113,
8468,
11478,
5591,
1551,
1121,
1103,
1148,
13618,
6455,
1235,
19114,
1243,
18349,
119,
1124,
3816,
1103,
2035,
1165,
1119,
3370,
18349,
119,
13615,
117,
8093,
2249,
1818,
1119,
4642,
1106,
1231,
2246,
10587,
1110,
142,
4880,
2591,
13821,
24805,
130,
2857,
1126,
19114,
12535,
1851,
110,
19903,
1540,
117,
1290,
3651,
2616,
1110,
1315,
2211,
1190,
1103,
8172,
2616,
117,
1122,
1110,
3123,
1115,
1119,
2326,
2035,
1263,
1159,
119,
9841,
117,
1119,
1231,
2246,
23202,
1167,
5511,
117,
12535,
1167,
22278,
119,
13615,
117,
1167,
1159,
1121,
1103,
1148,
13618,
1104,
2702,
118,
5369,
182,
3329,
18851,
1116,
1140,
119,
15982,
124,
2196,
1293,
1263,
1159,
1106,
15784,
1206,
1851,
110,
2035,
2616,
1105,
22278,
119,
1130,
1504,
117,
2211,
1190,
1275,
118,
2396,
2035,
1108,
15784,
119,
143,
23413,
19556,
2036,
124,
131,
13704,
1159,
1106,
15784,
1206,
2616,
1105,
10703,
15374,
21669,
11414,
131,
13219,
23413,
13821,
24805,
11345,
13020,
9159,
1658,
2428,
15969,
10954,
15681,
26140,
1370,
10878,
182,
3329,
18851,
2702,
118,
5369,
117,
170,
6800,
7634,
170,
3945,
1104,
22559,
1116,
1113
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"-",
"spending",
"attack",
"by",
"50",
"%",
"attack",
".",
"Hence",
",",
"a",
"situation",
"that",
"the",
"security",
"is",
"guaranteed",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"8",
"Then",
",",
"we",
"analyze",
"the",
"condition",
"of",
"security",
"in",
"Bit",
"##co",
"##in",
"from",
"static",
"##al",
"information",
"reported",
"by",
"Block",
"##cha",
"##in",
".",
"info",
"[",
"5",
"]",
".",
"In",
"this",
"analyze",
",",
"we",
"estimate",
"miners",
"use",
"An",
"##t",
"##mine",
"##r",
"S",
"##9",
"##i",
"[",
"4",
"]",
",",
"one",
"of",
"##ma",
"##in",
"##ly",
"used",
"AS",
"##IC",
"for",
"mining",
".",
"Table",
"2",
"shows",
"the",
"s",
"##pec",
"of",
"##S",
"##9",
"##i",
".",
"T",
"##AB",
"##LE",
"2",
":",
"S",
"##9",
"##i",
"s",
"##pec",
"We",
"defined",
"the",
"electric",
"price",
"as",
"an",
"average",
"American",
"price",
"[",
"1",
"]",
",",
"0",
".",
"1",
"American",
"dollars",
".",
"In",
"Bit",
"##co",
"##in",
",",
"the",
"mining",
"difficulty",
"is",
"adjusted",
"so",
"that",
"an",
"average",
"mining",
"interval",
"is",
"10",
"minutes",
".",
"Hence",
",",
"mining",
"is",
"success",
"24",
"(",
"h",
")",
"Γ",
"##60",
"(",
"m",
")",
"=",
"144",
"times",
"in",
"10",
"(",
"m",
")",
"one",
"day",
".",
"We",
"estimate",
"50",
"%",
"attack",
",",
"then",
"an",
"attacker",
"β",
"s",
"has",
"##hra",
"##te",
"is",
"50",
"%",
".",
"Figure",
"2",
"shows",
"the",
"expected",
"value",
"of",
"mining",
"rewards",
"and",
"attack",
"cost",
"in",
"one",
"day",
".",
"F",
"##IG",
"##UR",
"##E",
"2",
":",
"Ex",
"##pect",
"##ed",
"value",
"of",
"rewards",
"and",
"attack",
"cost",
"With",
"considering",
"that",
"mining",
"machine",
"some",
"years",
"ago",
"is",
"lower",
"s",
"##pec",
"than",
"S",
"##9",
"##i",
",",
"the",
"cost",
"is",
"higher",
"than",
"this",
"figure",
".",
"Then",
",",
"except",
"the",
"high",
"jump",
"of",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"price",
"in",
"2017",
",",
"the",
"relation",
"of",
"##C",
"##ost",
"and",
"Re",
"##ward",
"##s",
"##14",
"##4",
"is",
"mainly",
"Co",
"##st",
">",
"Re",
"##ward",
"##s",
"##14",
"##4",
".",
"In",
"the",
"high",
"jump",
"of",
"price",
"in",
"2017",
",",
"attackers",
"are",
"motivated",
"by",
"any",
"profits",
"of",
"double",
"-",
"spending",
"L",
".",
"In",
"other",
"words",
",",
"a",
"merchant",
"should",
"suppose",
"that",
"a",
"buyer",
"may",
"operate",
"a",
"double",
"-",
"spending",
"attack",
".",
"How",
"many",
"blocks",
"attacker",
"try",
"to",
"re",
"##w",
"##rite",
"depends",
"on",
"el",
"##ap",
"##sed",
"times",
"from",
"the",
"first",
"transaction",
"generated",
"until",
"attacker",
"get",
"merchandise",
".",
"He",
"starts",
"the",
"attack",
"when",
"he",
"gets",
"merchandise",
".",
"Hence",
",",
"Block",
"##N",
"##um",
"he",
"tries",
"to",
"re",
"##w",
"##rite",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"9",
"Once",
"an",
"attacker",
"gains",
"50",
"%",
"computational",
"power",
",",
"since",
"electric",
"cost",
"is",
"too",
"lower",
"than",
"the",
"hardware",
"cost",
",",
"it",
"is",
"easy",
"that",
"he",
"runs",
"attack",
"long",
"time",
".",
"Moreover",
",",
"he",
"re",
"##w",
"##rites",
"more",
"blocks",
",",
"gains",
"more",
"rewards",
".",
"Hence",
",",
"more",
"time",
"from",
"the",
"first",
"transaction",
"of",
"double",
"-",
"spending",
"m",
"##ot",
"##ivate",
"##s",
"him",
".",
"Figure",
"3",
"shows",
"how",
"long",
"time",
"to",
"equilibrium",
"between",
"50",
"%",
"attack",
"cost",
"and",
"rewards",
".",
"In",
"2017",
",",
"lower",
"than",
"10",
"-",
"hour",
"attack",
"was",
"equilibrium",
".",
"F",
"##IG",
"##UR",
"##E",
"3",
":",
"Attack",
"time",
"to",
"equilibrium",
"between",
"cost",
"and",
"reward",
"SEC",
"##TI",
"##ON",
":",
"MIT",
"##IG",
"##AT",
"##ION",
"OF",
"AT",
"##TA",
"##C",
"##K",
"IN",
"##CE",
"##NT",
"##IVE",
"For",
"preventing",
"m",
"##ot",
"##ivate",
"double",
"-",
"spending",
",",
"a",
"merchant",
"keeps",
"a",
"price",
"of",
"token",
"##s",
"on"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 140 |
ps an append-only ledger, and by the appending rule the ledger keeps consistency even though each node operates independently.
FOOTNOTE: In this paper, Blockchain means the system, a blockchain means the ledger that each node keeps.
In Bitcoin, each node can verify transactions of cryptocurrencies by referring to a blockchain that is stored locally. Hence, nodes can detect βdouble-spendingβ in which an attacker pays the same cryptocurrency to different users.
Each node stores a set of verified transact | [
170,
3510,
7147,
1394,
1110,
2211,
119,
1130,
27400,
2528,
1394,
117,
1191,
1851,
110,
2035,
1110,
11168,
117,
1103,
3945,
1104,
2113,
2528,
4935,
1110,
1205,
1177,
1115,
4267,
10606,
8298,
2109,
1111,
19450,
119,
1130,
142,
8420,
14136,
117,
1103,
3945,
1104,
22559,
1116,
113,
174,
119,
176,
119,
117,
4508,
1758,
1118,
23580,
1658,
118,
1406,
114,
1110,
2121,
1136,
4634,
1118,
2443,
2699,
119,
1130,
3291,
2050,
133,
11336,
5984,
1116,
1179,
117,
1142,
2820,
1110,
4763,
119,
1130,
3291,
2050,
135,
11336,
5984,
1116,
168,
183,
117,
19114,
4361,
23692,
1191,
5022,
1104,
2702,
118,
5369,
149,
1110,
142,
4880,
2591,
13821,
24805,
1275,
1173,
117,
142,
4880,
2591,
13821,
24805,
1429,
13615,
117,
1103,
6800,
1169,
1321,
22559,
1116,
1115,
1157,
3945,
1110,
2211,
1190,
3291,
2050,
851,
11336,
5984,
1116,
168,
183,
119,
1130,
2415,
117,
11278,
1431,
8804,
1103,
19903,
1540,
1107,
1103,
2443,
1106,
10301,
1103,
2035,
2616,
119,
6240,
1193,
117,
15029,
1107,
1103,
2443,
2112,
1536,
19903,
1540,
117,
1103,
2035,
2616,
1107,
27400,
2528,
1394,
1110,
1315,
5865,
1106,
2415,
119,
1438,
117,
1165,
4713,
3076,
170,
2029,
2443,
1111,
22559,
3670,
117,
1105,
1152,
2834,
4511,
19903,
1540,
117,
1103,
2699,
1110,
1510,
1120,
3187,
1272,
19450,
1336,
1243,
1126,
23692,
119,
22801,
117,
1103,
2443,
1431,
1712,
1536,
1344,
19903,
1540,
1177,
1115,
19450,
1132,
1136,
13241,
3253,
119,
15374,
21669,
11414,
131,
141,
6258,
23520,
12480,
24805,
16151,
2346,
16830,
15969,
10954,
15681,
26140,
15969,
15678,
12412,
6258,
12880,
15517,
3663,
1130,
27400,
2528,
1394,
117,
1175,
1110,
1126,
2805,
1115,
4713,
3074,
1115,
1199,
5511,
7543,
1170,
170,
3510,
2075,
1117,
13618,
1272,
170,
3510,
1115,
1167,
3200,
8200,
1110,
2846,
1106,
1231,
2246,
10587,
119,
1130,
1103,
1168,
1493,
117,
1107,
2237,
125,
117,
1195,
2799,
1115,
1126,
19114,
1110,
13241,
1106,
1231,
2246,
10587,
1343,
5511,
1118,
22278,
119,
13615,
117,
1191,
1103,
1703,
1144,
20955,
1566,
1107,
1103,
2443,
1561,
2211,
117,
19450,
1132,
13241,
1167,
3253,
1118,
10926,
1158,
1167,
5511,
119,
1135,
1110,
23692,
1107,
7235,
22398,
9517,
1106,
2699,
119,
15586,
6451,
13335,
2149,
5123,
9805,
1176,
27400,
2528,
1394,
1105,
142,
8420,
14136,
1132,
1678,
1112,
170,
4010,
1104,
5151,
119,
13615,
117,
1242,
1234,
1132,
5666,
1106,
1147,
3945,
119,
15982,
125,
2196,
3945,
1105,
1144,
1324,
1540,
1107,
1103,
27400,
2528,
1394,
2443,
119,
143,
23413,
19556,
2036,
125,
131,
27400,
2528,
1394,
3998,
1457,
7698,
1116,
10736,
1324,
1109,
3945,
1110,
1344,
10857,
11745,
11796,
117,
1105,
3154,
1106,
2035,
23692,
119,
7282,
117,
1144,
1324,
1540,
7096,
1421,
1551,
1121,
1314,
1214,
119,
4354,
1110,
13008,
1118,
1103,
7262,
1104,
5369,
1851,
110,
1144,
1324,
1540,
119,
8094,
117,
1142,
1144,
1324,
1540,
7096,
2196,
1115,
1122,
1144,
1151,
4451,
1104,
5321,
1851,
110,
1144,
1324,
1540,
119,
13615,
117,
1103,
2699,
1104,
27400,
2528,
1394,
1110,
1136,
13008,
119,
1247,
1132,
1844,
1279,
1164,
5354,
6451,
13335,
2149,
5123,
9805,
9397,
164,
1405,
117,
1659,
166,
119,
4435,
1844,
1279,
1209,
8681
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
5,
6,
6,
0,
0,
0,
0,
1,
2,
2,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
5,
6,
6,
0,
0,
0,
0,
1,
2,
2,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
19,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9,
10,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"a",
"block",
"##cha",
"##in",
"is",
"lower",
".",
"In",
"Bit",
"##co",
"##in",
",",
"if",
"50",
"%",
"attack",
"is",
"detected",
",",
"the",
"price",
"of",
"bit",
"##co",
"##ins",
"is",
"down",
"so",
"that",
"di",
"##sin",
"##cent",
"##ive",
"for",
"attackers",
".",
"In",
"E",
"##ther",
"##eum",
",",
"the",
"price",
"of",
"token",
"##s",
"(",
"e",
".",
"g",
".",
",",
"lands",
"described",
"by",
"ER",
"##C",
"-",
"20",
")",
"is",
"sometimes",
"not",
"affected",
"by",
"network",
"security",
".",
"In",
"Co",
"##st",
"<",
"Re",
"##ward",
"##s",
"##n",
",",
"this",
"situation",
"is",
"impossible",
".",
"In",
"Co",
"##st",
">",
"Re",
"##ward",
"##s",
"_",
"n",
",",
"attacker",
"gain",
"incentive",
"if",
"profit",
"of",
"double",
"-",
"spending",
"L",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"10",
"then",
",",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"11",
"Hence",
",",
"the",
"merchant",
"can",
"take",
"token",
"##s",
"that",
"its",
"price",
"is",
"lower",
"than",
"Co",
"##st",
"β",
"Re",
"##ward",
"##s",
"_",
"n",
".",
"In",
"practice",
",",
"merchants",
"should",
"monitor",
"the",
"computational",
"power",
"in",
"the",
"network",
"to",
"estimate",
"the",
"attack",
"cost",
".",
"Natural",
"##ly",
",",
"nodes",
"in",
"the",
"network",
"post",
"enough",
"computational",
"power",
",",
"the",
"attack",
"cost",
"in",
"Bit",
"##co",
"##in",
"is",
"too",
"expensive",
"to",
"practice",
".",
"However",
",",
"when",
"users",
"build",
"a",
"private",
"network",
"for",
"token",
"exchange",
",",
"and",
"they",
"cannot",
"spend",
"computational",
"power",
",",
"the",
"security",
"is",
"often",
"at",
"risk",
"because",
"attackers",
"may",
"get",
"an",
"incentive",
".",
"Accordingly",
",",
"the",
"network",
"should",
"keep",
"enough",
"high",
"computational",
"power",
"so",
"that",
"attackers",
"are",
"not",
"motivated",
"easily",
".",
"SEC",
"##TI",
"##ON",
":",
"D",
"##IS",
"##CU",
"##SS",
"##ION",
"AB",
"##O",
"##UT",
"IN",
"##CE",
"##NT",
"##IVE",
"IN",
"##CO",
"##NS",
"##IS",
"##TE",
"##NC",
"##Y",
"In",
"Bit",
"##co",
"##in",
",",
"there",
"is",
"an",
"operation",
"that",
"users",
"wait",
"that",
"some",
"blocks",
"connect",
"after",
"a",
"block",
"includes",
"his",
"transaction",
"because",
"a",
"block",
"that",
"more",
"ones",
"connects",
"is",
"difficult",
"to",
"re",
"##w",
"##rite",
".",
"In",
"the",
"other",
"hands",
",",
"in",
"section",
"4",
",",
"we",
"showed",
"that",
"an",
"attacker",
"is",
"motivated",
"to",
"re",
"##w",
"##rite",
"those",
"blocks",
"by",
"rewards",
".",
"Hence",
",",
"if",
"the",
"total",
"has",
"##hra",
"##te",
"in",
"the",
"network",
"become",
"lower",
",",
"attackers",
"are",
"motivated",
"more",
"easily",
"by",
"stack",
"##ing",
"more",
"blocks",
".",
"It",
"is",
"incentive",
"in",
"##con",
"##sist",
"##ency",
"to",
"security",
".",
"Cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"like",
"Bit",
"##co",
"##in",
"and",
"E",
"##ther",
"##eum",
"are",
"taken",
"as",
"a",
"target",
"of",
"investment",
".",
"Hence",
",",
"many",
"people",
"are",
"attracted",
"to",
"their",
"price",
".",
"Figure",
"4",
"shows",
"price",
"and",
"has",
"##h",
"power",
"in",
"the",
"Bit",
"##co",
"##in",
"network",
".",
"F",
"##IG",
"##UR",
"##E",
"4",
":",
"Bit",
"##co",
"##in",
"Network",
"St",
"##atic",
"##s",
"Has",
"##h",
"The",
"price",
"is",
"high",
"vol",
"##ati",
"##lity",
",",
"and",
"effects",
"to",
"attack",
"incentive",
".",
"Furthermore",
",",
"has",
"##h",
"power",
"grows",
"five",
"times",
"from",
"last",
"year",
".",
"Security",
"is",
"guaranteed",
"by",
"the",
"difficulty",
"of",
"spending",
"50",
"%",
"has",
"##h",
"power",
".",
"Nevertheless",
",",
"this",
"has",
"##h",
"power",
"grows",
"shows",
"that",
"it",
"has",
"been",
"capable",
"of",
"adding",
"50",
"%",
"has",
"##h",
"power",
".",
"Hence",
",",
"the",
"security",
"of",
"Bit",
"##co",
"##in",
"is",
"not",
"guaranteed",
".",
"There",
"are",
"research",
"##es",
"about",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"stability",
"[",
"15",
",",
"22",
"]",
".",
"Those",
"research",
"##es",
"will",
"contribute"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 141 |
ps an append-only ledger, and by the appending rule the ledger keeps consistency even though each node operates independently.
FOOTNOTE: In this paper, Blockchain means the system, a blockchain means the ledger that each node keeps.
In Bitcoin, each node can verify transactions of cryptocurrencies by referring to a blockchain that is stored locally. Hence, nodes can detect βdouble-spendingβ in which an attacker pays the same cryptocurrency to different users.
Each node stores a set of verified transact | [
170,
3510,
7147,
1394,
1110,
2211,
119,
1130,
27400,
2528,
1394,
117,
1191,
1851,
110,
2035,
1110,
11168,
117,
1103,
3945,
1104,
2113,
2528,
4935,
1110,
1205,
1177,
1115,
4267,
10606,
8298,
2109,
1111,
19450,
119,
1130,
142,
8420,
14136,
117,
1103,
3945,
1104,
22559,
1116,
113,
174,
119,
176,
119,
117,
4508,
1758,
1118,
23580,
1658,
118,
1406,
114,
1110,
2121,
1136,
4634,
1118,
2443,
2699,
119,
1130,
3291,
2050,
133,
11336,
5984,
1116,
1179,
117,
1142,
2820,
1110,
4763,
119,
1130,
3291,
2050,
135,
11336,
5984,
1116,
168,
183,
117,
19114,
4361,
23692,
1191,
5022,
1104,
2702,
118,
5369,
149,
1110,
142,
4880,
2591,
13821,
24805,
1275,
1173,
117,
142,
4880,
2591,
13821,
24805,
1429,
13615,
117,
1103,
6800,
1169,
1321,
22559,
1116,
1115,
1157,
3945,
1110,
2211,
1190,
3291,
2050,
851,
11336,
5984,
1116,
168,
183,
119,
1130,
2415,
117,
11278,
1431,
8804,
1103,
19903,
1540,
1107,
1103,
2443,
1106,
10301,
1103,
2035,
2616,
119,
6240,
1193,
117,
15029,
1107,
1103,
2443,
2112,
1536,
19903,
1540,
117,
1103,
2035,
2616,
1107,
27400,
2528,
1394,
1110,
1315,
5865,
1106,
2415,
119,
1438,
117,
1165,
4713,
3076,
170,
2029,
2443,
1111,
22559,
3670,
117,
1105,
1152,
2834,
4511,
19903,
1540,
117,
1103,
2699,
1110,
1510,
1120,
3187,
1272,
19450,
1336,
1243,
1126,
23692,
119,
22801,
117,
1103,
2443,
1431,
1712,
1536,
1344,
19903,
1540,
1177,
1115,
19450,
1132,
1136,
13241,
3253,
119,
15374,
21669,
11414,
131,
141,
6258,
23520,
12480,
24805,
16151,
2346,
16830,
15969,
10954,
15681,
26140,
15969,
15678,
12412,
6258,
12880,
15517,
3663,
1130,
27400,
2528,
1394,
117,
1175,
1110,
1126,
2805,
1115,
4713,
3074,
1115,
1199,
5511,
7543,
1170,
170,
3510,
2075,
1117,
13618,
1272,
170,
3510,
1115,
1167,
3200,
8200,
1110,
2846,
1106,
1231,
2246,
10587,
119,
1130,
1103,
1168,
1493,
117,
1107,
2237,
125,
117,
1195,
2799,
1115,
1126,
19114,
1110,
13241,
1106,
1231,
2246,
10587,
1343,
5511,
1118,
22278,
119,
13615,
117,
1191,
1103,
1703,
1144,
20955,
1566,
1107,
1103,
2443,
1561,
2211,
117,
19450,
1132,
13241,
1167,
3253,
1118,
10926,
1158,
1167,
5511,
119,
1135,
1110,
23692,
1107,
7235,
22398,
9517,
1106,
2699,
119,
15586,
6451,
13335,
2149,
5123,
9805,
1176,
27400,
2528,
1394,
1105,
142,
8420,
14136,
1132,
1678,
1112,
170,
4010,
1104,
5151,
119,
13615,
117,
1242,
1234,
1132,
5666,
1106,
1147,
3945,
119,
15982,
125,
2196,
3945,
1105,
1144,
1324,
1540,
1107,
1103,
27400,
2528,
1394,
2443,
119,
143,
23413,
19556,
2036,
125,
131,
27400,
2528,
1394,
3998,
1457,
7698,
1116,
10736,
1324,
1109,
3945,
1110,
1344,
10857,
11745,
11796,
117,
1105,
3154,
1106,
2035,
23692,
119,
7282,
117,
1144,
1324,
1540,
7096,
1421,
1551,
1121,
1314,
1214,
119,
4354,
1110,
13008,
1118,
1103,
7262,
1104,
5369,
1851,
110,
1144,
1324,
1540,
119,
8094,
117,
1142,
1144,
1324,
1540,
7096,
2196,
1115,
1122,
1144,
1151,
4451,
1104,
5321,
1851,
110,
1144,
1324,
1540,
119,
13615,
117,
1103,
2699,
1104,
27400,
2528,
1394,
1110,
1136,
13008,
119,
1247,
1132,
1844,
1279,
1164,
5354,
6451,
13335,
2149,
5123,
9805,
9397,
164,
1405,
117,
1659,
166,
119,
4435,
1844,
1279,
1209,
8681
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"a",
"block",
"##cha",
"##in",
"is",
"lower",
".",
"In",
"Bit",
"##co",
"##in",
",",
"if",
"50",
"%",
"attack",
"is",
"detected",
",",
"the",
"price",
"of",
"bit",
"##co",
"##ins",
"is",
"down",
"so",
"that",
"di",
"##sin",
"##cent",
"##ive",
"for",
"attackers",
".",
"In",
"E",
"##ther",
"##eum",
",",
"the",
"price",
"of",
"token",
"##s",
"(",
"e",
".",
"g",
".",
",",
"lands",
"described",
"by",
"ER",
"##C",
"-",
"20",
")",
"is",
"sometimes",
"not",
"affected",
"by",
"network",
"security",
".",
"In",
"Co",
"##st",
"<",
"Re",
"##ward",
"##s",
"##n",
",",
"this",
"situation",
"is",
"impossible",
".",
"In",
"Co",
"##st",
">",
"Re",
"##ward",
"##s",
"_",
"n",
",",
"attacker",
"gain",
"incentive",
"if",
"profit",
"of",
"double",
"-",
"spending",
"L",
"is",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"10",
"then",
",",
"E",
"##Q",
"##U",
"##AT",
"##ION",
"11",
"Hence",
",",
"the",
"merchant",
"can",
"take",
"token",
"##s",
"that",
"its",
"price",
"is",
"lower",
"than",
"Co",
"##st",
"β",
"Re",
"##ward",
"##s",
"_",
"n",
".",
"In",
"practice",
",",
"merchants",
"should",
"monitor",
"the",
"computational",
"power",
"in",
"the",
"network",
"to",
"estimate",
"the",
"attack",
"cost",
".",
"Natural",
"##ly",
",",
"nodes",
"in",
"the",
"network",
"post",
"enough",
"computational",
"power",
",",
"the",
"attack",
"cost",
"in",
"Bit",
"##co",
"##in",
"is",
"too",
"expensive",
"to",
"practice",
".",
"However",
",",
"when",
"users",
"build",
"a",
"private",
"network",
"for",
"token",
"exchange",
",",
"and",
"they",
"cannot",
"spend",
"computational",
"power",
",",
"the",
"security",
"is",
"often",
"at",
"risk",
"because",
"attackers",
"may",
"get",
"an",
"incentive",
".",
"Accordingly",
",",
"the",
"network",
"should",
"keep",
"enough",
"high",
"computational",
"power",
"so",
"that",
"attackers",
"are",
"not",
"motivated",
"easily",
".",
"SEC",
"##TI",
"##ON",
":",
"D",
"##IS",
"##CU",
"##SS",
"##ION",
"AB",
"##O",
"##UT",
"IN",
"##CE",
"##NT",
"##IVE",
"IN",
"##CO",
"##NS",
"##IS",
"##TE",
"##NC",
"##Y",
"In",
"Bit",
"##co",
"##in",
",",
"there",
"is",
"an",
"operation",
"that",
"users",
"wait",
"that",
"some",
"blocks",
"connect",
"after",
"a",
"block",
"includes",
"his",
"transaction",
"because",
"a",
"block",
"that",
"more",
"ones",
"connects",
"is",
"difficult",
"to",
"re",
"##w",
"##rite",
".",
"In",
"the",
"other",
"hands",
",",
"in",
"section",
"4",
",",
"we",
"showed",
"that",
"an",
"attacker",
"is",
"motivated",
"to",
"re",
"##w",
"##rite",
"those",
"blocks",
"by",
"rewards",
".",
"Hence",
",",
"if",
"the",
"total",
"has",
"##hra",
"##te",
"in",
"the",
"network",
"become",
"lower",
",",
"attackers",
"are",
"motivated",
"more",
"easily",
"by",
"stack",
"##ing",
"more",
"blocks",
".",
"It",
"is",
"incentive",
"in",
"##con",
"##sist",
"##ency",
"to",
"security",
".",
"Cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"like",
"Bit",
"##co",
"##in",
"and",
"E",
"##ther",
"##eum",
"are",
"taken",
"as",
"a",
"target",
"of",
"investment",
".",
"Hence",
",",
"many",
"people",
"are",
"attracted",
"to",
"their",
"price",
".",
"Figure",
"4",
"shows",
"price",
"and",
"has",
"##h",
"power",
"in",
"the",
"Bit",
"##co",
"##in",
"network",
".",
"F",
"##IG",
"##UR",
"##E",
"4",
":",
"Bit",
"##co",
"##in",
"Network",
"St",
"##atic",
"##s",
"Has",
"##h",
"The",
"price",
"is",
"high",
"vol",
"##ati",
"##lity",
",",
"and",
"effects",
"to",
"attack",
"incentive",
".",
"Furthermore",
",",
"has",
"##h",
"power",
"grows",
"five",
"times",
"from",
"last",
"year",
".",
"Security",
"is",
"guaranteed",
"by",
"the",
"difficulty",
"of",
"spending",
"50",
"%",
"has",
"##h",
"power",
".",
"Nevertheless",
",",
"this",
"has",
"##h",
"power",
"grows",
"shows",
"that",
"it",
"has",
"been",
"capable",
"of",
"adding",
"50",
"%",
"has",
"##h",
"power",
".",
"Hence",
",",
"the",
"security",
"of",
"Bit",
"##co",
"##in",
"is",
"not",
"guaranteed",
".",
"There",
"are",
"research",
"##es",
"about",
"cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cies",
"stability",
"[",
"15",
",",
"22",
"]",
".",
"Those",
"research",
"##es",
"will",
"contribute"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 142 |
ions as βBlockβ in a blockchain. A block includes the cryptographic hash number of the last one in the blockchain. By this structure, if an attacker rewrites a previous transaction, the hash number of a block that includes it is changed, and the hash of the next one is changed too. Hence, an attacker needs to update all blocks starting from the rewritten one to the last one.
To keep consistency and difficulty of rewriting, block maker needs to solve a mathematical puzzle called βProof-of-Work(PoW)β and i | [
1103,
2699,
1121,
23692,
5402,
119,
5798,
117,
1103,
5463,
10703,
1110,
1126,
23692,
1111,
170,
13618,
9221,
1891,
1759,
119,
1332,
1103,
18959,
2924,
3510,
7147,
1394,
2344,
1127,
1136,
2505,
117,
5463,
22278,
1189,
24273,
1115,
13418,
2866,
1103,
2443,
119,
15088,
117,
1242,
4713,
1132,
5666,
1106,
3510,
7147,
1394,
2344,
1118,
1157,
5924,
119,
1220,
2222,
1106,
6058,
1106,
1242,
3872,
119,
1130,
1142,
2820,
117,
5463,
22278,
1138,
1136,
1444,
117,
1105,
1122,
1144,
170,
19403,
2629,
1121,
2035,
23692,
7631,
119,
3458,
5835,
26410,
13499,
1916,
23692,
1110,
170,
1603,
1159,
5072,
119,
4804,
15874,
3084,
2393,
119,
6352,
1103,
20482,
1104,
27400,
2528,
1394,
1443,
3510,
22278,
164,
127,
166,
119,
1706,
4607,
3510,
7147,
1394,
2344,
117,
1112,
2174,
1250,
117,
1195,
1431,
19774,
24273,
1104,
1851,
110,
2035,
1107,
3510,
7147,
1394,
19534,
1443,
5463,
10703,
119,
15374,
21669,
11414,
131,
155,
21678,
13821,
10069,
160,
9565,
25370,
5798,
117,
5096,
10008,
118,
1104,
118,
6955,
1108,
3000,
1112,
170,
4073,
3263,
2225,
3313,
1106,
22620,
1306,
24853,
1118,
8753,
22620,
10951,
19903,
4692,
164,
123,
166,
119,
1247,
1132,
1317,
7553,
1104,
1844,
1164,
2098,
2670,
5402,
164,
1407,
117,
1627,
166,
119,
4914,
170,
2440,
3879,
117,
1122,
1110,
1136,
3903,
1113,
2670,
4267,
10606,
8298,
2109,
119,
1109,
2670,
7631,
3622,
1104,
2101,
1186,
2924,
1394,
8093,
7147,
4935,
117,
16677,
1158,
3497,
2749,
164,
1275,
117,
1489,
117,
1479,
166,
117,
1110,
1126,
1696,
8366,
119,
1130,
1142,
2526,
117,
1107,
2440,
117,
1195,
1758,
1103,
2670,
7631,
1104,
1851,
110,
2035,
1113,
18959,
2924,
3510,
7147,
1394,
119,
1109,
6436,
1104,
16677,
1158,
18959,
2924,
1107,
27400,
2528,
1394,
1110,
9901,
2670,
2616,
1105,
2699,
17816,
119,
4354,
3622,
1113,
3510,
7147,
1394,
1359,
1113,
18959,
2924,
2196,
170,
9750,
1104,
2035,
2244,
1105,
2616,
1110,
5865,
164,
1626,
166,
119,
1438,
117,
1107,
1142,
2526,
117,
1195,
2799,
1115,
1175,
1110,
170,
2820,
1115,
1940,
24557,
16030,
1172,
1118,
170,
3945,
1104,
22559,
1116,
119,
1247,
1132,
1317,
10700,
1106,
9381,
2702,
118,
5369,
2035,
117,
3510,
1114,
20139,
164,
124,
117,
128,
166,
117,
15589,
5463,
164,
1429,
117,
1695,
166,
1105,
1177,
1113,
119,
1284,
3555,
23692,
1111,
22607,
18414,
119,
13615,
117,
1343,
1132,
2174,
1759,
1115,
1195,
17459,
23692,
1113,
1317,
10700,
119,
23274,
2572,
3084,
2393,
119,
6352,
1940,
24557,
6943,
1158,
23692,
1105,
2699,
164,
1512,
166,
119,
1220,
3000,
1126,
4048,
10348,
3442,
1165,
170,
3510,
7147,
1394,
117,
1126,
4048,
9113,
1113,
117,
7322,
119,
3458,
3622,
7203,
1113,
170,
22559,
3670,
1113,
1103,
3510,
7147,
1394,
119,
13615,
117,
4713,
1169,
26410,
25342,
2699,
3187,
1118,
9437,
7352,
119,
1130,
1168,
4683,
16677,
1158,
170,
3510,
7147,
1394,
1112,
170,
4901,
21340,
1197,
117,
1136,
1138,
6796,
1114,
7352,
117,
1412,
3442,
2834,
16677,
119,
15374,
21669,
11414,
131,
18732,
15517,
2162,
13329,
24805,
1130,
1142,
2526,
117,
1195,
1758,
1103,
2616,
1105,
5022,
2235,
1104,
1851,
110,
2035,
1113,
18959,
2924,
3510,
7147,
1394,
119
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
5,
6,
6,
6,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
5,
6,
6,
6,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"security",
"from",
"incentive",
"aspects",
".",
"Originally",
",",
"the",
"mining",
"reward",
"is",
"an",
"incentive",
"for",
"a",
"transaction",
"valid",
"##ation",
"works",
".",
"When",
"the",
"Po",
"##W",
"block",
"##cha",
"##in",
"systems",
"were",
"not",
"famous",
",",
"mining",
"rewards",
"made",
"incentives",
"that",
"miners",
"join",
"the",
"network",
".",
"Recently",
",",
"many",
"users",
"are",
"attracted",
"to",
"block",
"##cha",
"##in",
"systems",
"by",
"its",
"characteristics",
".",
"They",
"try",
"to",
"apply",
"to",
"many",
"fields",
".",
"In",
"this",
"situation",
",",
"mining",
"rewards",
"have",
"not",
"need",
",",
"and",
"it",
"has",
"a",
"harmful",
"effect",
"from",
"attack",
"incentive",
"aspect",
".",
"Our",
"proposal",
"mit",
"##iga",
"##ting",
"incentive",
"is",
"a",
"short",
"time",
"solution",
".",
"Carl",
"##sten",
"et",
"al",
".",
"discussed",
"the",
"instability",
"of",
"Bit",
"##co",
"##in",
"without",
"block",
"rewards",
"[",
"6",
"]",
".",
"To",
"improve",
"block",
"##cha",
"##in",
"systems",
",",
"as",
"future",
"work",
",",
"we",
"should",
"analyze",
"incentives",
"of",
"50",
"%",
"attack",
"in",
"block",
"##cha",
"##in",
"ecosystem",
"without",
"mining",
"reward",
".",
"SEC",
"##TI",
"##ON",
":",
"R",
"##EL",
"##AT",
"##ED",
"W",
"##OR",
"##KS",
"Originally",
",",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"was",
"proposed",
"as",
"a",
"counter",
"##me",
"##as",
"##ure",
"to",
"spa",
"##m",
"emails",
"by",
"requiring",
"spa",
"##mmer",
"computational",
"costs",
"[",
"2",
"]",
".",
"There",
"are",
"several",
"kinds",
"of",
"research",
"about",
"Its",
"economic",
"aspects",
"[",
"18",
",",
"19",
"]",
".",
"Without",
"a",
"particular",
"condition",
",",
"it",
"is",
"not",
"effective",
"on",
"economic",
"di",
"##sin",
"##cent",
"##ive",
".",
"The",
"economic",
"aspect",
"analysis",
"of",
"##P",
"##o",
"##W",
"##in",
"Block",
"##cha",
"##ins",
",",
"adapt",
"##ing",
"Game",
"theory",
"[",
"10",
",",
"14",
",",
"16",
"]",
",",
"is",
"an",
"important",
"topic",
".",
"In",
"this",
"paper",
",",
"in",
"particular",
",",
"we",
"described",
"the",
"economic",
"aspect",
"of",
"50",
"%",
"attack",
"on",
"Po",
"##W",
"block",
"##cha",
"##in",
".",
"The",
"contribution",
"of",
"adapt",
"##ing",
"Po",
"##W",
"in",
"Bit",
"##co",
"##in",
"is",
"matching",
"economic",
"cost",
"and",
"security",
"parameter",
".",
"Security",
"analysis",
"on",
"block",
"##cha",
"##in",
"based",
"on",
"Po",
"##W",
"shows",
"a",
"probability",
"of",
"attack",
"success",
"and",
"cost",
"is",
"expensive",
"[",
"21",
"]",
".",
"However",
",",
"in",
"this",
"paper",
",",
"we",
"showed",
"that",
"there",
"is",
"a",
"situation",
"that",
"mi",
"##sma",
"##tches",
"them",
"by",
"a",
"price",
"of",
"token",
"##s",
".",
"There",
"are",
"several",
"strategies",
"to",
"succeed",
"double",
"-",
"spending",
"attack",
",",
"block",
"with",
"##holding",
"[",
"3",
",",
"7",
"]",
",",
"selfish",
"mining",
"[",
"11",
",",
"23",
"]",
"and",
"so",
"on",
".",
"We",
"estimated",
"incentive",
"for",
"naive",
"scenarios",
".",
"Hence",
",",
"those",
"are",
"future",
"works",
"that",
"we",
"evaluate",
"incentive",
"on",
"several",
"strategies",
".",
"Shu",
"##do",
"et",
"al",
".",
"discussed",
"mi",
"##sma",
"##tch",
"##ing",
"incentive",
"and",
"security",
"[",
"25",
"]",
".",
"They",
"proposed",
"an",
"application",
"migration",
"method",
"when",
"a",
"block",
"##cha",
"##in",
",",
"an",
"application",
"depends",
"on",
",",
"collapsed",
".",
"Our",
"analysis",
"focuses",
"on",
"a",
"token",
"exchange",
"on",
"the",
"block",
"##cha",
"##in",
".",
"Hence",
",",
"users",
"can",
"mit",
"##igate",
"security",
"risk",
"by",
"monitoring",
"prices",
".",
"In",
"other",
"applications",
"adapt",
"##ing",
"a",
"block",
"##cha",
"##in",
"as",
"a",
"distributed",
"ledge",
"##r",
",",
"not",
"have",
"relation",
"with",
"prices",
",",
"our",
"method",
"cannot",
"adapt",
".",
"SEC",
"##TI",
"##ON",
":",
"CO",
"##NC",
"##L",
"##US",
"##ION",
"In",
"this",
"paper",
",",
"we",
"described",
"the",
"cost",
"and",
"profit",
"model",
"of",
"50",
"%",
"attack",
"on",
"Po",
"##W",
"block",
"##cha",
"##in",
"."
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 143 |
ions as βBlockβ in a blockchain. A block includes the cryptographic hash number of the last one in the blockchain. By this structure, if an attacker rewrites a previous transaction, the hash number of a block that includes it is changed, and the hash of the next one is changed too. Hence, an attacker needs to update all blocks starting from the rewritten one to the last one.
To keep consistency and difficulty of rewriting, block maker needs to solve a mathematical puzzle called βProof-of-Work(PoW)β and i | [
1103,
2699,
1121,
23692,
5402,
119,
5798,
117,
1103,
5463,
10703,
1110,
1126,
23692,
1111,
170,
13618,
9221,
1891,
1759,
119,
1332,
1103,
18959,
2924,
3510,
7147,
1394,
2344,
1127,
1136,
2505,
117,
5463,
22278,
1189,
24273,
1115,
13418,
2866,
1103,
2443,
119,
15088,
117,
1242,
4713,
1132,
5666,
1106,
3510,
7147,
1394,
2344,
1118,
1157,
5924,
119,
1220,
2222,
1106,
6058,
1106,
1242,
3872,
119,
1130,
1142,
2820,
117,
5463,
22278,
1138,
1136,
1444,
117,
1105,
1122,
1144,
170,
19403,
2629,
1121,
2035,
23692,
7631,
119,
3458,
5835,
26410,
13499,
1916,
23692,
1110,
170,
1603,
1159,
5072,
119,
4804,
15874,
3084,
2393,
119,
6352,
1103,
20482,
1104,
27400,
2528,
1394,
1443,
3510,
22278,
164,
127,
166,
119,
1706,
4607,
3510,
7147,
1394,
2344,
117,
1112,
2174,
1250,
117,
1195,
1431,
19774,
24273,
1104,
1851,
110,
2035,
1107,
3510,
7147,
1394,
19534,
1443,
5463,
10703,
119,
15374,
21669,
11414,
131,
155,
21678,
13821,
10069,
160,
9565,
25370,
5798,
117,
5096,
10008,
118,
1104,
118,
6955,
1108,
3000,
1112,
170,
4073,
3263,
2225,
3313,
1106,
22620,
1306,
24853,
1118,
8753,
22620,
10951,
19903,
4692,
164,
123,
166,
119,
1247,
1132,
1317,
7553,
1104,
1844,
1164,
2098,
2670,
5402,
164,
1407,
117,
1627,
166,
119,
4914,
170,
2440,
3879,
117,
1122,
1110,
1136,
3903,
1113,
2670,
4267,
10606,
8298,
2109,
119,
1109,
2670,
7631,
3622,
1104,
2101,
1186,
2924,
1394,
8093,
7147,
4935,
117,
16677,
1158,
3497,
2749,
164,
1275,
117,
1489,
117,
1479,
166,
117,
1110,
1126,
1696,
8366,
119,
1130,
1142,
2526,
117,
1107,
2440,
117,
1195,
1758,
1103,
2670,
7631,
1104,
1851,
110,
2035,
1113,
18959,
2924,
3510,
7147,
1394,
119,
1109,
6436,
1104,
16677,
1158,
18959,
2924,
1107,
27400,
2528,
1394,
1110,
9901,
2670,
2616,
1105,
2699,
17816,
119,
4354,
3622,
1113,
3510,
7147,
1394,
1359,
1113,
18959,
2924,
2196,
170,
9750,
1104,
2035,
2244,
1105,
2616,
1110,
5865,
164,
1626,
166,
119,
1438,
117,
1107,
1142,
2526,
117,
1195,
2799,
1115,
1175,
1110,
170,
2820,
1115,
1940,
24557,
16030,
1172,
1118,
170,
3945,
1104,
22559,
1116,
119,
1247,
1132,
1317,
10700,
1106,
9381,
2702,
118,
5369,
2035,
117,
3510,
1114,
20139,
164,
124,
117,
128,
166,
117,
15589,
5463,
164,
1429,
117,
1695,
166,
1105,
1177,
1113,
119,
1284,
3555,
23692,
1111,
22607,
18414,
119,
13615,
117,
1343,
1132,
2174,
1759,
1115,
1195,
17459,
23692,
1113,
1317,
10700,
119,
23274,
2572,
3084,
2393,
119,
6352,
1940,
24557,
6943,
1158,
23692,
1105,
2699,
164,
1512,
166,
119,
1220,
3000,
1126,
4048,
10348,
3442,
1165,
170,
3510,
7147,
1394,
117,
1126,
4048,
9113,
1113,
117,
7322,
119,
3458,
3622,
7203,
1113,
170,
22559,
3670,
1113,
1103,
3510,
7147,
1394,
119,
13615,
117,
4713,
1169,
26410,
25342,
2699,
3187,
1118,
9437,
7352,
119,
1130,
1168,
4683,
16677,
1158,
170,
3510,
7147,
1394,
1112,
170,
4901,
21340,
1197,
117,
1136,
1138,
6796,
1114,
7352,
117,
1412,
3442,
2834,
16677,
119,
15374,
21669,
11414,
131,
18732,
15517,
2162,
13329,
24805,
1130,
1142,
2526,
117,
1195,
1758,
1103,
2616,
1105,
5022,
2235,
1104,
1851,
110,
2035,
1113,
18959,
2924,
3510,
7147,
1394,
119
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"the",
"security",
"from",
"incentive",
"aspects",
".",
"Originally",
",",
"the",
"mining",
"reward",
"is",
"an",
"incentive",
"for",
"a",
"transaction",
"valid",
"##ation",
"works",
".",
"When",
"the",
"Po",
"##W",
"block",
"##cha",
"##in",
"systems",
"were",
"not",
"famous",
",",
"mining",
"rewards",
"made",
"incentives",
"that",
"miners",
"join",
"the",
"network",
".",
"Recently",
",",
"many",
"users",
"are",
"attracted",
"to",
"block",
"##cha",
"##in",
"systems",
"by",
"its",
"characteristics",
".",
"They",
"try",
"to",
"apply",
"to",
"many",
"fields",
".",
"In",
"this",
"situation",
",",
"mining",
"rewards",
"have",
"not",
"need",
",",
"and",
"it",
"has",
"a",
"harmful",
"effect",
"from",
"attack",
"incentive",
"aspect",
".",
"Our",
"proposal",
"mit",
"##iga",
"##ting",
"incentive",
"is",
"a",
"short",
"time",
"solution",
".",
"Carl",
"##sten",
"et",
"al",
".",
"discussed",
"the",
"instability",
"of",
"Bit",
"##co",
"##in",
"without",
"block",
"rewards",
"[",
"6",
"]",
".",
"To",
"improve",
"block",
"##cha",
"##in",
"systems",
",",
"as",
"future",
"work",
",",
"we",
"should",
"analyze",
"incentives",
"of",
"50",
"%",
"attack",
"in",
"block",
"##cha",
"##in",
"ecosystem",
"without",
"mining",
"reward",
".",
"SEC",
"##TI",
"##ON",
":",
"R",
"##EL",
"##AT",
"##ED",
"W",
"##OR",
"##KS",
"Originally",
",",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"was",
"proposed",
"as",
"a",
"counter",
"##me",
"##as",
"##ure",
"to",
"spa",
"##m",
"emails",
"by",
"requiring",
"spa",
"##mmer",
"computational",
"costs",
"[",
"2",
"]",
".",
"There",
"are",
"several",
"kinds",
"of",
"research",
"about",
"Its",
"economic",
"aspects",
"[",
"18",
",",
"19",
"]",
".",
"Without",
"a",
"particular",
"condition",
",",
"it",
"is",
"not",
"effective",
"on",
"economic",
"di",
"##sin",
"##cent",
"##ive",
".",
"The",
"economic",
"aspect",
"analysis",
"of",
"##P",
"##o",
"##W",
"##in",
"Block",
"##cha",
"##ins",
",",
"adapt",
"##ing",
"Game",
"theory",
"[",
"10",
",",
"14",
",",
"16",
"]",
",",
"is",
"an",
"important",
"topic",
".",
"In",
"this",
"paper",
",",
"in",
"particular",
",",
"we",
"described",
"the",
"economic",
"aspect",
"of",
"50",
"%",
"attack",
"on",
"Po",
"##W",
"block",
"##cha",
"##in",
".",
"The",
"contribution",
"of",
"adapt",
"##ing",
"Po",
"##W",
"in",
"Bit",
"##co",
"##in",
"is",
"matching",
"economic",
"cost",
"and",
"security",
"parameter",
".",
"Security",
"analysis",
"on",
"block",
"##cha",
"##in",
"based",
"on",
"Po",
"##W",
"shows",
"a",
"probability",
"of",
"attack",
"success",
"and",
"cost",
"is",
"expensive",
"[",
"21",
"]",
".",
"However",
",",
"in",
"this",
"paper",
",",
"we",
"showed",
"that",
"there",
"is",
"a",
"situation",
"that",
"mi",
"##sma",
"##tches",
"them",
"by",
"a",
"price",
"of",
"token",
"##s",
".",
"There",
"are",
"several",
"strategies",
"to",
"succeed",
"double",
"-",
"spending",
"attack",
",",
"block",
"with",
"##holding",
"[",
"3",
",",
"7",
"]",
",",
"selfish",
"mining",
"[",
"11",
",",
"23",
"]",
"and",
"so",
"on",
".",
"We",
"estimated",
"incentive",
"for",
"naive",
"scenarios",
".",
"Hence",
",",
"those",
"are",
"future",
"works",
"that",
"we",
"evaluate",
"incentive",
"on",
"several",
"strategies",
".",
"Shu",
"##do",
"et",
"al",
".",
"discussed",
"mi",
"##sma",
"##tch",
"##ing",
"incentive",
"and",
"security",
"[",
"25",
"]",
".",
"They",
"proposed",
"an",
"application",
"migration",
"method",
"when",
"a",
"block",
"##cha",
"##in",
",",
"an",
"application",
"depends",
"on",
",",
"collapsed",
".",
"Our",
"analysis",
"focuses",
"on",
"a",
"token",
"exchange",
"on",
"the",
"block",
"##cha",
"##in",
".",
"Hence",
",",
"users",
"can",
"mit",
"##igate",
"security",
"risk",
"by",
"monitoring",
"prices",
".",
"In",
"other",
"applications",
"adapt",
"##ing",
"a",
"block",
"##cha",
"##in",
"as",
"a",
"distributed",
"ledge",
"##r",
",",
"not",
"have",
"relation",
"with",
"prices",
",",
"our",
"method",
"cannot",
"adapt",
".",
"SEC",
"##TI",
"##ON",
":",
"CO",
"##NC",
"##L",
"##US",
"##ION",
"In",
"this",
"paper",
",",
"we",
"described",
"the",
"cost",
"and",
"profit",
"model",
"of",
"50",
"%",
"attack",
"on",
"Po",
"##W",
"block",
"##cha",
"##in",
"."
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 144 |
nclude the answer in the new block. PoW has the characteristics that solving needs much computational power but verifying the answer is simple. If some block maker makes blocks that include conflicting transactions by rewriting the past, nodes detect the conflict as a βforkβ. When a fork happens, each node regards the chain having the highest sum of the PoW answers difficulty as correct. Hence, each node keeps the blockchain that spent the largest computational power in the network.
Additionally, when an | [
1109,
3945,
1104,
170,
22559,
1113,
170,
3510,
7147,
1394,
13974,
1103,
23692,
1104,
2702,
118,
5369,
2035,
119,
1622,
27400,
2528,
1394,
787,
188,
3009,
2233,
117,
1195,
1169,
1267,
1115,
1103,
27400,
2528,
1394,
2443,
1108,
1120,
3187,
1104,
182,
3329,
19012,
2702,
118,
5369,
1219,
1103,
1504,
1344,
12814,
1104,
27400,
2528,
1394,
787,
188,
3945,
119,
1130,
1103,
22559,
3670,
1113,
18959,
2924,
3510,
7147,
1394,
117,
4713,
1431,
8804,
19903,
1540,
1107,
1103,
2443,
1106,
3843,
182,
3329,
19012,
2702,
118,
5369,
1104,
1103,
22559,
119,
1448,
1104,
1103,
1263,
118,
1858,
7995,
1110,
170,
10923,
9932,
1136,
2272,
1106,
1103,
3945,
1104,
22559,
1116,
119,
1438,
117,
1122,
1110,
1126,
1501,
2463,
1111,
170,
1470,
2443,
119,
9690,
2428,
2249,
17056,
17516,
2137,
23169,
11680,
11365,
1188,
1844,
1110,
1126,
8337,
1104,
170,
1148,
2351,
787,
188,
27265,
1120,
2508,
15615,
4164,
117,
3561,
119,
117,
1134,
1110,
170,
7049,
1104,
2508,
23433,
2047,
117,
3561,
119,
1284,
1156,
1176,
1106,
6243,
138,
21932,
16890,
1732,
21943,
11781,
3354,
1111,
19730,
1483,
119,
155,
14663,
9637,
11680,
10954,
1708,
164,
122,
166,
158,
119,
156,
119,
5514,
4219,
4918,
119,
1857,
119,
18098,
7510,
1104,
23017,
1106,
11618,
25456,
1468,
1118,
5135,
118,
11696,
17063,
119,
18630,
131,
120,
120,
7001,
119,
174,
1465,
119,
1301,
1964,
120,
6495,
120,
7868,
120,
174,
9952,
168,
1952,
168,
10873,
1200,
119,
185,
16194,
136,
189,
134,
174,
9952,
1204,
168,
126,
168,
5037,
168,
170,
164,
123,
166,
3379,
4388,
3084,
2393,
119,
1617,
119,
10736,
1324,
21995,
1324,
118,
170,
16926,
1104,
1555,
4073,
118,
4929,
119,
164,
124,
166,
19741,
4047,
18757,
1403,
117,
15463,
2737,
9084,
1161,
155,
1358,
3361,
117,
1105,
19892,
6592,
4313,
26364,
1182,
119,
1504,
119,
27400,
2528,
1394,
8093,
1556,
20139,
13704,
131,
12504,
1105,
12107,
3121,
10716,
119,
16206,
13809,
22946,
1113,
4219,
1370,
5026,
4724,
1105,
4354,
1367,
117,
129,
113,
12686,
1403,
1504,
114,
117,
2573,
782,
2406,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
157,
15499,
1708,
119,
1446,
119,
24280,
19297,
1604,
1604,
164,
125,
166,
139,
12150,
8271,
11607,
119,
1857,
119,
113,
1857,
114,
119,
18630,
131,
120,
120,
7001,
119,
1112,
1596,
9685,
13461,
19224,
119,
3254,
120,
13418,
120,
2113,
1918,
1394,
120,
22904,
9685,
1197,
118,
188,
1580,
1182,
118,
5740,
164,
126,
166,
8093,
7147,
1394,
119,
3254,
119,
1857,
119,
3510,
7147,
1394,
119,
3254,
119,
18630,
131,
120,
120,
7001,
119,
3510,
7147,
1394,
119,
3254,
120,
16171,
164,
127,
166,
7726,
4804,
15874,
117,
3466,
14812,
2858,
22834,
1200,
117,
156,
119,
4754,
12068,
8904,
117,
1105,
138,
22466,
1181,
27520,
1389,
119,
1446,
119,
1212,
1103,
1130,
8419,
5474,
1104,
27400,
2528,
1394,
4914,
1103,
8093,
11336,
5984,
119,
20661,
1104,
1103,
1446,
9690,
2107,
156,
23413,
8055,
1658,
3047,
1113,
6701,
1105,
6345,
4354,
118,
21362,
1708,
787,
1479,
113,
1446,
114,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
12620
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
9,
10,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"The",
"price",
"of",
"a",
"token",
"on",
"a",
"block",
"##cha",
"##in",
"affects",
"the",
"incentive",
"of",
"double",
"-",
"spending",
"attack",
".",
"From",
"Bit",
"##co",
"##in",
"β",
"s",
"historical",
"data",
",",
"we",
"can",
"see",
"that",
"the",
"Bit",
"##co",
"##in",
"network",
"was",
"at",
"risk",
"of",
"m",
"##ot",
"##ivating",
"double",
"-",
"spending",
"during",
"the",
"2017",
"high",
"surge",
"of",
"Bit",
"##co",
"##in",
"β",
"s",
"price",
".",
"In",
"the",
"token",
"exchange",
"on",
"Po",
"##W",
"block",
"##cha",
"##in",
",",
"users",
"should",
"monitor",
"computational",
"power",
"in",
"the",
"network",
"to",
"prevent",
"m",
"##ot",
"##ivating",
"double",
"-",
"spending",
"of",
"the",
"token",
".",
"One",
"of",
"the",
"long",
"-",
"term",
"solutions",
"is",
"a",
"consensus",
"algorithm",
"not",
"related",
"to",
"the",
"price",
"of",
"token",
"##s",
".",
"However",
",",
"it",
"is",
"an",
"open",
"problem",
"for",
"a",
"public",
"network",
".",
"AC",
"##K",
"##N",
"##OW",
"##LE",
"##D",
"##GM",
"##EN",
"##TS",
"This",
"research",
"is",
"an",
"achievement",
"of",
"a",
"first",
"author",
"β",
"s",
"internship",
"at",
"Me",
"##rp",
"##ay",
",",
"Inc",
".",
",",
"which",
"is",
"a",
"subsidiary",
"of",
"Me",
"##rca",
"##ri",
",",
"Inc",
".",
"We",
"would",
"like",
"to",
"thank",
"A",
"##gro",
"Ra",
"##ch",
"##mat",
"##ull",
"##ah",
"for",
"reviewing",
"English",
".",
"R",
"##EF",
"##ER",
"##EN",
"##CE",
"##S",
"[",
"1",
"]",
"U",
".",
"S",
".",
"Energy",
"Information",
"Administration",
".",
"2018",
".",
"Average",
"Price",
"of",
"Electricity",
"to",
"Ultimate",
"Custom",
"##ers",
"by",
"End",
"-",
"Use",
"Sector",
".",
"https",
":",
"/",
"/",
"www",
".",
"e",
"##ia",
".",
"go",
"##v",
"/",
"electricity",
"/",
"monthly",
"/",
"e",
"##pm",
"_",
"table",
"_",
"graph",
"##er",
".",
"p",
"##hp",
"?",
"t",
"=",
"e",
"##pm",
"##t",
"_",
"5",
"_",
"06",
"_",
"a",
"[",
"2",
"]",
"Adam",
"Back",
"et",
"al",
".",
"2002",
".",
"Has",
"##h",
"##cas",
"##h",
"-",
"a",
"denial",
"of",
"service",
"counter",
"-",
"measure",
".",
"[",
"3",
"]",
"Sami",
"##ran",
"Ba",
"##g",
",",
"Su",
"##sh",
"##mit",
"##a",
"R",
"##u",
"##j",
",",
"and",
"Ko",
"##ui",
"##chi",
"Sakura",
"##i",
".",
"2017",
".",
"Bit",
"##co",
"##in",
"Block",
"With",
"##holding",
"Attack",
":",
"Analysis",
"and",
"Mi",
"##ti",
"##gation",
".",
"IEEE",
"Trans",
"##actions",
"on",
"Information",
"For",
"##ens",
"##ics",
"and",
"Security",
"12",
",",
"8",
"(",
"au",
"##g",
"2017",
")",
",",
"1967",
"β",
"1978",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"T",
"##IF",
"##S",
".",
"2016",
".",
"262",
"##35",
"##8",
"##8",
"[",
"4",
"]",
"B",
"##IT",
"##MA",
"##IN",
".",
"2018",
".",
"(",
"2018",
")",
".",
"https",
":",
"/",
"/",
"www",
".",
"as",
"##ic",
"##mine",
"##rva",
"##lue",
".",
"com",
"/",
"miners",
"/",
"bit",
"##ma",
"##in",
"/",
"ant",
"##mine",
"##r",
"-",
"s",
"##9",
"##i",
"-",
"14th",
"[",
"5",
"]",
"Block",
"##cha",
"##in",
".",
"com",
".",
"2018",
".",
"block",
"##cha",
"##in",
".",
"com",
".",
"https",
":",
"/",
"/",
"www",
".",
"block",
"##cha",
"##in",
".",
"com",
"/",
"explorer",
"[",
"6",
"]",
"Miles",
"Carl",
"##sten",
",",
"Harry",
"Ka",
"##lo",
"##dn",
"##er",
",",
"S",
".",
"Matthew",
"Wei",
"##nberg",
",",
"and",
"A",
"##rvin",
"##d",
"Narayan",
"##an",
".",
"2016",
".",
"On",
"the",
"In",
"##sta",
"##bility",
"of",
"Bit",
"##co",
"##in",
"Without",
"the",
"Block",
"Re",
"##ward",
".",
"Proceedings",
"of",
"the",
"2016",
"AC",
"##M",
"S",
"##IG",
"##SA",
"##C",
"Conference",
"on",
"Computer",
"and",
"Communications",
"Security",
"-",
"CC",
"##S",
"β",
"16",
"(",
"2016",
")",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"114"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 145 |
attacker rewrites a previous transaction and tries to remake blocks until the last one, at the same time honest nodes are making new blocks that connect the last one. Hence, honest nodes typically choose blocks that were made by honest miners. To succeed in an attack, attackers need to make blocks the fastest in the network by spending computational power larger than honest ones. In other words, the attacker needs over 50% of computational power in the network for sure to succeed. The attack of getting m | [
1571,
120,
1853,
1559,
1545,
1559,
1527,
1580,
119,
1853,
1559,
1604,
12882,
1604,
164,
128,
166,
10418,
157,
119,
2031,
8586,
1105,
12958,
1197,
18757,
17907,
119,
1387,
119,
1212,
12859,
10704,
2109,
9139,
1197,
1457,
5498,
19310,
1105,
8093,
1556,
20139,
13704,
1107,
27400,
2528,
1394,
6082,
140,
2149,
5123,
3457,
119,
113,
179,
1389,
1387,
114,
119,
170,
1197,
3190,
11083,
131,
8183,
1477,
119,
19619,
1604,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
8183,
1477,
119,
19619,
1604,
164,
129,
166,
23058,
27177,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
2492,
120,
22803,
164,
130,
166,
142,
8420,
14136,
119,
1446,
119,
20375,
1785,
119,
18630,
131,
120,
120,
4600,
1785,
119,
2373,
10681,
2572,
6063,
119,
178,
1186,
120,
4035,
120,
191,
1568,
119,
125,
119,
1572,
120,
164,
1275,
166,
1135,
1777,
1183,
142,
18543,
119,
1410,
119,
1109,
9139,
1197,
787,
188,
12120,
23397,
119,
1130,
1410,
16206,
26520,
1113,
4354,
1105,
153,
2047,
2497,
3457,
119,
16206,
117,
5840,
782,
9550,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
16625,
119,
1410,
119,
1492,
164,
1429,
166,
1135,
1777,
1183,
142,
18543,
1105,
18653,
1394,
144,
17176,
1179,
2203,
1200,
119,
1857,
119,
23670,
1110,
1136,
1536,
119,
3291,
6262,
3488,
119,
9690,
2107,
5391,
117,
128,
113,
179,
3488,
1857,
114,
117,
4573,
782,
9081,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
12620,
1571,
120,
26963,
26752,
1580,
1604,
164,
1367,
166,
159,
27732,
13894,
9860,
25318,
1105,
1252,
9866,
1179,
25118,
19921,
119,
1410,
119,
23580,
1658,
118,
1406,
1706,
6378,
6433,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
171,
2858,
1830,
120,
3283,
120,
142,
11410,
1708,
120,
174,
9717,
118,
1406,
119,
182,
1181,
164,
1492,
166,
14104,
2895,
1358,
23219,
14535,
117,
8790,
24830,
1182,
160,
6575,
1605,
3962,
117,
1335,
14410,
3031,
11896,
1968,
14117,
1611,
117,
2545,
9865,
10337,
14680,
24817,
117,
138,
2293,
17481,
1186,
138,
4786,
9552,
117,
1105,
5525,
12865,
11985,
14477,
5933,
27997,
119,
1410,
119,
26660,
23413,
18784,
131,
138,
3400,
1111,
170,
11858,
4412,
2200,
2266,
2635,
1449,
1359,
1113,
3510,
7147,
1394,
119,
1130,
1410,
16206,
4025,
1570,
3047,
1113,
17122,
13983,
118,
3206,
113,
17502,
2036,
118,
3206,
114,
119,
16206,
117,
26625,
782,
3236,
1545,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
17502,
2036,
118,
3206,
119,
1410,
119,
5766,
1580,
11964,
26253,
164,
1489,
166,
10418,
9800,
20257,
119,
1387,
119,
1109,
27400,
2528,
1394,
15280,
3497,
119,
22916,
2249,
10952,
3603,
113,
12477,
1197,
1387,
114,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
21640,
1580,
120,
188,
1116,
4558,
119,
11202,
1559,
1604,
23124,
164,
1405,
166,
12107,
9552,
5082,
146,
3624,
14535,
117,
10684,
4314,
12809,
1358,
18284,
2312,
4084,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
3,
4,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##5",
"/",
"29",
"##7",
"##6",
"##7",
"##4",
"##9",
".",
"29",
"##7",
"##8",
"##40",
"##8",
"[",
"7",
"]",
"Nicolas",
"T",
".",
"Court",
"##ois",
"and",
"Lea",
"##r",
"Ba",
"##hack",
".",
"2014",
".",
"On",
"Sub",
"##vers",
"##ive",
"Mine",
"##r",
"St",
"##rate",
"##gies",
"and",
"Block",
"With",
"##holding",
"Attack",
"in",
"Bit",
"##co",
"##in",
"Digital",
"C",
"##ur",
"##ren",
"##cy",
".",
"(",
"j",
"##an",
"2014",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"140",
"##2",
".",
"171",
"##8",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"140",
"##2",
".",
"171",
"##8",
"[",
"8",
"]",
"Dex",
"##aran",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"issues",
"/",
"223",
"[",
"9",
"]",
"E",
"##ther",
"##eum",
".",
"2016",
".",
"Solid",
"##ity",
".",
"https",
":",
"/",
"/",
"solid",
"##ity",
".",
"read",
"##the",
"##do",
"##cs",
".",
"i",
"##o",
"/",
"en",
"/",
"v",
"##0",
".",
"4",
".",
"24",
"/",
"[",
"10",
"]",
"It",
"##ta",
"##y",
"E",
"##yal",
".",
"2015",
".",
"The",
"Mine",
"##r",
"β",
"s",
"Di",
"##lemma",
".",
"In",
"2015",
"IEEE",
"Symposium",
"on",
"Security",
"and",
"P",
"##ri",
"##va",
"##cy",
".",
"IEEE",
",",
"89",
"β",
"103",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"SP",
".",
"2015",
".",
"13",
"[",
"11",
"]",
"It",
"##ta",
"##y",
"E",
"##yal",
"and",
"Em",
"##in",
"G",
"##ΓΌ",
"##n",
"Sir",
"##er",
".",
"2018",
".",
"Majority",
"is",
"not",
"enough",
".",
"Co",
"##mm",
"##un",
".",
"AC",
"##M",
"61",
",",
"7",
"(",
"j",
"##un",
"2018",
")",
",",
"95",
"β",
"102",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"114",
"##5",
"/",
"321",
"##29",
"##9",
"##8",
"[",
"12",
"]",
"V",
"##ogel",
"##ste",
"##ller",
"Fabian",
"and",
"But",
"##eri",
"##n",
"Vita",
"##lik",
".",
"2015",
".",
"ER",
"##C",
"-",
"20",
"To",
"##ken",
"Standard",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"b",
"##lo",
"##b",
"/",
"master",
"/",
"E",
"##IP",
"##S",
"/",
"e",
"##ip",
"-",
"20",
".",
"m",
"##d",
"[",
"13",
"]",
"Shi",
"##ger",
"##u",
"Fuji",
"##mura",
",",
"Hi",
"##rok",
"##i",
"W",
"##ata",
"##na",
"##be",
",",
"At",
"##sus",
"##hi",
"Na",
"##ka",
"##dai",
"##ra",
",",
"Tom",
"##oka",
"##zu",
"Ya",
"##mada",
",",
"A",
"##ki",
"##hit",
"##o",
"A",
"##ku",
"##tsu",
",",
"and",
"Jay",
"Jun",
"##ichi",
"Ki",
"##shi",
"##gami",
".",
"2015",
".",
"BR",
"##IG",
"##HT",
":",
"A",
"concept",
"for",
"a",
"decent",
"##ral",
"##ized",
"rights",
"management",
"system",
"based",
"on",
"block",
"##cha",
"##in",
".",
"In",
"2015",
"IEEE",
"5th",
"International",
"Conference",
"on",
"Consumer",
"Electronics",
"-",
"Berlin",
"(",
"ICC",
"##E",
"-",
"Berlin",
")",
".",
"IEEE",
",",
"345",
"β",
"34",
"##6",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"ICC",
"##E",
"-",
"Berlin",
".",
"2015",
".",
"73",
"##9",
"##12",
"##75",
"[",
"14",
"]",
"Nicolas",
"Ho",
"##uy",
".",
"2014",
".",
"The",
"Bit",
"##co",
"##in",
"Mining",
"Game",
".",
"SSR",
"##N",
"Electronic",
"Journal",
"(",
"ma",
"##r",
"2014",
")",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"213",
"##9",
"/",
"s",
"##s",
"##rn",
".",
"240",
"##7",
"##8",
"##34",
"[",
"15",
"]",
"Mi",
"##tsu",
"##ru",
"I",
"##wa",
"##mura",
",",
"Yu",
"##kin",
"##ob",
"##u",
"Kit",
"##am",
"##ura",
","
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 146 |
attacker rewrites a previous transaction and tries to remake blocks until the last one, at the same time honest nodes are making new blocks that connect the last one. Hence, honest nodes typically choose blocks that were made by honest miners. To succeed in an attack, attackers need to make blocks the fastest in the network by spending computational power larger than honest ones. In other words, the attacker needs over 50% of computational power in the network for sure to succeed. The attack of getting m | [
1571,
120,
1853,
1559,
1545,
1559,
1527,
1580,
119,
1853,
1559,
1604,
12882,
1604,
164,
128,
166,
10418,
157,
119,
2031,
8586,
1105,
12958,
1197,
18757,
17907,
119,
1387,
119,
1212,
12859,
10704,
2109,
9139,
1197,
1457,
5498,
19310,
1105,
8093,
1556,
20139,
13704,
1107,
27400,
2528,
1394,
6082,
140,
2149,
5123,
3457,
119,
113,
179,
1389,
1387,
114,
119,
170,
1197,
3190,
11083,
131,
8183,
1477,
119,
19619,
1604,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
8183,
1477,
119,
19619,
1604,
164,
129,
166,
23058,
27177,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
2492,
120,
22803,
164,
130,
166,
142,
8420,
14136,
119,
1446,
119,
20375,
1785,
119,
18630,
131,
120,
120,
4600,
1785,
119,
2373,
10681,
2572,
6063,
119,
178,
1186,
120,
4035,
120,
191,
1568,
119,
125,
119,
1572,
120,
164,
1275,
166,
1135,
1777,
1183,
142,
18543,
119,
1410,
119,
1109,
9139,
1197,
787,
188,
12120,
23397,
119,
1130,
1410,
16206,
26520,
1113,
4354,
1105,
153,
2047,
2497,
3457,
119,
16206,
117,
5840,
782,
9550,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
16625,
119,
1410,
119,
1492,
164,
1429,
166,
1135,
1777,
1183,
142,
18543,
1105,
18653,
1394,
144,
17176,
1179,
2203,
1200,
119,
1857,
119,
23670,
1110,
1136,
1536,
119,
3291,
6262,
3488,
119,
9690,
2107,
5391,
117,
128,
113,
179,
3488,
1857,
114,
117,
4573,
782,
9081,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
12620,
1571,
120,
26963,
26752,
1580,
1604,
164,
1367,
166,
159,
27732,
13894,
9860,
25318,
1105,
1252,
9866,
1179,
25118,
19921,
119,
1410,
119,
23580,
1658,
118,
1406,
1706,
6378,
6433,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
171,
2858,
1830,
120,
3283,
120,
142,
11410,
1708,
120,
174,
9717,
118,
1406,
119,
182,
1181,
164,
1492,
166,
14104,
2895,
1358,
23219,
14535,
117,
8790,
24830,
1182,
160,
6575,
1605,
3962,
117,
1335,
14410,
3031,
11896,
1968,
14117,
1611,
117,
2545,
9865,
10337,
14680,
24817,
117,
138,
2293,
17481,
1186,
138,
4786,
9552,
117,
1105,
5525,
12865,
11985,
14477,
5933,
27997,
119,
1410,
119,
26660,
23413,
18784,
131,
138,
3400,
1111,
170,
11858,
4412,
2200,
2266,
2635,
1449,
1359,
1113,
3510,
7147,
1394,
119,
1130,
1410,
16206,
4025,
1570,
3047,
1113,
17122,
13983,
118,
3206,
113,
17502,
2036,
118,
3206,
114,
119,
16206,
117,
26625,
782,
3236,
1545,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
17502,
2036,
118,
3206,
119,
1410,
119,
5766,
1580,
11964,
26253,
164,
1489,
166,
10418,
9800,
20257,
119,
1387,
119,
1109,
27400,
2528,
1394,
15280,
3497,
119,
22916,
2249,
10952,
3603,
113,
12477,
1197,
1387,
114,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
21640,
1580,
120,
188,
1116,
4558,
119,
11202,
1559,
1604,
23124,
164,
1405,
166,
12107,
9552,
5082,
146,
3624,
14535,
117,
10684,
4314,
12809,
1358,
18284,
2312,
4084,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##5",
"/",
"29",
"##7",
"##6",
"##7",
"##4",
"##9",
".",
"29",
"##7",
"##8",
"##40",
"##8",
"[",
"7",
"]",
"Nicolas",
"T",
".",
"Court",
"##ois",
"and",
"Lea",
"##r",
"Ba",
"##hack",
".",
"2014",
".",
"On",
"Sub",
"##vers",
"##ive",
"Mine",
"##r",
"St",
"##rate",
"##gies",
"and",
"Block",
"With",
"##holding",
"Attack",
"in",
"Bit",
"##co",
"##in",
"Digital",
"C",
"##ur",
"##ren",
"##cy",
".",
"(",
"j",
"##an",
"2014",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"140",
"##2",
".",
"171",
"##8",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"140",
"##2",
".",
"171",
"##8",
"[",
"8",
"]",
"Dex",
"##aran",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"issues",
"/",
"223",
"[",
"9",
"]",
"E",
"##ther",
"##eum",
".",
"2016",
".",
"Solid",
"##ity",
".",
"https",
":",
"/",
"/",
"solid",
"##ity",
".",
"read",
"##the",
"##do",
"##cs",
".",
"i",
"##o",
"/",
"en",
"/",
"v",
"##0",
".",
"4",
".",
"24",
"/",
"[",
"10",
"]",
"It",
"##ta",
"##y",
"E",
"##yal",
".",
"2015",
".",
"The",
"Mine",
"##r",
"β",
"s",
"Di",
"##lemma",
".",
"In",
"2015",
"IEEE",
"Symposium",
"on",
"Security",
"and",
"P",
"##ri",
"##va",
"##cy",
".",
"IEEE",
",",
"89",
"β",
"103",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"SP",
".",
"2015",
".",
"13",
"[",
"11",
"]",
"It",
"##ta",
"##y",
"E",
"##yal",
"and",
"Em",
"##in",
"G",
"##ΓΌ",
"##n",
"Sir",
"##er",
".",
"2018",
".",
"Majority",
"is",
"not",
"enough",
".",
"Co",
"##mm",
"##un",
".",
"AC",
"##M",
"61",
",",
"7",
"(",
"j",
"##un",
"2018",
")",
",",
"95",
"β",
"102",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"114",
"##5",
"/",
"321",
"##29",
"##9",
"##8",
"[",
"12",
"]",
"V",
"##ogel",
"##ste",
"##ller",
"Fabian",
"and",
"But",
"##eri",
"##n",
"Vita",
"##lik",
".",
"2015",
".",
"ER",
"##C",
"-",
"20",
"To",
"##ken",
"Standard",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"b",
"##lo",
"##b",
"/",
"master",
"/",
"E",
"##IP",
"##S",
"/",
"e",
"##ip",
"-",
"20",
".",
"m",
"##d",
"[",
"13",
"]",
"Shi",
"##ger",
"##u",
"Fuji",
"##mura",
",",
"Hi",
"##rok",
"##i",
"W",
"##ata",
"##na",
"##be",
",",
"At",
"##sus",
"##hi",
"Na",
"##ka",
"##dai",
"##ra",
",",
"Tom",
"##oka",
"##zu",
"Ya",
"##mada",
",",
"A",
"##ki",
"##hit",
"##o",
"A",
"##ku",
"##tsu",
",",
"and",
"Jay",
"Jun",
"##ichi",
"Ki",
"##shi",
"##gami",
".",
"2015",
".",
"BR",
"##IG",
"##HT",
":",
"A",
"concept",
"for",
"a",
"decent",
"##ral",
"##ized",
"rights",
"management",
"system",
"based",
"on",
"block",
"##cha",
"##in",
".",
"In",
"2015",
"IEEE",
"5th",
"International",
"Conference",
"on",
"Consumer",
"Electronics",
"-",
"Berlin",
"(",
"ICC",
"##E",
"-",
"Berlin",
")",
".",
"IEEE",
",",
"345",
"β",
"34",
"##6",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"ICC",
"##E",
"-",
"Berlin",
".",
"2015",
".",
"73",
"##9",
"##12",
"##75",
"[",
"14",
"]",
"Nicolas",
"Ho",
"##uy",
".",
"2014",
".",
"The",
"Bit",
"##co",
"##in",
"Mining",
"Game",
".",
"SSR",
"##N",
"Electronic",
"Journal",
"(",
"ma",
"##r",
"2014",
")",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"213",
"##9",
"/",
"s",
"##s",
"##rn",
".",
"240",
"##7",
"##8",
"##34",
"[",
"15",
"]",
"Mi",
"##tsu",
"##ru",
"I",
"##wa",
"##mura",
",",
"Yu",
"##kin",
"##ob",
"##u",
"Kit",
"##am",
"##ura",
","
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 147 |
ore than 50% computational power is called the β50% attack.β The assumption that a blockchain is secure because double-spending by rewriting does not happen is guaranteed by the difficulty of getting 50% computational power and the difference between the attack cost and the profit.
To motivate nodes to make blocks, the system rewards some cryptocurrencies to the maker who succeeds in making a block. In Bitcoin, the system allows block maker to insert a βcoinbase transactionβ that pays maker some bitcoins | [
157,
6385,
18778,
1358,
25702,
6385,
12610,
117,
1105,
5928,
3454,
25185,
2430,
119,
1387,
119,
2825,
1284,
1457,
23156,
2646,
3171,
1103,
7510,
1104,
170,
15586,
6451,
13335,
2149,
5123,
3457,
136,
131,
21300,
1103,
4800,
1104,
27400,
2528,
1394,
1105,
2098,
18959,
5208,
16764,
1106,
3291,
8223,
16618,
1114,
1970,
2950,
8948,
119,
22916,
2249,
10952,
3603,
113,
184,
5822,
1387,
114,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
21640,
1580,
120,
188,
1116,
4558,
119,
25101,
1580,
22997,
1559,
164,
1479,
166,
138,
9705,
19773,
1116,
14477,
4164,
7346,
117,
16325,
19892,
10793,
6094,
15748,
1116,
117,
3406,
148,
12577,
4184,
6094,
24491,
117,
1105,
14141,
11657,
1548,
157,
11510,
4820,
6094,
7221,
119,
1446,
119,
8093,
7147,
1394,
15280,
2957,
119,
113,
1446,
114,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
12620,
1571,
120,
1853,
12882,
1559,
16229,
119,
1853,
12882,
1559,
1559,
1495,
170,
1197,
3190,
11083,
131,
7690,
1559,
119,
5507,
23117,
1568,
164,
1542,
166,
12865,
11985,
14477,
5933,
27997,
117,
14104,
2895,
1358,
23219,
14535,
117,
8790,
24830,
1182,
160,
6575,
1605,
3962,
117,
1335,
14410,
3031,
11896,
1968,
14117,
1611,
117,
1105,
138,
2293,
24617,
138,
4786,
9552,
119,
1410,
119,
1109,
8093,
7147,
1394,
118,
7457,
6082,
27551,
19806,
3910,
119,
1130,
1410,
16206,
9638,
1570,
3047,
1113,
2562,
7154,
1105,
11804,
20463,
119,
16206,
117,
21168,
782,
11876,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
139,
15556,
24491,
1181,
119,
1410,
119,
2539,
164,
1407,
166,
3096,
17470,
1105,
2055,
11867,
119,
1516,
119,
5096,
10008,
118,
1104,
118,
6955,
5096,
5710,
1753,
1106,
6955,
119,
1130,
4180,
28039,
23414,
1113,
1103,
7525,
1104,
2240,
1179,
24152,
4354,
119,
11338,
117,
150,
2249,
117,
119,
8413,
131,
120,
120,
23992,
2217,
7235,
119,
5795,
120,
10819,
120,
26477,
120,
1516,
120,
185,
1181,
2087,
120,
8785,
1633,
119,
185,
1181,
2087,
164,
1627,
166,
3177,
7939,
8411,
1105,
2893,
5503,
119,
1386,
119,
5096,
10008,
1104,
6955,
1169,
6955,
119,
1130,
1109,
9638,
16350,
1113,
1103,
7525,
1104,
4219,
4354,
113,
160,
27514,
1708,
1386,
114,
119,
1652,
119,
18630,
131,
120,
120,
7001,
119,
174,
7235,
1394,
14467,
2217,
1665,
119,
8916,
120,
12406,
120,
1195,
1548,
10973,
1568,
1545,
120,
1202,
6063,
120,
1851,
119,
185,
1181,
2087,
164,
1406,
166,
26824,
5933,
11896,
1968,
12610,
119,
1369,
119,
27400,
2528,
1394,
131,
138,
8536,
118,
1106,
118,
8536,
4828,
5948,
1449,
119,
113,
1369,
114,
119,
164,
1626,
166,
3401,
1182,
24580,
7355,
119,
1387,
119,
12504,
1104,
10736,
20955,
1566,
118,
7457,
8543,
156,
11741,
3408,
119,
113,
175,
15581,
1387,
114,
119,
170,
1197,
3190,
11083,
131,
8183,
1477,
119,
1371,
18630,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
8183,
1477,
119,
1371,
164,
1659,
166,
5928,
3454,
25185,
2430,
1105,
12107,
9552,
5082,
146,
3624,
14535,
119,
1857,
119,
1731,
1106,
7102,
170,
6082,
140,
2149,
5123,
3457,
1113,
170,
8093,
7147
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"T",
"##su",
"##tom",
"##u",
"Mat",
"##su",
"##moto",
",",
"and",
"Ken",
"##ji",
"Sai",
"##to",
".",
"2014",
".",
"Can",
"We",
"St",
"##abi",
"##li",
"##ze",
"the",
"Price",
"of",
"a",
"Cry",
"##pt",
"##oc",
"##ur",
"##ren",
"##cy",
"?",
":",
"Understanding",
"the",
"Design",
"of",
"Bit",
"##co",
"##in",
"and",
"Its",
"Po",
"##ten",
"##tial",
"to",
"Co",
"##mp",
"##ete",
"with",
"Central",
"Bank",
"Money",
".",
"SSR",
"##N",
"Electronic",
"Journal",
"(",
"o",
"##ct",
"2014",
")",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"213",
"##9",
"/",
"s",
"##s",
"##rn",
".",
"251",
"##9",
"##36",
"##7",
"[",
"16",
"]",
"A",
"##gg",
"##elo",
"##s",
"Ki",
"##ay",
"##ias",
",",
"Elias",
"Ko",
"##uts",
"##ou",
"##pia",
"##s",
",",
"Maria",
"K",
"##yr",
"##op",
"##ou",
"##lou",
",",
"and",
"Yi",
"##ann",
"##is",
"T",
"##sel",
"##ek",
"##ou",
"##nis",
".",
"2016",
".",
"Block",
"##cha",
"##in",
"Mining",
"Games",
".",
"(",
"2016",
")",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"114",
"##5",
"/",
"29",
"##40",
"##7",
"##16",
".",
"29",
"##40",
"##7",
"##7",
"##3",
"a",
"##r",
"##X",
"##iv",
":",
"160",
"##7",
".",
"02",
"##42",
"##0",
"[",
"17",
"]",
"Jun",
"##ichi",
"Ki",
"##shi",
"##gami",
",",
"Shi",
"##ger",
"##u",
"Fuji",
"##mura",
",",
"Hi",
"##rok",
"##i",
"W",
"##ata",
"##na",
"##be",
",",
"At",
"##sus",
"##hi",
"Na",
"##ka",
"##dai",
"##ra",
",",
"and",
"A",
"##ki",
"##hiko",
"A",
"##ku",
"##tsu",
".",
"2015",
".",
"The",
"Block",
"##cha",
"##in",
"-",
"Based",
"Digital",
"Content",
"Distribution",
"System",
".",
"In",
"2015",
"IEEE",
"Fifth",
"International",
"Conference",
"on",
"Big",
"Data",
"and",
"Cloud",
"Computing",
".",
"IEEE",
",",
"187",
"β",
"190",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"B",
"##DC",
"##lou",
"##d",
".",
"2015",
".",
"60",
"[",
"18",
"]",
"Ben",
"Laurie",
"and",
"Richard",
"Clayton",
".",
"2004",
".",
"Pro",
"##of",
"-",
"of",
"-",
"Work",
"Pro",
"##ves",
"Not",
"to",
"Work",
".",
"In",
"Third",
"##Works",
"##hop",
"on",
"the",
"Economics",
"of",
"##I",
"##n",
"##formation",
"Security",
".",
"Minneapolis",
",",
"M",
"##N",
",",
".",
"http",
":",
"/",
"/",
"info",
"##se",
"##con",
".",
"net",
"/",
"workshop",
"/",
"downloads",
"/",
"2004",
"/",
"p",
"##d",
"##f",
"/",
"clay",
"##ton",
".",
"p",
"##d",
"##f",
"[",
"19",
"]",
"De",
"##bin",
"Liu",
"and",
"Jean",
"Camp",
".",
"2006",
".",
"Pro",
"##of",
"of",
"Work",
"can",
"Work",
".",
"In",
"The",
"Fifth",
"Workshop",
"on",
"the",
"Economics",
"of",
"Information",
"Security",
"(",
"W",
"##EI",
"##S",
"2006",
")",
".",
"England",
".",
"https",
":",
"/",
"/",
"www",
".",
"e",
"##con",
"##in",
"##fo",
"##se",
"##c",
".",
"org",
"/",
"archive",
"/",
"we",
"##is",
"##20",
"##0",
"##6",
"/",
"do",
"##cs",
"/",
"50",
".",
"p",
"##d",
"##f",
"[",
"20",
"]",
"Sato",
"##shi",
"Na",
"##ka",
"##moto",
".",
"2008",
".",
"Bit",
"##co",
"##in",
":",
"A",
"peer",
"-",
"to",
"-",
"peer",
"electronic",
"cash",
"system",
".",
"(",
"2008",
")",
".",
"[",
"21",
"]",
"Men",
"##i",
"Rosen",
"##feld",
".",
"2014",
".",
"Analysis",
"of",
"Has",
"##hra",
"##te",
"-",
"Based",
"Double",
"S",
"##pen",
"##ding",
".",
"(",
"f",
"##eb",
"2014",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"140",
"##2",
".",
"2009",
"https",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"140",
"##2",
".",
"2009",
"[",
"22",
"]",
"Ken",
"##ji",
"Sai",
"##to",
"and",
"Mi",
"##tsu",
"##ru",
"I",
"##wa",
"##mura",
".",
"2018",
".",
"How",
"to",
"Make",
"a",
"Digital",
"C",
"##ur",
"##ren",
"##cy",
"on",
"a",
"Block",
"##cha"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 148 |
in the block. This mechanism looks like mining gold by spending costs, so making a block by solving PoW is called βminingβ, and block maker is called βminer.β
SUB-SECTION: TOKEN EXCHANGE ON BLOCKCHAIN
Instead of cryptocurrencies, There are several proposals that manage the rights of tokens control(e.g., a physical asset like lands, digital on | [
1394,
1457,
1895,
119,
113,
179,
1389,
1857,
114,
119,
170,
1197,
3190,
11083,
131,
12561,
119,
5037,
1559,
1559,
1475,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
12561,
119,
5037,
1559,
1559,
1475,
164,
1695,
166,
16837,
5765,
17784,
8508,
1733,
17439,
20309,
117,
14941,
24226,
1389,
1573,
24729,
17828,
3781,
117,
1105,
12927,
163,
10559,
1813,
119,
1504,
119,
9126,
3121,
7435,
9434,
2944,
15280,
1457,
5498,
19310,
1107,
27400,
2528,
1394,
119,
18919,
117,
3206,
117,
17880,
117,
4062,
1571,
782,
4389,
1477,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
1620,
1559,
120,
4087,
118,
124,
118,
5046,
1477,
118,
4335,
1580,
20829,
118,
125,
168,
1476,
164,
1572,
166,
6578,
1153,
23632,
5792,
119,
1857,
119,
9434,
118,
16522,
5230,
9765,
119,
6701,
4062,
117,
122,
113,
179,
1389,
1857,
114,
117,
9377,
782,
9377,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
12029,
119,
1857,
119,
10520,
20150,
1559,
164,
1512,
166,
14812,
10337,
19404,
23274,
2572,
117,
11336,
12635,
14812,
7807,
117,
1105,
5928,
3454,
25185,
2430,
119,
1857,
119,
16220,
22491,
3905,
6328,
1113,
8093,
7147,
4935,
119,
113,
179,
1389,
1857,
114,
119,
170,
1197,
3190,
11083,
131,
12561,
119,
5187,
23117,
1475,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
12561,
119,
5187,
23117,
1475,
164,
1744,
166,
13832,
19091,
6378,
1613,
117,
11281,
22327,
1200,
117,
5549,
5826,
117,
1105,
25585,
11896,
8419,
19828,
1161,
119,
1857,
119,
23580,
1658,
118,
5117,
1475,
7922,
118,
16068,
12192,
1706,
6378,
6433,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
171,
2858,
1830,
120,
3283,
120,
142,
11410,
1708,
120,
174,
9717,
118,
5117,
1475,
119,
182,
1181,
164,
1765,
166,
9152,
5296,
119,
1387,
119,
142,
8420,
14136,
131,
138,
5343,
11858,
4412,
3673,
1704,
3673,
13618,
21340,
1197,
119,
142,
8420,
14136,
1933,
3431,
2526,
17576,
113,
1387,
114,
117,
122,
782,
2724
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##in",
"St",
"##able",
".",
"(",
"j",
"##an",
"2018",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"1801",
".",
"06",
"##7",
"##7",
"##1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1801",
".",
"06",
"##7",
"##7",
"##1",
"[",
"23",
"]",
"Aye",
"##let",
"Sa",
"##pi",
"##rs",
"##ht",
"##ein",
",",
"Yo",
"##nat",
"##an",
"So",
"##mpo",
"##lins",
"##ky",
",",
"and",
"Aviv",
"Z",
"##oh",
"##ar",
".",
"2017",
".",
"Op",
"##ti",
"##mal",
"Self",
"##ish",
"Mining",
"St",
"##rate",
"##gies",
"in",
"Bit",
"##co",
"##in",
".",
"Springer",
",",
"Berlin",
",",
"Heidelberg",
",",
"51",
"##5",
"β",
"53",
"##2",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"100",
"##7",
"/",
"978",
"-",
"3",
"-",
"66",
"##2",
"-",
"54",
"##9",
"##70",
"-",
"4",
"_",
"30",
"[",
"24",
"]",
"Nathan",
"She",
"##dr",
"##off",
".",
"2018",
".",
"Self",
"-",
"Managing",
"Real",
"Estate",
".",
"Computer",
"51",
",",
"1",
"(",
"j",
"##an",
"2018",
")",
",",
"104",
"β",
"104",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"MC",
".",
"2018",
".",
"115",
"##100",
"##7",
"[",
"25",
"]",
"Ka",
"##zu",
"##yuki",
"Shu",
"##do",
",",
"Re",
"##iki",
"Ka",
"##nda",
",",
"and",
"Ken",
"##ji",
"Sai",
"##to",
".",
"2018",
".",
"Towards",
"Application",
"Port",
"##ability",
"on",
"Block",
"##cha",
"##ins",
".",
"(",
"j",
"##an",
"2018",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"1801",
".",
"01",
"##42",
"##1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1801",
".",
"01",
"##42",
"##1",
"[",
"26",
"]",
"En",
"##tri",
"##ken",
"William",
",",
"Shirley",
"Diet",
"##er",
",",
"Jacob",
"Evans",
",",
"and",
"Sachs",
"Na",
"##sta",
"##ssi",
"##a",
".",
"2018",
".",
"ER",
"##C",
"-",
"72",
"##1",
"Non",
"-",
"Fun",
"##gible",
"To",
"##ken",
"Standard",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"b",
"##lo",
"##b",
"/",
"master",
"/",
"E",
"##IP",
"##S",
"/",
"e",
"##ip",
"-",
"72",
"##1",
".",
"m",
"##d",
"[",
"27",
"]",
"Gavin",
"Wood",
".",
"2014",
".",
"E",
"##ther",
"##eum",
":",
"A",
"secure",
"decent",
"##ral",
"##ised",
"general",
"##ised",
"transaction",
"ledge",
"##r",
".",
"E",
"##ther",
"##eum",
"project",
"yellow",
"paper",
"151",
"(",
"2014",
")",
",",
"1",
"β",
"32"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 149 |
in the block. This mechanism looks like mining gold by spending costs, so making a block by solving PoW is called βminingβ, and block maker is called βminer.β
SUB-SECTION: TOKEN EXCHANGE ON BLOCKCHAIN
Instead of cryptocurrencies, There are several proposals that manage the rights of tokens control(e.g., a physical asset like lands, digital on | [
1394,
1457,
1895,
119,
113,
179,
1389,
1857,
114,
119,
170,
1197,
3190,
11083,
131,
12561,
119,
5037,
1559,
1559,
1475,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
12561,
119,
5037,
1559,
1559,
1475,
164,
1695,
166,
16837,
5765,
17784,
8508,
1733,
17439,
20309,
117,
14941,
24226,
1389,
1573,
24729,
17828,
3781,
117,
1105,
12927,
163,
10559,
1813,
119,
1504,
119,
9126,
3121,
7435,
9434,
2944,
15280,
1457,
5498,
19310,
1107,
27400,
2528,
1394,
119,
18919,
117,
3206,
117,
17880,
117,
4062,
1571,
782,
4389,
1477,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
1620,
1559,
120,
4087,
118,
124,
118,
5046,
1477,
118,
4335,
1580,
20829,
118,
125,
168,
1476,
164,
1572,
166,
6578,
1153,
23632,
5792,
119,
1857,
119,
9434,
118,
16522,
5230,
9765,
119,
6701,
4062,
117,
122,
113,
179,
1389,
1857,
114,
117,
9377,
782,
9377,
119,
18630,
131,
120,
120,
9465,
119,
8916,
120,
1275,
119,
6745,
1580,
120,
12029,
119,
1857,
119,
10520,
20150,
1559,
164,
1512,
166,
14812,
10337,
19404,
23274,
2572,
117,
11336,
12635,
14812,
7807,
117,
1105,
5928,
3454,
25185,
2430,
119,
1857,
119,
16220,
22491,
3905,
6328,
1113,
8093,
7147,
4935,
119,
113,
179,
1389,
1857,
114,
119,
170,
1197,
3190,
11083,
131,
12561,
119,
5187,
23117,
1475,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
12561,
119,
5187,
23117,
1475,
164,
1744,
166,
13832,
19091,
6378,
1613,
117,
11281,
22327,
1200,
117,
5549,
5826,
117,
1105,
25585,
11896,
8419,
19828,
1161,
119,
1857,
119,
23580,
1658,
118,
5117,
1475,
7922,
118,
16068,
12192,
1706,
6378,
6433,
119,
18630,
131,
120,
120,
176,
7088,
10354,
119,
3254,
120,
3084,
12807,
1818,
120,
142,
11410,
1116,
120,
171,
2858,
1830,
120,
3283,
120,
142,
11410,
1708,
120,
174,
9717,
118,
5117,
1475,
119,
182,
1181,
164,
1765,
166,
9152,
5296,
119,
1387,
119,
142,
8420,
14136,
131,
138,
5343,
11858,
4412,
3673,
1704,
3673,
13618,
21340,
1197,
119,
142,
8420,
14136,
1933,
3431,
2526,
17576,
113,
1387,
114,
117,
122,
782,
2724
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##in",
"St",
"##able",
".",
"(",
"j",
"##an",
"2018",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"1801",
".",
"06",
"##7",
"##7",
"##1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1801",
".",
"06",
"##7",
"##7",
"##1",
"[",
"23",
"]",
"Aye",
"##let",
"Sa",
"##pi",
"##rs",
"##ht",
"##ein",
",",
"Yo",
"##nat",
"##an",
"So",
"##mpo",
"##lins",
"##ky",
",",
"and",
"Aviv",
"Z",
"##oh",
"##ar",
".",
"2017",
".",
"Op",
"##ti",
"##mal",
"Self",
"##ish",
"Mining",
"St",
"##rate",
"##gies",
"in",
"Bit",
"##co",
"##in",
".",
"Springer",
",",
"Berlin",
",",
"Heidelberg",
",",
"51",
"##5",
"β",
"53",
"##2",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"100",
"##7",
"/",
"978",
"-",
"3",
"-",
"66",
"##2",
"-",
"54",
"##9",
"##70",
"-",
"4",
"_",
"30",
"[",
"24",
"]",
"Nathan",
"She",
"##dr",
"##off",
".",
"2018",
".",
"Self",
"-",
"Managing",
"Real",
"Estate",
".",
"Computer",
"51",
",",
"1",
"(",
"j",
"##an",
"2018",
")",
",",
"104",
"β",
"104",
".",
"https",
":",
"/",
"/",
"doi",
".",
"org",
"/",
"10",
".",
"110",
"##9",
"/",
"MC",
".",
"2018",
".",
"115",
"##100",
"##7",
"[",
"25",
"]",
"Ka",
"##zu",
"##yuki",
"Shu",
"##do",
",",
"Re",
"##iki",
"Ka",
"##nda",
",",
"and",
"Ken",
"##ji",
"Sai",
"##to",
".",
"2018",
".",
"Towards",
"Application",
"Port",
"##ability",
"on",
"Block",
"##cha",
"##ins",
".",
"(",
"j",
"##an",
"2018",
")",
".",
"a",
"##r",
"##X",
"##iv",
":",
"1801",
".",
"01",
"##42",
"##1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1801",
".",
"01",
"##42",
"##1",
"[",
"26",
"]",
"En",
"##tri",
"##ken",
"William",
",",
"Shirley",
"Diet",
"##er",
",",
"Jacob",
"Evans",
",",
"and",
"Sachs",
"Na",
"##sta",
"##ssi",
"##a",
".",
"2018",
".",
"ER",
"##C",
"-",
"72",
"##1",
"Non",
"-",
"Fun",
"##gible",
"To",
"##ken",
"Standard",
".",
"https",
":",
"/",
"/",
"g",
"##ith",
"##ub",
".",
"com",
"/",
"et",
"##here",
"##um",
"/",
"E",
"##IP",
"##s",
"/",
"b",
"##lo",
"##b",
"/",
"master",
"/",
"E",
"##IP",
"##S",
"/",
"e",
"##ip",
"-",
"72",
"##1",
".",
"m",
"##d",
"[",
"27",
"]",
"Gavin",
"Wood",
".",
"2014",
".",
"E",
"##ther",
"##eum",
":",
"A",
"secure",
"decent",
"##ral",
"##ised",
"general",
"##ised",
"transaction",
"ledge",
"##r",
".",
"E",
"##ther",
"##eum",
"project",
"yellow",
"paper",
"151",
"(",
"2014",
")",
",",
"1",
"β",
"32"
] | Attack Incentive and Security of Exchanging Tokens on Proof of Work Blockchain | 150 |
Analysis of the XRP Ledger Consensus Protocol
Brad Chase Ethan MacBrough
Ripple Research
{bchase,emacbrough}@ripple.com
February 21, 2018
Abstract
The XRP Ledger Consensus Protocol is a previously developed con-
sensus protocol powering the XRP Ledger. It is a low-latency Byzantine
agreement protocol, capable of reaching consensus without full agreement
on which nodes are members of the network. We present a detailed expla-
nation of the algorithm and derive conditions for its safety and livenes | [
12504,
1104,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
7796,
5870,
5386,
6603,
2064,
14929,
155,
9717,
7136,
2713,
196,
171,
18956,
117,
9712,
7409,
12725,
6289,
198,
137,
13579,
7136,
119,
3254,
1428,
1626,
117,
1857,
138,
4832,
15017,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
1110,
170,
2331,
1872,
14255,
118,
14516,
2316,
1361,
11309,
1540,
1158,
1103,
161,
20336,
18657,
2895,
119,
1135,
1110,
170,
1822,
118,
1523,
7232,
8377,
3311,
11309,
117,
4451,
1104,
3634,
10923,
1443,
1554,
3311,
1113,
1134,
15029,
1132,
1484,
1104,
1103,
2443,
119,
1284,
1675,
170,
6448,
4252,
1643,
1742,
118,
3790,
1104,
1103,
9932,
1105,
20292,
2975,
1111,
1157,
3429,
1105,
1686,
1757,
119,
122,
13813,
1109,
161,
20336,
18657,
2895,
1110,
170,
4901,
7727,
1449,
12619,
4713,
1106,
4036,
2860,
2343,
1306,
8709,
1213,
1103,
1362,
119,
20961,
1439,
170,
4901,
8536,
118,
1106,
118,
8536,
2443,
117,
1103,
161,
20336,
18657,
2895,
4876,
1103,
1269,
7806,
1112,
1168,
3539,
16408,
11604,
9885,
1107,
10878,
2702,
118,
5369,
1104,
4381,
1105,
13291,
2443,
118,
2043,
10923,
1113,
1103,
1352,
1104,
4795,
5756,
1105,
5233,
1116,
119,
1752,
3000,
1105,
1173,
7042,
1118,
17834,
3084,
2393,
119,
164,
1275,
166,
117,
1103,
9932,
10311,
161,
20336,
9474,
1116,
1292,
2645,
1606,
170,
8377,
6088,
26827,
3311,
11309,
1166,
14998,
9373,
4841,
6097,
9975,
117,
1303,
2665,
2752,
1106,
1112,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
117,
1137,
161,
20336,
149,
13113,
1111,
1603,
119,
138,
4832,
15017,
1193,
117,
1103,
161,
20336,
18657,
2895,
2443,
1110,
170,
16498,
1906,
1352,
3395,
164,
130,
166,
119,
1109,
16498,
1906,
1352,
1110,
1103,
21340,
1197,
4441,
1118,
1296,
14372,
1107,
1103,
2443,
1105,
1352,
26829,
18420,
1106,
14409,
7402,
1118,
7550,
1104,
1103,
2443,
119,
2857,
15029,
5340,
1113,
3741,
1104,
14409,
1106,
6058,
1106,
1103,
1352,
117,
170,
13618,
6165,
11309,
188,
25392,
9387,
1260,
2083,
25685,
5668,
2995,
1111,
13649,
14409,
1439,
1296,
1383,
1105,
1293,
1106,
6058,
14409,
1106,
9509,
1103,
1207,
21340,
1197,
1352,
119,
4516,
117,
1103,
1648,
1104,
161,
20336,
149,
13113,
1110,
1178,
1106,
1294,
1103,
2443,
2519,
3311,
1113,
3741,
1104,
14409,
117,
1136,
1113,
1103,
3438,
1137,
9386,
1104,
1343,
14409,
119,
1249,
1263,
1112,
15029,
5340,
1113,
170,
13618,
1383,
117,
1103,
13618,
6165,
11309,
24512,
1115,
1451,
14372,
21241,
170,
8080,
21340,
1197,
119,
1249,
170,
8377,
6088,
26827,
11309,
117,
161,
20336,
149,
13113,
1538,
4732,
1256,
1107,
1103,
2915,
1104,
6088,
1183,
1137,
12477,
8031,
4179,
6635,
119,
8377,
6088,
26827,
10923,
19755,
1138,
170,
3987,
1607,
117,
1133,
1211,
4752,
3073,
11708,
1776,
1158,
3311,
1113,
1103,
11309,
6635,
164,
129,
117,
124,
166,
119,
1109,
4267,
2050,
1394,
118,
176,
6592,
12802,
7987,
1104,
161,
20336,
149,
13113,
1110,
1115,
1122,
24512,
20904,
1114,
1178,
122,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
13847,
119,
5004,
19598,
1477,
1964,
1475,
7597,
3311,
1113,
1150,
18557,
117,
3525,
170,
11858,
4412,
2200,
1501,
2443
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
13,
14,
13,
14,
14,
14,
13,
14,
14,
0,
0,
13,
14,
0,
13,
14,
14,
14,
0,
0,
13,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
5,
6,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
5,
6,
6,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
21,
22,
22,
22,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
13,
14,
13,
14,
14,
14,
13,
14,
14,
0,
0,
13,
14,
0,
13,
14,
14,
14,
0,
0,
13,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
5,
6,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
20,
20,
0,
5,
6,
6,
6,
6,
6,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
5,
6,
6,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
21,
22,
22,
22,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"Analysis",
"of",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"Brad",
"Chase",
"Ethan",
"Mac",
"##B",
"##rough",
"R",
"##ip",
"##ple",
"Research",
"{",
"b",
"##chase",
",",
"em",
"##ac",
"##bro",
"##ugh",
"}",
"@",
"rip",
"##ple",
".",
"com",
"February",
"21",
",",
"2018",
"A",
"##bs",
"##tract",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"is",
"a",
"previously",
"developed",
"con",
"-",
"se",
"##ns",
"##us",
"protocol",
"power",
"##ing",
"the",
"X",
"##RP",
"Led",
"##ger",
".",
"It",
"is",
"a",
"low",
"-",
"late",
"##ncy",
"Byzantine",
"agreement",
"protocol",
",",
"capable",
"of",
"reaching",
"consensus",
"without",
"full",
"agreement",
"on",
"which",
"nodes",
"are",
"members",
"of",
"the",
"network",
".",
"We",
"present",
"a",
"detailed",
"ex",
"##p",
"##la",
"-",
"nation",
"of",
"the",
"algorithm",
"and",
"derive",
"conditions",
"for",
"its",
"safety",
"and",
"live",
"##ness",
".",
"1",
"Introduction",
"The",
"X",
"##RP",
"Led",
"##ger",
"is",
"a",
"distributed",
"payment",
"system",
"enabling",
"users",
"to",
"transfer",
"value",
"sea",
"##m",
"##lessly",
"around",
"the",
"world",
".",
"Operating",
"within",
"a",
"distributed",
"peer",
"-",
"to",
"-",
"peer",
"network",
",",
"the",
"X",
"##RP",
"Led",
"##ger",
"faces",
"the",
"same",
"challenges",
"as",
"other",
"digital",
"cu",
"##rre",
"##ncies",
"in",
"preventing",
"double",
"-",
"spending",
"of",
"funds",
"and",
"ensuring",
"network",
"-",
"wide",
"consensus",
"on",
"the",
"state",
"of",
"user",
"accounts",
"and",
"balance",
"##s",
".",
"First",
"proposed",
"and",
"then",
"implemented",
"by",
"Schwartz",
"et",
"al",
".",
"[",
"10",
"]",
",",
"the",
"algorithm",
"underlying",
"X",
"##RP",
"solve",
"##s",
"these",
"problems",
"using",
"a",
"Byzantine",
"fault",
"tolerant",
"agreement",
"protocol",
"over",
"collectively",
"trusted",
"sub",
"##net",
"##works",
",",
"here",
"##by",
"referred",
"to",
"as",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
",",
"or",
"X",
"##RP",
"L",
"##CP",
"for",
"short",
".",
"A",
"##bs",
"##tract",
"##ly",
",",
"the",
"X",
"##RP",
"Led",
"##ger",
"network",
"is",
"a",
"replica",
"##ted",
"state",
"machine",
"[",
"9",
"]",
".",
"The",
"replica",
"##ted",
"state",
"is",
"the",
"ledge",
"##r",
"maintained",
"by",
"each",
"node",
"in",
"the",
"network",
"and",
"state",
"transitions",
"correspond",
"to",
"transactions",
"submitted",
"by",
"clients",
"of",
"the",
"network",
".",
"Once",
"nodes",
"agree",
"on",
"sets",
"of",
"transactions",
"to",
"apply",
"to",
"the",
"state",
",",
"a",
"transaction",
"processing",
"protocol",
"s",
"##pec",
"##ifies",
"de",
"##ter",
"##mini",
"##stic",
"rules",
"for",
"ordering",
"transactions",
"within",
"each",
"set",
"and",
"how",
"to",
"apply",
"transactions",
"to",
"generate",
"the",
"new",
"ledge",
"##r",
"state",
".",
"Thus",
",",
"the",
"role",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"only",
"to",
"make",
"the",
"network",
"reach",
"agreement",
"on",
"sets",
"of",
"transactions",
",",
"not",
"on",
"the",
"content",
"or",
"outcome",
"of",
"those",
"transactions",
".",
"As",
"long",
"as",
"nodes",
"agree",
"on",
"a",
"transaction",
"set",
",",
"the",
"transaction",
"processing",
"protocol",
"guarantees",
"that",
"every",
"node",
"generates",
"a",
"consistent",
"ledge",
"##r",
".",
"As",
"a",
"Byzantine",
"fault",
"tolerant",
"protocol",
",",
"X",
"##RP",
"L",
"##CP",
"must",
"operate",
"even",
"in",
"the",
"presence",
"of",
"fault",
"##y",
"or",
"ma",
"##lic",
"##ious",
"participants",
".",
"Byzantine",
"fault",
"tolerant",
"consensus",
"protocols",
"have",
"a",
"rich",
"history",
",",
"but",
"most",
"require",
"pre",
"##ex",
"##ist",
"##ing",
"agreement",
"on",
"the",
"protocol",
"participants",
"[",
"8",
",",
"3",
"]",
".",
"The",
"di",
"##st",
"##in",
"-",
"g",
"##ui",
"##shing",
"characteristic",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"that",
"it",
"guarantees",
"consistency",
"with",
"only",
"1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1802",
".",
"07",
"##24",
"##2",
"##v",
"##1",
"partial",
"agreement",
"on",
"who",
"participates",
",",
"allowing",
"a",
"decent",
"##ral",
"##ized",
"open",
"network"
] | Analysis of the XRP Ledger Consensus Protocol | 151 |
Analysis of the XRP Ledger Consensus Protocol
Brad Chase Ethan MacBrough
Ripple Research
{bchase,emacbrough}@ripple.com
February 21, 2018
Abstract
The XRP Ledger Consensus Protocol is a previously developed con-
sensus protocol powering the XRP Ledger. It is a low-latency Byzantine
agreement protocol, capable of reaching consensus without full agreement
on which nodes are members of the network. We present a detailed expla-
nation of the algorithm and derive conditions for its safety and livenes | [
12504,
1104,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
7796,
5870,
5386,
6603,
2064,
14929,
155,
9717,
7136,
2713,
196,
171,
18956,
117,
9712,
7409,
12725,
6289,
198,
137,
13579,
7136,
119,
3254,
1428,
1626,
117,
1857,
138,
4832,
15017,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
1110,
170,
2331,
1872,
14255,
118,
14516,
2316,
1361,
11309,
1540,
1158,
1103,
161,
20336,
18657,
2895,
119,
1135,
1110,
170,
1822,
118,
1523,
7232,
8377,
3311,
11309,
117,
4451,
1104,
3634,
10923,
1443,
1554,
3311,
1113,
1134,
15029,
1132,
1484,
1104,
1103,
2443,
119,
1284,
1675,
170,
6448,
4252,
1643,
1742,
118,
3790,
1104,
1103,
9932,
1105,
20292,
2975,
1111,
1157,
3429,
1105,
1686,
1757,
119,
122,
13813,
1109,
161,
20336,
18657,
2895,
1110,
170,
4901,
7727,
1449,
12619,
4713,
1106,
4036,
2860,
2343,
1306,
8709,
1213,
1103,
1362,
119,
20961,
1439,
170,
4901,
8536,
118,
1106,
118,
8536,
2443,
117,
1103,
161,
20336,
18657,
2895,
4876,
1103,
1269,
7806,
1112,
1168,
3539,
16408,
11604,
9885,
1107,
10878,
2702,
118,
5369,
1104,
4381,
1105,
13291,
2443,
118,
2043,
10923,
1113,
1103,
1352,
1104,
4795,
5756,
1105,
5233,
1116,
119,
1752,
3000,
1105,
1173,
7042,
1118,
17834,
3084,
2393,
119,
164,
1275,
166,
117,
1103,
9932,
10311,
161,
20336,
9474,
1116,
1292,
2645,
1606,
170,
8377,
6088,
26827,
3311,
11309,
1166,
14998,
9373,
4841,
6097,
9975,
117,
1303,
2665,
2752,
1106,
1112,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
117,
1137,
161,
20336,
149,
13113,
1111,
1603,
119,
138,
4832,
15017,
1193,
117,
1103,
161,
20336,
18657,
2895,
2443,
1110,
170,
16498,
1906,
1352,
3395,
164,
130,
166,
119,
1109,
16498,
1906,
1352,
1110,
1103,
21340,
1197,
4441,
1118,
1296,
14372,
1107,
1103,
2443,
1105,
1352,
26829,
18420,
1106,
14409,
7402,
1118,
7550,
1104,
1103,
2443,
119,
2857,
15029,
5340,
1113,
3741,
1104,
14409,
1106,
6058,
1106,
1103,
1352,
117,
170,
13618,
6165,
11309,
188,
25392,
9387,
1260,
2083,
25685,
5668,
2995,
1111,
13649,
14409,
1439,
1296,
1383,
1105,
1293,
1106,
6058,
14409,
1106,
9509,
1103,
1207,
21340,
1197,
1352,
119,
4516,
117,
1103,
1648,
1104,
161,
20336,
149,
13113,
1110,
1178,
1106,
1294,
1103,
2443,
2519,
3311,
1113,
3741,
1104,
14409,
117,
1136,
1113,
1103,
3438,
1137,
9386,
1104,
1343,
14409,
119,
1249,
1263,
1112,
15029,
5340,
1113,
170,
13618,
1383,
117,
1103,
13618,
6165,
11309,
24512,
1115,
1451,
14372,
21241,
170,
8080,
21340,
1197,
119,
1249,
170,
8377,
6088,
26827,
11309,
117,
161,
20336,
149,
13113,
1538,
4732,
1256,
1107,
1103,
2915,
1104,
6088,
1183,
1137,
12477,
8031,
4179,
6635,
119,
8377,
6088,
26827,
10923,
19755,
1138,
170,
3987,
1607,
117,
1133,
1211,
4752,
3073,
11708,
1776,
1158,
3311,
1113,
1103,
11309,
6635,
164,
129,
117,
124,
166,
119,
1109,
4267,
2050,
1394,
118,
176,
6592,
12802,
7987,
1104,
161,
20336,
149,
13113,
1110,
1115,
1122,
24512,
20904,
1114,
1178,
122,
8413,
131,
120,
120,
170,
1197,
8745,
1964,
119,
8916,
120,
170,
4832,
120,
13847,
119,
5004,
19598,
1477,
1964,
1475,
7597,
3311,
1113,
1150,
18557,
117,
3525,
170,
11858,
4412,
2200,
1501,
2443
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
19,
20,
2,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
5,
0,
0,
0,
0,
0,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
19,
20,
2,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
5,
0,
0,
0,
0,
0,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"Analysis",
"of",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"Brad",
"Chase",
"Ethan",
"Mac",
"##B",
"##rough",
"R",
"##ip",
"##ple",
"Research",
"{",
"b",
"##chase",
",",
"em",
"##ac",
"##bro",
"##ugh",
"}",
"@",
"rip",
"##ple",
".",
"com",
"February",
"21",
",",
"2018",
"A",
"##bs",
"##tract",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"is",
"a",
"previously",
"developed",
"con",
"-",
"se",
"##ns",
"##us",
"protocol",
"power",
"##ing",
"the",
"X",
"##RP",
"Led",
"##ger",
".",
"It",
"is",
"a",
"low",
"-",
"late",
"##ncy",
"Byzantine",
"agreement",
"protocol",
",",
"capable",
"of",
"reaching",
"consensus",
"without",
"full",
"agreement",
"on",
"which",
"nodes",
"are",
"members",
"of",
"the",
"network",
".",
"We",
"present",
"a",
"detailed",
"ex",
"##p",
"##la",
"-",
"nation",
"of",
"the",
"algorithm",
"and",
"derive",
"conditions",
"for",
"its",
"safety",
"and",
"live",
"##ness",
".",
"1",
"Introduction",
"The",
"X",
"##RP",
"Led",
"##ger",
"is",
"a",
"distributed",
"payment",
"system",
"enabling",
"users",
"to",
"transfer",
"value",
"sea",
"##m",
"##lessly",
"around",
"the",
"world",
".",
"Operating",
"within",
"a",
"distributed",
"peer",
"-",
"to",
"-",
"peer",
"network",
",",
"the",
"X",
"##RP",
"Led",
"##ger",
"faces",
"the",
"same",
"challenges",
"as",
"other",
"digital",
"cu",
"##rre",
"##ncies",
"in",
"preventing",
"double",
"-",
"spending",
"of",
"funds",
"and",
"ensuring",
"network",
"-",
"wide",
"consensus",
"on",
"the",
"state",
"of",
"user",
"accounts",
"and",
"balance",
"##s",
".",
"First",
"proposed",
"and",
"then",
"implemented",
"by",
"Schwartz",
"et",
"al",
".",
"[",
"10",
"]",
",",
"the",
"algorithm",
"underlying",
"X",
"##RP",
"solve",
"##s",
"these",
"problems",
"using",
"a",
"Byzantine",
"fault",
"tolerant",
"agreement",
"protocol",
"over",
"collectively",
"trusted",
"sub",
"##net",
"##works",
",",
"here",
"##by",
"referred",
"to",
"as",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
",",
"or",
"X",
"##RP",
"L",
"##CP",
"for",
"short",
".",
"A",
"##bs",
"##tract",
"##ly",
",",
"the",
"X",
"##RP",
"Led",
"##ger",
"network",
"is",
"a",
"replica",
"##ted",
"state",
"machine",
"[",
"9",
"]",
".",
"The",
"replica",
"##ted",
"state",
"is",
"the",
"ledge",
"##r",
"maintained",
"by",
"each",
"node",
"in",
"the",
"network",
"and",
"state",
"transitions",
"correspond",
"to",
"transactions",
"submitted",
"by",
"clients",
"of",
"the",
"network",
".",
"Once",
"nodes",
"agree",
"on",
"sets",
"of",
"transactions",
"to",
"apply",
"to",
"the",
"state",
",",
"a",
"transaction",
"processing",
"protocol",
"s",
"##pec",
"##ifies",
"de",
"##ter",
"##mini",
"##stic",
"rules",
"for",
"ordering",
"transactions",
"within",
"each",
"set",
"and",
"how",
"to",
"apply",
"transactions",
"to",
"generate",
"the",
"new",
"ledge",
"##r",
"state",
".",
"Thus",
",",
"the",
"role",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"only",
"to",
"make",
"the",
"network",
"reach",
"agreement",
"on",
"sets",
"of",
"transactions",
",",
"not",
"on",
"the",
"content",
"or",
"outcome",
"of",
"those",
"transactions",
".",
"As",
"long",
"as",
"nodes",
"agree",
"on",
"a",
"transaction",
"set",
",",
"the",
"transaction",
"processing",
"protocol",
"guarantees",
"that",
"every",
"node",
"generates",
"a",
"consistent",
"ledge",
"##r",
".",
"As",
"a",
"Byzantine",
"fault",
"tolerant",
"protocol",
",",
"X",
"##RP",
"L",
"##CP",
"must",
"operate",
"even",
"in",
"the",
"presence",
"of",
"fault",
"##y",
"or",
"ma",
"##lic",
"##ious",
"participants",
".",
"Byzantine",
"fault",
"tolerant",
"consensus",
"protocols",
"have",
"a",
"rich",
"history",
",",
"but",
"most",
"require",
"pre",
"##ex",
"##ist",
"##ing",
"agreement",
"on",
"the",
"protocol",
"participants",
"[",
"8",
",",
"3",
"]",
".",
"The",
"di",
"##st",
"##in",
"-",
"g",
"##ui",
"##shing",
"characteristic",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"that",
"it",
"guarantees",
"consistency",
"with",
"only",
"1",
"http",
":",
"/",
"/",
"a",
"##r",
"##xi",
"##v",
".",
"org",
"/",
"a",
"##bs",
"/",
"1802",
".",
"07",
"##24",
"##2",
"##v",
"##1",
"partial",
"agreement",
"on",
"who",
"participates",
",",
"allowing",
"a",
"decent",
"##ral",
"##ized",
"open",
"network"
] | Analysis of the XRP Ledger Consensus Protocol | 152 |
s.
1 Introduction
The XRP Ledger is a distributed payment system enabling users to transfer
value seamlessly around the world. Operating within a distributed peer-to-peer
network, the XRP Ledger faces the same challenges as other digital currencies
in preventing double-spending of funds and ensuring network-wide consensus on
the state of user accounts and balances. First proposed and then implemented
by Schwartz et al. [10], the algorithm underlying XRP solves these problems
using a Byzantine fault tole | [
119,
22439,
1106,
1168,
11858,
4412,
2200,
10923,
14975,
1176,
6777,
118,
1104,
118,
1250,
164,
128,
166,
1137,
6777,
118,
1104,
118,
8219,
164,
123,
166,
117,
161,
20336,
149,
13113,
1144,
1290,
1157,
12548,
2136,
2211,
13618,
1523,
7232,
1105,
2299,
1194,
16156,
1111,
1157,
4713,
119,
1438,
117,
1443,
6029,
5340,
118,
1441,
1204,
1113,
1103,
2443,
6635,
117,
4713,
1253,
1444,
170,
1236,
1106,
4959,
2480,
1147,
3026,
1104,
2443,
14097,
1209,
1730,
1106,
170,
8080,
2443,
1352,
119,
1130,
1142,
3545,
117,
1296,
4795,
15473,
12028,
170,
3527,
14372,
2190,
1137,
7414,
2162,
117,
1134,
1110,
1103,
1383,
1104,
15029,
2133,
7416,
1122,
1209,
5113,
1106,
1165,
1543,
6134,
1164,
1103,
2443,
1352,
119,
1135,
1110,
1103,
6326,
1104,
1251,
3111,
1104,
5663,
15029,
112,
7414,
2162,
1116,
1115,
17579,
2443,
3429,
119,
1249,
1758,
1107,
1103,
1560,
1653,
26311,
164,
1275,
166,
117,
1103,
5867,
19235,
8875,
1108,
2034,
2475,
1106,
1129,
4986,
1406,
110,
1104,
1103,
7414,
2162,
119,
1760,
2457,
3622,
1224,
3228,
1103,
5663,
4930,
1108,
1939,
4986,
135,
1969,
110,
164,
122,
166,
119,
10470,
1142,
6406,
117,
1412,
2273,
1107,
1142,
1250,
1110,
1106,
1660,
170,
2330,
1105,
6448,
7108,
1104,
161,
20336,
149,
13113,
1105,
20292,
1103,
3238,
2975,
1113,
7414,
2162,
19235,
1111,
20904,
1105,
1686,
1757,
119,
1284,
1209,
1136,
6265,
1103,
13618,
1348,
27921,
1116,
1104,
161,
20336,
112,
188,
21340,
1197,
1137,
161,
20336,
112,
188,
6245,
1112,
170,
3539,
10202,
117,
1133,
1939,
2458,
1103,
9932,
1112,
170,
1704,
10923,
11309,
119,
1284,
1231,
118,
17459,
1103,
1160,
2988,
19235,
2686,
1105,
2194,
170,
1423,
13808,
4930,
1134,
1110,
1226,
2787,
1206,
1103,
22379,
1104,
164,
1275,
166,
1105,
164,
122,
166,
119,
1284,
1145,
1437,
1115,
1223,
170,
1167,
1704,
6088,
2235,
1134,
1108,
1136,
1737,
1107,
1103,
1560,
1653,
26311,
1133,
1110,
21768,
1193,
1215,
1107,
1103,
1844,
3783,
117,
1103,
5867,
19235,
1110,
2140,
4986,
135,
3078,
110,
1104,
1103,
7414,
2162,
119,
4428,
117,
1195,
1437,
1115,
1219,
1103,
1675,
5251,
1104,
22767,
8985,
9373,
2443,
9298,
164,
1367,
166,
117,
1103,
161,
20336,
2443,
1110,
1241,
2914,
1105,
2834,
1561,
107,
5342,
107,
1543,
1185,
1977,
5070,
119,
1188,
1844,
2790,
170,
18379,
1871,
1164,
1103,
3429,
1104,
161,
20336,
18657,
2895,
1107,
1157,
1954,
1352,
119,
1438,
117,
1106,
8343,
3407,
18605,
1107,
11027,
7414,
2162,
1116,
1107,
1103,
2174,
117,
1195,
1156,
9353,
1126,
9932,
1115,
3370,
2739,
1106,
1103,
1560,
2637,
19235,
22379,
119,
1130,
170,
26563,
2526,
164,
127,
166,
117,
1195,
1675,
170,
2281,
4174,
10923,
9932,
1270,
3291,
26443,
1115,
2211,
1116,
1103,
19235,
4930,
1106,
1178,
135,
2539,
110,
1107,
1103,
1704,
6088,
2235,
117,
2834,
1243,
5342,
1107,
1251,
2443,
1115,
2068,
1548,
16847,
1103,
19235,
4930,
117,
1105,
1144,
1317,
1168,
4625,
1115,
1294,
1122,
6736,
1111,
2028,
5861,
161,
20336,
149,
13113,
119,
1188,
2526,
2456,
3411,
3120,
1106,
1437,
1115,
1103,
161,
20336,
18657,
2895,
1110,
2914,
1107,
1103,
10572,
1229,
6468,
1158,
1106,
3291,
26443,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
5,
6,
5,
6,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
23,
24,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
5,
6,
5,
6,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
23,
24,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
7,
8,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
".",
"Compared",
"to",
"other",
"decent",
"##ral",
"##ized",
"consensus",
"algorithms",
"like",
"proof",
"-",
"of",
"-",
"work",
"[",
"7",
"]",
"or",
"proof",
"-",
"of",
"-",
"stake",
"[",
"2",
"]",
",",
"X",
"##RP",
"L",
"##CP",
"has",
"since",
"its",
"inception",
"provided",
"lower",
"transaction",
"late",
"##ncy",
"and",
"higher",
"through",
"##put",
"for",
"its",
"users",
".",
"However",
",",
"without",
"uniform",
"agree",
"-",
"men",
"##t",
"on",
"the",
"network",
"participants",
",",
"users",
"still",
"need",
"a",
"way",
"to",
"determine",
"whether",
"their",
"choice",
"of",
"network",
"peers",
"will",
"lead",
"to",
"a",
"consistent",
"network",
"state",
".",
"In",
"this",
"setting",
",",
"each",
"user",
"individually",
"defines",
"a",
"unique",
"node",
"list",
"or",
"UN",
"##L",
",",
"which",
"is",
"the",
"set",
"of",
"nodes",
"whose",
"messages",
"it",
"will",
"listen",
"to",
"when",
"making",
"decisions",
"about",
"the",
"network",
"state",
".",
"It",
"is",
"the",
"intersection",
"of",
"any",
"pair",
"of",
"correct",
"nodes",
"'",
"UN",
"##L",
"##s",
"that",
"determines",
"network",
"safety",
".",
"As",
"described",
"in",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
",",
"the",
"minimum",
"overlap",
"requirement",
"was",
"originally",
"believed",
"to",
"be",
"roughly",
"20",
"%",
"of",
"the",
"UN",
"##L",
".",
"An",
"independent",
"analysis",
"later",
"suggested",
"the",
"correct",
"bound",
"was",
"instead",
"roughly",
">",
"40",
"%",
"[",
"1",
"]",
".",
"Given",
"this",
"confusion",
",",
"our",
"goal",
"in",
"this",
"work",
"is",
"to",
"give",
"a",
"clear",
"and",
"detailed",
"explanation",
"of",
"X",
"##RP",
"L",
"##CP",
"and",
"derive",
"the",
"necessary",
"conditions",
"on",
"UN",
"##L",
"overlap",
"for",
"consistency",
"and",
"live",
"##ness",
".",
"We",
"will",
"not",
"discuss",
"the",
"transaction",
"##al",
"semantic",
"##s",
"of",
"X",
"##RP",
"'",
"s",
"ledge",
"##r",
"or",
"X",
"##RP",
"'",
"s",
"benefits",
"as",
"a",
"digital",
"currency",
",",
"but",
"instead",
"view",
"the",
"algorithm",
"as",
"a",
"general",
"consensus",
"protocol",
".",
"We",
"re",
"-",
"evaluate",
"the",
"two",
"prior",
"overlap",
"results",
"and",
"provide",
"a",
"single",
"corrected",
"bound",
"which",
"is",
"part",
"##way",
"between",
"the",
"bounds",
"of",
"[",
"10",
"]",
"and",
"[",
"1",
"]",
".",
"We",
"also",
"show",
"that",
"under",
"a",
"more",
"general",
"fault",
"model",
"which",
"was",
"not",
"considered",
"in",
"the",
"original",
"white",
"##paper",
"but",
"is",
"canonical",
"##ly",
"used",
"in",
"the",
"research",
"literature",
",",
"the",
"minimum",
"overlap",
"is",
"actually",
"roughly",
">",
"90",
"%",
"of",
"the",
"UN",
"##L",
".",
"Finally",
",",
"we",
"show",
"that",
"during",
"the",
"present",
"stages",
"of",
"divers",
"##ifying",
"trusted",
"network",
"operators",
"[",
"12",
"]",
",",
"the",
"X",
"##RP",
"network",
"is",
"both",
"safe",
"and",
"cannot",
"become",
"\"",
"stuck",
"\"",
"making",
"no",
"forward",
"progress",
".",
"This",
"research",
"provides",
"a",
"definitive",
"result",
"about",
"the",
"safety",
"of",
"X",
"##RP",
"Led",
"##ger",
"in",
"its",
"current",
"state",
".",
"However",
",",
"to",
"encourage",
"greater",
"flexibility",
"in",
"choosing",
"UN",
"##L",
"##s",
"in",
"the",
"future",
",",
"we",
"would",
"prefer",
"an",
"algorithm",
"that",
"gets",
"closer",
"to",
"the",
"original",
"expected",
"overlap",
"bounds",
".",
"In",
"a",
"sibling",
"paper",
"[",
"6",
"]",
",",
"we",
"present",
"a",
"novel",
"alternative",
"consensus",
"algorithm",
"called",
"Co",
"##balt",
"that",
"lower",
"##s",
"the",
"overlap",
"bound",
"to",
"only",
">",
"60",
"%",
"in",
"the",
"general",
"fault",
"model",
",",
"cannot",
"get",
"stuck",
"in",
"any",
"network",
"that",
"sat",
"##is",
"##fies",
"the",
"overlap",
"bound",
",",
"and",
"has",
"several",
"other",
"properties",
"that",
"make",
"it",
"suitable",
"for",
"eventually",
"replacing",
"X",
"##RP",
"L",
"##CP",
".",
"This",
"paper",
"thus",
"serves",
"primarily",
"to",
"show",
"that",
"the",
"X",
"##RP",
"Led",
"##ger",
"is",
"safe",
"in",
"the",
"interim",
"while",
"transition",
"##ing",
"to",
"Co",
"##balt",
","
] | Analysis of the XRP Ledger Consensus Protocol | 153 |
s.
1 Introduction
The XRP Ledger is a distributed payment system enabling users to transfer
value seamlessly around the world. Operating within a distributed peer-to-peer
network, the XRP Ledger faces the same challenges as other digital currencies
in preventing double-spending of funds and ensuring network-wide consensus on
the state of user accounts and balances. First proposed and then implemented
by Schwartz et al. [10], the algorithm underlying XRP solves these problems
using a Byzantine fault tole | [
119,
22439,
1106,
1168,
11858,
4412,
2200,
10923,
14975,
1176,
6777,
118,
1104,
118,
1250,
164,
128,
166,
1137,
6777,
118,
1104,
118,
8219,
164,
123,
166,
117,
161,
20336,
149,
13113,
1144,
1290,
1157,
12548,
2136,
2211,
13618,
1523,
7232,
1105,
2299,
1194,
16156,
1111,
1157,
4713,
119,
1438,
117,
1443,
6029,
5340,
118,
1441,
1204,
1113,
1103,
2443,
6635,
117,
4713,
1253,
1444,
170,
1236,
1106,
4959,
2480,
1147,
3026,
1104,
2443,
14097,
1209,
1730,
1106,
170,
8080,
2443,
1352,
119,
1130,
1142,
3545,
117,
1296,
4795,
15473,
12028,
170,
3527,
14372,
2190,
1137,
7414,
2162,
117,
1134,
1110,
1103,
1383,
1104,
15029,
2133,
7416,
1122,
1209,
5113,
1106,
1165,
1543,
6134,
1164,
1103,
2443,
1352,
119,
1135,
1110,
1103,
6326,
1104,
1251,
3111,
1104,
5663,
15029,
112,
7414,
2162,
1116,
1115,
17579,
2443,
3429,
119,
1249,
1758,
1107,
1103,
1560,
1653,
26311,
164,
1275,
166,
117,
1103,
5867,
19235,
8875,
1108,
2034,
2475,
1106,
1129,
4986,
1406,
110,
1104,
1103,
7414,
2162,
119,
1760,
2457,
3622,
1224,
3228,
1103,
5663,
4930,
1108,
1939,
4986,
135,
1969,
110,
164,
122,
166,
119,
10470,
1142,
6406,
117,
1412,
2273,
1107,
1142,
1250,
1110,
1106,
1660,
170,
2330,
1105,
6448,
7108,
1104,
161,
20336,
149,
13113,
1105,
20292,
1103,
3238,
2975,
1113,
7414,
2162,
19235,
1111,
20904,
1105,
1686,
1757,
119,
1284,
1209,
1136,
6265,
1103,
13618,
1348,
27921,
1116,
1104,
161,
20336,
112,
188,
21340,
1197,
1137,
161,
20336,
112,
188,
6245,
1112,
170,
3539,
10202,
117,
1133,
1939,
2458,
1103,
9932,
1112,
170,
1704,
10923,
11309,
119,
1284,
1231,
118,
17459,
1103,
1160,
2988,
19235,
2686,
1105,
2194,
170,
1423,
13808,
4930,
1134,
1110,
1226,
2787,
1206,
1103,
22379,
1104,
164,
1275,
166,
1105,
164,
122,
166,
119,
1284,
1145,
1437,
1115,
1223,
170,
1167,
1704,
6088,
2235,
1134,
1108,
1136,
1737,
1107,
1103,
1560,
1653,
26311,
1133,
1110,
21768,
1193,
1215,
1107,
1103,
1844,
3783,
117,
1103,
5867,
19235,
1110,
2140,
4986,
135,
3078,
110,
1104,
1103,
7414,
2162,
119,
4428,
117,
1195,
1437,
1115,
1219,
1103,
1675,
5251,
1104,
22767,
8985,
9373,
2443,
9298,
164,
1367,
166,
117,
1103,
161,
20336,
2443,
1110,
1241,
2914,
1105,
2834,
1561,
107,
5342,
107,
1543,
1185,
1977,
5070,
119,
1188,
1844,
2790,
170,
18379,
1871,
1164,
1103,
3429,
1104,
161,
20336,
18657,
2895,
1107,
1157,
1954,
1352,
119,
1438,
117,
1106,
8343,
3407,
18605,
1107,
11027,
7414,
2162,
1116,
1107,
1103,
2174,
117,
1195,
1156,
9353,
1126,
9932,
1115,
3370,
2739,
1106,
1103,
1560,
2637,
19235,
22379,
119,
1130,
170,
26563,
2526,
164,
127,
166,
117,
1195,
1675,
170,
2281,
4174,
10923,
9932,
1270,
3291,
26443,
1115,
2211,
1116,
1103,
19235,
4930,
1106,
1178,
135,
2539,
110,
1107,
1103,
1704,
6088,
2235,
117,
2834,
1243,
5342,
1107,
1251,
2443,
1115,
2068,
1548,
16847,
1103,
19235,
4930,
117,
1105,
1144,
1317,
1168,
4625,
1115,
1294,
1122,
6736,
1111,
2028,
5861,
161,
20336,
149,
13113,
119,
1188,
2526,
2456,
3411,
3120,
1106,
1437,
1115,
1103,
161,
20336,
18657,
2895,
1110,
2914,
1107,
1103,
10572,
1229,
6468,
1158,
1106,
3291,
26443,
117
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
".",
"Compared",
"to",
"other",
"decent",
"##ral",
"##ized",
"consensus",
"algorithms",
"like",
"proof",
"-",
"of",
"-",
"work",
"[",
"7",
"]",
"or",
"proof",
"-",
"of",
"-",
"stake",
"[",
"2",
"]",
",",
"X",
"##RP",
"L",
"##CP",
"has",
"since",
"its",
"inception",
"provided",
"lower",
"transaction",
"late",
"##ncy",
"and",
"higher",
"through",
"##put",
"for",
"its",
"users",
".",
"However",
",",
"without",
"uniform",
"agree",
"-",
"men",
"##t",
"on",
"the",
"network",
"participants",
",",
"users",
"still",
"need",
"a",
"way",
"to",
"determine",
"whether",
"their",
"choice",
"of",
"network",
"peers",
"will",
"lead",
"to",
"a",
"consistent",
"network",
"state",
".",
"In",
"this",
"setting",
",",
"each",
"user",
"individually",
"defines",
"a",
"unique",
"node",
"list",
"or",
"UN",
"##L",
",",
"which",
"is",
"the",
"set",
"of",
"nodes",
"whose",
"messages",
"it",
"will",
"listen",
"to",
"when",
"making",
"decisions",
"about",
"the",
"network",
"state",
".",
"It",
"is",
"the",
"intersection",
"of",
"any",
"pair",
"of",
"correct",
"nodes",
"'",
"UN",
"##L",
"##s",
"that",
"determines",
"network",
"safety",
".",
"As",
"described",
"in",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
",",
"the",
"minimum",
"overlap",
"requirement",
"was",
"originally",
"believed",
"to",
"be",
"roughly",
"20",
"%",
"of",
"the",
"UN",
"##L",
".",
"An",
"independent",
"analysis",
"later",
"suggested",
"the",
"correct",
"bound",
"was",
"instead",
"roughly",
">",
"40",
"%",
"[",
"1",
"]",
".",
"Given",
"this",
"confusion",
",",
"our",
"goal",
"in",
"this",
"work",
"is",
"to",
"give",
"a",
"clear",
"and",
"detailed",
"explanation",
"of",
"X",
"##RP",
"L",
"##CP",
"and",
"derive",
"the",
"necessary",
"conditions",
"on",
"UN",
"##L",
"overlap",
"for",
"consistency",
"and",
"live",
"##ness",
".",
"We",
"will",
"not",
"discuss",
"the",
"transaction",
"##al",
"semantic",
"##s",
"of",
"X",
"##RP",
"'",
"s",
"ledge",
"##r",
"or",
"X",
"##RP",
"'",
"s",
"benefits",
"as",
"a",
"digital",
"currency",
",",
"but",
"instead",
"view",
"the",
"algorithm",
"as",
"a",
"general",
"consensus",
"protocol",
".",
"We",
"re",
"-",
"evaluate",
"the",
"two",
"prior",
"overlap",
"results",
"and",
"provide",
"a",
"single",
"corrected",
"bound",
"which",
"is",
"part",
"##way",
"between",
"the",
"bounds",
"of",
"[",
"10",
"]",
"and",
"[",
"1",
"]",
".",
"We",
"also",
"show",
"that",
"under",
"a",
"more",
"general",
"fault",
"model",
"which",
"was",
"not",
"considered",
"in",
"the",
"original",
"white",
"##paper",
"but",
"is",
"canonical",
"##ly",
"used",
"in",
"the",
"research",
"literature",
",",
"the",
"minimum",
"overlap",
"is",
"actually",
"roughly",
">",
"90",
"%",
"of",
"the",
"UN",
"##L",
".",
"Finally",
",",
"we",
"show",
"that",
"during",
"the",
"present",
"stages",
"of",
"divers",
"##ifying",
"trusted",
"network",
"operators",
"[",
"12",
"]",
",",
"the",
"X",
"##RP",
"network",
"is",
"both",
"safe",
"and",
"cannot",
"become",
"\"",
"stuck",
"\"",
"making",
"no",
"forward",
"progress",
".",
"This",
"research",
"provides",
"a",
"definitive",
"result",
"about",
"the",
"safety",
"of",
"X",
"##RP",
"Led",
"##ger",
"in",
"its",
"current",
"state",
".",
"However",
",",
"to",
"encourage",
"greater",
"flexibility",
"in",
"choosing",
"UN",
"##L",
"##s",
"in",
"the",
"future",
",",
"we",
"would",
"prefer",
"an",
"algorithm",
"that",
"gets",
"closer",
"to",
"the",
"original",
"expected",
"overlap",
"bounds",
".",
"In",
"a",
"sibling",
"paper",
"[",
"6",
"]",
",",
"we",
"present",
"a",
"novel",
"alternative",
"consensus",
"algorithm",
"called",
"Co",
"##balt",
"that",
"lower",
"##s",
"the",
"overlap",
"bound",
"to",
"only",
">",
"60",
"%",
"in",
"the",
"general",
"fault",
"model",
",",
"cannot",
"get",
"stuck",
"in",
"any",
"network",
"that",
"sat",
"##is",
"##fies",
"the",
"overlap",
"bound",
",",
"and",
"has",
"several",
"other",
"properties",
"that",
"make",
"it",
"suitable",
"for",
"eventually",
"replacing",
"X",
"##RP",
"L",
"##CP",
".",
"This",
"paper",
"thus",
"serves",
"primarily",
"to",
"show",
"that",
"the",
"X",
"##RP",
"Led",
"##ger",
"is",
"safe",
"in",
"the",
"interim",
"while",
"transition",
"##ing",
"to",
"Co",
"##balt",
","
] | Analysis of the XRP Ledger Consensus Protocol | 154 |
rant agreement protocol over collectively trusted
subnetworks, hereby referred to as the XRP Ledger Consensus Protocol, or
XRP LCP for short.
Abstractly, the XRP Ledger network is a replicated state machine [9]. The
replicated state is the ledger maintained by each node in the network and state
transitions correspond to transactions submitted by clients of the network. Once
nodes agree on sets of transactions to apply to the state, a transaction processing
protocol specifies deterministic rules for order | [
1105,
1103,
3860,
9382,
5420,
1113,
7414,
2162,
25209,
1223,
161,
20336,
149,
13113,
1431,
1129,
6497,
1107,
1609,
1104,
1142,
2919,
6468,
119,
6177,
123,
12028,
1103,
2443,
2235,
1105,
12028,
1103,
10923,
2463,
119,
22087,
1665,
118,
189,
1988,
124,
1110,
170,
6448,
6136,
1104,
1103,
155,
9717,
7136,
10923,
9932,
119,
1130,
2237,
125,
117,
1195,
5424,
1103,
2443,
2975,
1834,
1106,
11865,
5663,
1757,
1104,
1103,
2393,
2758,
118,
187,
7088,
1306,
119,
4428,
117,
2237,
126,
15382,
1114,
170,
6145,
1104,
1103,
2686,
1105,
7768,
1111,
8331,
119,
123,
123,
3998,
6747,
1105,
21710,
3177,
16598,
8934,
2421,
21902,
1129,
170,
14372,
1107,
1103,
2443,
1114,
3527,
25021,
3452,
17792,
178,
117,
1216,
1112,
170,
5354,
6451,
9597,
1470,
2501,
119,
2994,
14372,
21902,
1110,
1714,
1106,
4835,
170,
3527,
14372,
2190,
7414,
2162,
1182,
117,
1134,
1110,
1103,
1383,
1104,
15029,
113,
3566,
1259,
2111,
114,
2133,
7416,
21902,
1209,
5113,
1106,
1112,
1226,
1104,
1103,
161,
20336,
149,
13113,
119,
1109,
7414,
2162,
5149,
170,
18005,
1104,
1103,
2443,
1134,
117,
1165,
1678,
14998,
117,
1110,
9373,
1118,
21902,
1106,
1136,
1884,
2339,
10308,
1107,
1126,
2661,
1106,
19353,
1611,
4867,
1103,
2443,
113,
1267,
164,
1275,
166,
1111,
1103,
15710,
1104,
1142,
1271,
114,
119,
1109,
7414,
2162,
1116,
1660,
2401,
1106,
1103,
2443,
117,
1114,
170,
14372,
1115,
1110,
1675,
1107,
1167,
7414,
2162,
1116,
24034,
18726,
1193,
1515,
1167,
2933,
119,
1760,
2510,
14372,
1144,
2335,
21435,
1107,
1103,
3026,
1104,
1147,
7414,
2162,
117,
1780,
1195,
1437,
1107,
2237,
125,
1115,
5867,
19235,
1114,
1168,
7414,
2162,
1116,
1110,
3238,
1111,
20904,
1105,
1686,
1757,
1114,
1168,
7345,
15029,
119,
1284,
1202,
1136,
7568,
1115,
3496,
1110,
21852,
117,
1177,
1111,
5374,
1175,
1336,
1129,
170,
14372,
153,
3361,
850,
7414,
2162,
1182,
1216,
1115,
21902,
120,
850,
7414,
2162,
3361,
119,
15982,
122,
2196,
1126,
1859,
3496,
2443,
119,
138,
14372,
1115,
1110,
1136,
7573,
1105,
18492,
1116,
2839,
2452,
1106,
1103,
161,
20336,
149,
13113,
14911,
1110,
1163,
1106,
1129,
7345,
1137,
5663,
132,
1195,
1329,
1103,
1160,
2538,
9455,
118,
1849,
5382,
119,
6291,
14372,
1115,
1674,
1136,
18492,
2452,
1106,
11309,
1110,
1163,
1106,
1129,
8377,
119,
8377,
4658,
1169,
1511,
1136,
16322,
1106,
7416,
117,
5416,
18238,
7416,
117,
1105,
1256,
5416,
1472,
7416,
1106,
1472,
3512,
119,
1130,
2237,
125,
117,
1195,
2786,
4615,
170,
18760,
1113,
1103,
8050,
10704,
3113,
1270,
8377,
3300,
6328,
117,
1134,
2231,
1115,
1155,
15029,
782,
1256,
8377,
3200,
782,
2834,
3952,
1472,
7416,
1106,
1472,
15029,
119,
1188,
1108,
1226,
1104,
1103,
1560,
1653,
26311,
164,
1275,
166,
117,
1134,
4260,
1216,
4658,
1107,
170,
8536,
118,
1106,
118,
8536,
2443,
1180,
1129,
3626,
1105,
13808,
1118,
7345,
15029,
119,
1438,
117,
1496,
1106,
1112,
27250,
8167,
10031,
1105,
1103,
5417,
1104,
7345,
15029,
1217,
7818,
16416,
1174,
117,
1142,
13457,
1110,
1107,
2415,
1995,
8163,
1120,
1436,
119,
4516,
1103,
9634,
1104,
1412,
2686,
1202,
1136,
12864,
1113,
1142,
13457,
1105,
1195,
1209,
3817,
1352
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
23,
24,
24,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
5,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
23,
24,
24,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
5,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"and",
"the",
"relatively",
"strict",
"requirements",
"on",
"UN",
"##L",
"configurations",
"under",
"X",
"##RP",
"L",
"##CP",
"should",
"be",
"viewed",
"in",
"light",
"of",
"this",
"planned",
"transition",
".",
"Section",
"2",
"defines",
"the",
"network",
"model",
"and",
"defines",
"the",
"consensus",
"problem",
".",
"Se",
"##c",
"-",
"t",
"##ion",
"3",
"is",
"a",
"detailed",
"description",
"of",
"the",
"R",
"##ip",
"##ple",
"consensus",
"algorithm",
".",
"In",
"section",
"4",
",",
"we",
"prove",
"the",
"network",
"conditions",
"needed",
"to",
"guarantee",
"correct",
"##ness",
"of",
"the",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
".",
"Finally",
",",
"section",
"5",
"concludes",
"with",
"a",
"discussion",
"of",
"the",
"results",
"and",
"directions",
"for",
"improvement",
".",
"2",
"2",
"Network",
"Model",
"and",
"Problem",
"De",
"##fin",
"##ition",
"Let",
"Pi",
"be",
"a",
"node",
"in",
"the",
"network",
"with",
"unique",
"id",
"##ent",
"##ifier",
"i",
",",
"such",
"as",
"a",
"cry",
"##pt",
"##ographic",
"public",
"key",
".",
"Each",
"node",
"Pi",
"is",
"free",
"to",
"choose",
"a",
"unique",
"node",
"list",
"UN",
"##L",
"##i",
",",
"which",
"is",
"the",
"set",
"of",
"nodes",
"(",
"possibly",
"including",
"itself",
")",
"whose",
"messages",
"Pi",
"will",
"listen",
"to",
"as",
"part",
"of",
"the",
"X",
"##RP",
"L",
"##CP",
".",
"The",
"UN",
"##L",
"represents",
"a",
"subset",
"of",
"the",
"network",
"which",
",",
"when",
"taken",
"collectively",
",",
"is",
"trusted",
"by",
"Pi",
"to",
"not",
"co",
"##ll",
"##ude",
"in",
"an",
"attempt",
"to",
"def",
"##ra",
"##ud",
"the",
"network",
"(",
"see",
"[",
"10",
"]",
"for",
"the",
"motivation",
"of",
"this",
"name",
")",
".",
"The",
"UN",
"##L",
"##s",
"give",
"structure",
"to",
"the",
"network",
",",
"with",
"a",
"node",
"that",
"is",
"present",
"in",
"more",
"UN",
"##L",
"##s",
"imp",
"##licit",
"##ly",
"having",
"more",
"influence",
".",
"An",
"individual",
"node",
"has",
"complete",
"discretion",
"in",
"the",
"choice",
"of",
"their",
"UN",
"##L",
",",
"although",
"we",
"show",
"in",
"section",
"4",
"that",
"minimum",
"overlap",
"with",
"other",
"UN",
"##L",
"##s",
"is",
"necessary",
"for",
"consistency",
"and",
"live",
"##ness",
"with",
"other",
"honest",
"nodes",
".",
"We",
"do",
"not",
"assume",
"that",
"trust",
"is",
"symmetric",
",",
"so",
"for",
"instance",
"there",
"may",
"be",
"a",
"node",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
"such",
"that",
"Pi",
"/",
"β",
"UN",
"##L",
"##j",
".",
"Figure",
"1",
"shows",
"an",
"example",
"trust",
"network",
".",
"A",
"node",
"that",
"is",
"not",
"crashed",
"and",
"behave",
"##s",
"exactly",
"according",
"to",
"the",
"X",
"##RP",
"L",
"##CP",
"specification",
"is",
"said",
"to",
"be",
"honest",
"or",
"correct",
";",
"we",
"use",
"the",
"two",
"terms",
"inter",
"-",
"change",
"##ably",
".",
"Any",
"node",
"that",
"does",
"not",
"behave",
"according",
"to",
"protocol",
"is",
"said",
"to",
"be",
"Byzantine",
".",
"Byzantine",
"behavior",
"can",
"include",
"not",
"responding",
"to",
"messages",
",",
"sending",
"incorrect",
"messages",
",",
"and",
"even",
"sending",
"different",
"messages",
"to",
"different",
"parties",
".",
"In",
"section",
"4",
",",
"we",
"initially",
"consider",
"a",
"restriction",
"on",
"the",
"ad",
"##vers",
"##ary",
"called",
"Byzantine",
"account",
"##ability",
",",
"which",
"states",
"that",
"all",
"nodes",
"β",
"even",
"Byzantine",
"ones",
"β",
"cannot",
"send",
"different",
"messages",
"to",
"different",
"nodes",
".",
"This",
"was",
"part",
"of",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
",",
"which",
"assumed",
"such",
"behavior",
"in",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
"could",
"be",
"identified",
"and",
"corrected",
"by",
"honest",
"nodes",
".",
"However",
",",
"due",
"to",
"as",
"##ync",
"##hr",
"##ony",
"and",
"the",
"possibility",
"of",
"honest",
"nodes",
"being",
"temporarily",
"partition",
"##ed",
",",
"this",
"assumption",
"is",
"in",
"practice",
"ten",
"##uous",
"at",
"best",
".",
"Thus",
"the",
"bulk",
"of",
"our",
"results",
"do",
"not",
"depend",
"on",
"this",
"assumption",
"and",
"we",
"will",
"clearly",
"state"
] | Analysis of the XRP Ledger Consensus Protocol | 155 |
rant agreement protocol over collectively trusted
subnetworks, hereby referred to as the XRP Ledger Consensus Protocol, or
XRP LCP for short.
Abstractly, the XRP Ledger network is a replicated state machine [9]. The
replicated state is the ledger maintained by each node in the network and state
transitions correspond to transactions submitted by clients of the network. Once
nodes agree on sets of transactions to apply to the state, a transaction processing
protocol specifies deterministic rules for order | [
1105,
1103,
3860,
9382,
5420,
1113,
7414,
2162,
25209,
1223,
161,
20336,
149,
13113,
1431,
1129,
6497,
1107,
1609,
1104,
1142,
2919,
6468,
119,
6177,
123,
12028,
1103,
2443,
2235,
1105,
12028,
1103,
10923,
2463,
119,
22087,
1665,
118,
189,
1988,
124,
1110,
170,
6448,
6136,
1104,
1103,
155,
9717,
7136,
10923,
9932,
119,
1130,
2237,
125,
117,
1195,
5424,
1103,
2443,
2975,
1834,
1106,
11865,
5663,
1757,
1104,
1103,
2393,
2758,
118,
187,
7088,
1306,
119,
4428,
117,
2237,
126,
15382,
1114,
170,
6145,
1104,
1103,
2686,
1105,
7768,
1111,
8331,
119,
123,
123,
3998,
6747,
1105,
21710,
3177,
16598,
8934,
2421,
21902,
1129,
170,
14372,
1107,
1103,
2443,
1114,
3527,
25021,
3452,
17792,
178,
117,
1216,
1112,
170,
5354,
6451,
9597,
1470,
2501,
119,
2994,
14372,
21902,
1110,
1714,
1106,
4835,
170,
3527,
14372,
2190,
7414,
2162,
1182,
117,
1134,
1110,
1103,
1383,
1104,
15029,
113,
3566,
1259,
2111,
114,
2133,
7416,
21902,
1209,
5113,
1106,
1112,
1226,
1104,
1103,
161,
20336,
149,
13113,
119,
1109,
7414,
2162,
5149,
170,
18005,
1104,
1103,
2443,
1134,
117,
1165,
1678,
14998,
117,
1110,
9373,
1118,
21902,
1106,
1136,
1884,
2339,
10308,
1107,
1126,
2661,
1106,
19353,
1611,
4867,
1103,
2443,
113,
1267,
164,
1275,
166,
1111,
1103,
15710,
1104,
1142,
1271,
114,
119,
1109,
7414,
2162,
1116,
1660,
2401,
1106,
1103,
2443,
117,
1114,
170,
14372,
1115,
1110,
1675,
1107,
1167,
7414,
2162,
1116,
24034,
18726,
1193,
1515,
1167,
2933,
119,
1760,
2510,
14372,
1144,
2335,
21435,
1107,
1103,
3026,
1104,
1147,
7414,
2162,
117,
1780,
1195,
1437,
1107,
2237,
125,
1115,
5867,
19235,
1114,
1168,
7414,
2162,
1116,
1110,
3238,
1111,
20904,
1105,
1686,
1757,
1114,
1168,
7345,
15029,
119,
1284,
1202,
1136,
7568,
1115,
3496,
1110,
21852,
117,
1177,
1111,
5374,
1175,
1336,
1129,
170,
14372,
153,
3361,
850,
7414,
2162,
1182,
1216,
1115,
21902,
120,
850,
7414,
2162,
3361,
119,
15982,
122,
2196,
1126,
1859,
3496,
2443,
119,
138,
14372,
1115,
1110,
1136,
7573,
1105,
18492,
1116,
2839,
2452,
1106,
1103,
161,
20336,
149,
13113,
14911,
1110,
1163,
1106,
1129,
7345,
1137,
5663,
132,
1195,
1329,
1103,
1160,
2538,
9455,
118,
1849,
5382,
119,
6291,
14372,
1115,
1674,
1136,
18492,
2452,
1106,
11309,
1110,
1163,
1106,
1129,
8377,
119,
8377,
4658,
1169,
1511,
1136,
16322,
1106,
7416,
117,
5416,
18238,
7416,
117,
1105,
1256,
5416,
1472,
7416,
1106,
1472,
3512,
119,
1130,
2237,
125,
117,
1195,
2786,
4615,
170,
18760,
1113,
1103,
8050,
10704,
3113,
1270,
8377,
3300,
6328,
117,
1134,
2231,
1115,
1155,
15029,
782,
1256,
8377,
3200,
782,
2834,
3952,
1472,
7416,
1106,
1472,
15029,
119,
1188,
1108,
1226,
1104,
1103,
1560,
1653,
26311,
164,
1275,
166,
117,
1134,
4260,
1216,
4658,
1107,
170,
8536,
118,
1106,
118,
8536,
2443,
1180,
1129,
3626,
1105,
13808,
1118,
7345,
15029,
119,
1438,
117,
1496,
1106,
1112,
27250,
8167,
10031,
1105,
1103,
5417,
1104,
7345,
15029,
1217,
7818,
16416,
1174,
117,
1142,
13457,
1110,
1107,
2415,
1995,
8163,
1120,
1436,
119,
4516,
1103,
9634,
1104,
1412,
2686,
1202,
1136,
12864,
1113,
1142,
13457,
1105,
1195,
1209,
3817,
1352
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"and",
"the",
"relatively",
"strict",
"requirements",
"on",
"UN",
"##L",
"configurations",
"under",
"X",
"##RP",
"L",
"##CP",
"should",
"be",
"viewed",
"in",
"light",
"of",
"this",
"planned",
"transition",
".",
"Section",
"2",
"defines",
"the",
"network",
"model",
"and",
"defines",
"the",
"consensus",
"problem",
".",
"Se",
"##c",
"-",
"t",
"##ion",
"3",
"is",
"a",
"detailed",
"description",
"of",
"the",
"R",
"##ip",
"##ple",
"consensus",
"algorithm",
".",
"In",
"section",
"4",
",",
"we",
"prove",
"the",
"network",
"conditions",
"needed",
"to",
"guarantee",
"correct",
"##ness",
"of",
"the",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
".",
"Finally",
",",
"section",
"5",
"concludes",
"with",
"a",
"discussion",
"of",
"the",
"results",
"and",
"directions",
"for",
"improvement",
".",
"2",
"2",
"Network",
"Model",
"and",
"Problem",
"De",
"##fin",
"##ition",
"Let",
"Pi",
"be",
"a",
"node",
"in",
"the",
"network",
"with",
"unique",
"id",
"##ent",
"##ifier",
"i",
",",
"such",
"as",
"a",
"cry",
"##pt",
"##ographic",
"public",
"key",
".",
"Each",
"node",
"Pi",
"is",
"free",
"to",
"choose",
"a",
"unique",
"node",
"list",
"UN",
"##L",
"##i",
",",
"which",
"is",
"the",
"set",
"of",
"nodes",
"(",
"possibly",
"including",
"itself",
")",
"whose",
"messages",
"Pi",
"will",
"listen",
"to",
"as",
"part",
"of",
"the",
"X",
"##RP",
"L",
"##CP",
".",
"The",
"UN",
"##L",
"represents",
"a",
"subset",
"of",
"the",
"network",
"which",
",",
"when",
"taken",
"collectively",
",",
"is",
"trusted",
"by",
"Pi",
"to",
"not",
"co",
"##ll",
"##ude",
"in",
"an",
"attempt",
"to",
"def",
"##ra",
"##ud",
"the",
"network",
"(",
"see",
"[",
"10",
"]",
"for",
"the",
"motivation",
"of",
"this",
"name",
")",
".",
"The",
"UN",
"##L",
"##s",
"give",
"structure",
"to",
"the",
"network",
",",
"with",
"a",
"node",
"that",
"is",
"present",
"in",
"more",
"UN",
"##L",
"##s",
"imp",
"##licit",
"##ly",
"having",
"more",
"influence",
".",
"An",
"individual",
"node",
"has",
"complete",
"discretion",
"in",
"the",
"choice",
"of",
"their",
"UN",
"##L",
",",
"although",
"we",
"show",
"in",
"section",
"4",
"that",
"minimum",
"overlap",
"with",
"other",
"UN",
"##L",
"##s",
"is",
"necessary",
"for",
"consistency",
"and",
"live",
"##ness",
"with",
"other",
"honest",
"nodes",
".",
"We",
"do",
"not",
"assume",
"that",
"trust",
"is",
"symmetric",
",",
"so",
"for",
"instance",
"there",
"may",
"be",
"a",
"node",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
"such",
"that",
"Pi",
"/",
"β",
"UN",
"##L",
"##j",
".",
"Figure",
"1",
"shows",
"an",
"example",
"trust",
"network",
".",
"A",
"node",
"that",
"is",
"not",
"crashed",
"and",
"behave",
"##s",
"exactly",
"according",
"to",
"the",
"X",
"##RP",
"L",
"##CP",
"specification",
"is",
"said",
"to",
"be",
"honest",
"or",
"correct",
";",
"we",
"use",
"the",
"two",
"terms",
"inter",
"-",
"change",
"##ably",
".",
"Any",
"node",
"that",
"does",
"not",
"behave",
"according",
"to",
"protocol",
"is",
"said",
"to",
"be",
"Byzantine",
".",
"Byzantine",
"behavior",
"can",
"include",
"not",
"responding",
"to",
"messages",
",",
"sending",
"incorrect",
"messages",
",",
"and",
"even",
"sending",
"different",
"messages",
"to",
"different",
"parties",
".",
"In",
"section",
"4",
",",
"we",
"initially",
"consider",
"a",
"restriction",
"on",
"the",
"ad",
"##vers",
"##ary",
"called",
"Byzantine",
"account",
"##ability",
",",
"which",
"states",
"that",
"all",
"nodes",
"β",
"even",
"Byzantine",
"ones",
"β",
"cannot",
"send",
"different",
"messages",
"to",
"different",
"nodes",
".",
"This",
"was",
"part",
"of",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
",",
"which",
"assumed",
"such",
"behavior",
"in",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
"could",
"be",
"identified",
"and",
"corrected",
"by",
"honest",
"nodes",
".",
"However",
",",
"due",
"to",
"as",
"##ync",
"##hr",
"##ony",
"and",
"the",
"possibility",
"of",
"honest",
"nodes",
"being",
"temporarily",
"partition",
"##ed",
",",
"this",
"assumption",
"is",
"in",
"practice",
"ten",
"##uous",
"at",
"best",
".",
"Thus",
"the",
"bulk",
"of",
"our",
"results",
"do",
"not",
"depend",
"on",
"this",
"assumption",
"and",
"we",
"will",
"clearly",
"state"
] | Analysis of the XRP Ledger Consensus Protocol | 156 |
ing transactions within each set
and how to apply transactions to generate the new ledger state. Thus, the role of
XRP LCP is only to make the network reach agreement on sets of transactions,
not on the content or outcome of those transactions. As long as nodes agree
on a transaction set, the transaction processing protocol guarantees that every
node generates a consistent ledger. As a Byzantine fault tolerant protocol, XRP
LCP must operate even in the presence of faulty or malicious participants.
Byzant | [
1165,
1122,
1110,
4260,
119,
1370,
1251,
14372,
21902,
117,
1195,
21185,
11437,
134,
197,
7414,
2162,
1182,
197,
1105,
9410,
1103,
186,
11848,
5697,
117,
21307,
186,
1182,
117,
170,
17816,
1134,
4986,
188,
25392,
9387,
1103,
5867,
1295,
1104,
17577,
15029,
1107,
7414,
2162,
1182,
1115,
21902,
2993,
1106,
2100,
1121,
1106,
10836,
1106,
170,
2383,
119,
2994,
14372,
3741,
186,
1182,
1106,
1129,
2908,
110,
1104,
1157,
7414,
2162,
2060,
117,
1137,
117,
1167,
2839,
117,
186,
1182,
134,
100,
121,
119,
129,
2605,
100,
119,
1284,
7568,
1120,
1211,
189,
1182,
127,
11437,
851,
186,
1182,
15029,
1107,
7414,
2162,
1182,
1336,
1129,
8377,
6088,
1183,
119,
2421,
149,
4248,
170,
21340,
1197,
117,
1134,
1110,
1103,
3416,
1352,
1104,
1103,
1449,
1105,
2075,
3300,
11106,
117,
5233,
1116,
117,
1546,
2146,
117,
3576,
119,
1960,
21340,
1733,
149,
117,
149,
797,
1132,
1103,
1269,
1191,
1152,
4248,
1103,
1269,
2802,
1607,
1104,
14409,
2547,
1121,
1103,
3527,
9077,
1548,
21340,
1197,
119,
2994,
21340,
1197,
1145,
1144,
4954,
1295,
14516,
4426,
113,
149,
114,
1115,
1110,
1141,
3407,
1190,
1157,
6486,
21340,
1197,
112,
188,
4954,
1295,
119,
1109,
9077,
1548,
21340,
1197,
1144,
14516,
4426,
113,
149,
114,
134,
122,
119,
138,
21340,
1197,
149,
1110,
1687,
1118,
11892,
170,
4954,
1104,
14409,
157,
134,
164,
193,
1568,
117,
193,
1475,
117,
119,
119,
119,
166,
1106,
1157,
6486,
6486,
113,
149,
114,
2452,
1106,
1103,
11309,
2995,
119,
1960,
21340,
1733,
1336,
1138,
1103,
1269,
6486,
21340,
1197,
1105,
4954,
1295,
117,
1133,
11271,
1272,
1152,
3666,
1472,
14409,
119,
5322,
1463,
1115,
1103,
11309,
188,
25392,
9387,
1115,
1451,
1383,
1104,
14409,
1144,
170,
1260,
2083,
25685,
5668,
13649,
117,
1177,
1122,
1110,
1136,
1936,
1111,
1160,
5663,
15029,
1106,
6058,
1103,
1269,
14409,
1133,
1107,
170,
1472,
1546,
119,
1109,
15029,
10621,
1166,
170,
8536,
118,
1106,
118,
8536,
2443,
1134,
1144,
1185,
17421,
6796,
1114,
1103,
7414,
2162,
2401,
119,
1284,
2566,
7568,
1115,
1111,
1451,
14372,
21902,
1105,
1451,
14372,
153,
3361,
850,
7414,
2162,
1182,
117,
1175,
1110,
170,
10682,
16047,
2913,
3094,
1111,
21902,
1106,
3531,
124,
170,
172,
171,
174,
173,
176,
175,
178,
177,
179,
15982,
122,
131,
16409,
26671,
3496,
10873,
119,
1109,
11634,
7521,
4248,
1103,
7414,
2162,
1104,
14372,
21902,
119,
7416,
1121,
153,
3361,
119,
1706,
10407,
1216,
1126,
16047,
2913,
3094,
117,
1155,
7416,
1132,
5354,
6451,
9597,
2716,
1878,
1105,
22480,
1118,
21535,
119,
2994,
14372,
2745,
170,
1423,
4909,
12130,
3012,
117,
1134,
1165,
1270,
1121,
14372,
153,
3361,
10130,
1103,
1269,
3802,
1106,
1155,
15029,
21902,
1111,
1134,
153,
3361,
850,
7414,
2162,
1182,
119,
1130,
1103,
14975,
2756,
1107,
12647,
6696,
7231,
138,
117,
1195,
1329,
170,
7671,
3531,
12130,
1134,
1110,
1270,
1112,
27250,
8167,
23038,
1361,
1193,
1852,
1103,
1231,
27333,
1104,
170,
3012,
3802,
119,
1109,
9386,
1104,
161,
20336,
149,
13113,
1110,
1111,
170,
14372,
1106,
3106,
9221,
2193,
21340,
1733,
119,
138,
3106,
9221,
2913,
21340,
1197,
1110,
178,
11604,
24553
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
21,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
5,
6,
6,
24,
24,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
21,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
5,
6,
6,
24,
24,
0,
0,
0,
0
] | [
"when",
"it",
"is",
"assumed",
".",
"For",
"any",
"node",
"Pi",
",",
"we",
"denote",
"ni",
"=",
"|",
"UN",
"##L",
"##i",
"|",
"and",
"define",
"the",
"q",
"##uo",
"##rum",
",",
"denoted",
"q",
"##i",
",",
"a",
"parameter",
"which",
"roughly",
"s",
"##pec",
"##ifies",
"the",
"minimum",
"number",
"of",
"agreeing",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"Pi",
"needs",
"to",
"hear",
"from",
"to",
"commit",
"to",
"a",
"decision",
".",
"Each",
"node",
"sets",
"q",
"##i",
"to",
"be",
"80",
"%",
"of",
"its",
"UN",
"##L",
"size",
",",
"or",
",",
"more",
"exactly",
",",
"q",
"##i",
"=",
"[UNK]",
"0",
".",
"8",
"##ni",
"[UNK]",
".",
"We",
"assume",
"at",
"most",
"t",
"##i",
"6",
"ni",
"β",
"q",
"##i",
"nodes",
"in",
"UN",
"##L",
"##i",
"may",
"be",
"Byzantine",
"fault",
"##y",
".",
"Let",
"L",
"represent",
"a",
"ledge",
"##r",
",",
"which",
"is",
"the",
"shared",
"state",
"of",
"the",
"system",
"and",
"includes",
"account",
"settings",
",",
"balance",
"##s",
",",
"order",
"books",
",",
"etc",
".",
"Two",
"ledge",
"##rs",
"L",
",",
"L",
"β²",
"are",
"the",
"same",
"if",
"they",
"represent",
"the",
"same",
"ordered",
"history",
"of",
"transactions",
"starting",
"from",
"the",
"unique",
"genes",
"##is",
"ledge",
"##r",
".",
"Each",
"ledge",
"##r",
"also",
"has",
"sequence",
"number",
"se",
"##q",
"(",
"L",
")",
"that",
"is",
"one",
"greater",
"than",
"its",
"parent",
"ledge",
"##r",
"'",
"s",
"sequence",
"number",
".",
"The",
"genes",
"##is",
"ledge",
"##r",
"has",
"se",
"##q",
"(",
"L",
")",
"=",
"1",
".",
"A",
"ledge",
"##r",
"L",
"is",
"created",
"by",
"applying",
"a",
"sequence",
"of",
"transactions",
"T",
"=",
"[",
"x",
"##0",
",",
"x",
"##1",
",",
".",
".",
".",
"]",
"to",
"its",
"parent",
"parent",
"(",
"L",
")",
"according",
"to",
"the",
"protocol",
"rules",
".",
"Two",
"ledge",
"##rs",
"may",
"have",
"the",
"same",
"parent",
"ledge",
"##r",
"and",
"sequence",
"number",
",",
"but",
"differ",
"because",
"they",
"applied",
"different",
"transactions",
".",
"Note",
"though",
"that",
"the",
"protocol",
"s",
"##pec",
"##ifies",
"that",
"every",
"set",
"of",
"transactions",
"has",
"a",
"de",
"##ter",
"##mini",
"##stic",
"ordering",
",",
"so",
"it",
"is",
"not",
"possible",
"for",
"two",
"correct",
"nodes",
"to",
"apply",
"the",
"same",
"transactions",
"but",
"in",
"a",
"different",
"order",
".",
"The",
"nodes",
"communicate",
"over",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
"which",
"has",
"no",
"prescribed",
"relation",
"with",
"the",
"UN",
"##L",
"structure",
".",
"We",
"simply",
"assume",
"that",
"for",
"every",
"node",
"Pi",
"and",
"every",
"node",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
",",
"there",
"is",
"a",
"reliable",
"authentic",
"##ated",
"channel",
"for",
"Pi",
"to",
"receive",
"3",
"a",
"c",
"b",
"e",
"d",
"g",
"f",
"i",
"h",
"j",
"Figure",
"1",
":",
"Ex",
"##ample",
"trust",
"graph",
".",
"The",
"highlighted",
"edges",
"represent",
"the",
"UN",
"##L",
"of",
"node",
"Pi",
".",
"messages",
"from",
"P",
"##j",
".",
"To",
"implement",
"such",
"an",
"authentic",
"##ated",
"channel",
",",
"all",
"messages",
"are",
"cry",
"##pt",
"##ographic",
"##ally",
"signed",
"and",
"verified",
"by",
"receivers",
".",
"Each",
"node",
"uses",
"a",
"single",
"communication",
"primitive",
"broadcast",
",",
"which",
"when",
"called",
"from",
"node",
"P",
"##j",
"sends",
"the",
"same",
"message",
"to",
"all",
"nodes",
"Pi",
"for",
"which",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
".",
"In",
"the",
"algorithms",
"presented",
"in",
"app",
"##end",
"##ix",
"A",
",",
"we",
"use",
"a",
"corresponding",
"receive",
"primitive",
"which",
"is",
"called",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
"upon",
"the",
"re",
"##ceipt",
"of",
"a",
"broadcast",
"message",
".",
"The",
"outcome",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"for",
"a",
"node",
"to",
"fully",
"valid",
"##ate",
"ledge",
"##rs",
".",
"A",
"fully",
"valid",
"##ated",
"ledge",
"##r",
"is",
"i",
"##rre",
"##voc"
] | Analysis of the XRP Ledger Consensus Protocol | 157 |
ing transactions within each set
and how to apply transactions to generate the new ledger state. Thus, the role of
XRP LCP is only to make the network reach agreement on sets of transactions,
not on the content or outcome of those transactions. As long as nodes agree
on a transaction set, the transaction processing protocol guarantees that every
node generates a consistent ledger. As a Byzantine fault tolerant protocol, XRP
LCP must operate even in the presence of faulty or malicious participants.
Byzant | [
1165,
1122,
1110,
4260,
119,
1370,
1251,
14372,
21902,
117,
1195,
21185,
11437,
134,
197,
7414,
2162,
1182,
197,
1105,
9410,
1103,
186,
11848,
5697,
117,
21307,
186,
1182,
117,
170,
17816,
1134,
4986,
188,
25392,
9387,
1103,
5867,
1295,
1104,
17577,
15029,
1107,
7414,
2162,
1182,
1115,
21902,
2993,
1106,
2100,
1121,
1106,
10836,
1106,
170,
2383,
119,
2994,
14372,
3741,
186,
1182,
1106,
1129,
2908,
110,
1104,
1157,
7414,
2162,
2060,
117,
1137,
117,
1167,
2839,
117,
186,
1182,
134,
100,
121,
119,
129,
2605,
100,
119,
1284,
7568,
1120,
1211,
189,
1182,
127,
11437,
851,
186,
1182,
15029,
1107,
7414,
2162,
1182,
1336,
1129,
8377,
6088,
1183,
119,
2421,
149,
4248,
170,
21340,
1197,
117,
1134,
1110,
1103,
3416,
1352,
1104,
1103,
1449,
1105,
2075,
3300,
11106,
117,
5233,
1116,
117,
1546,
2146,
117,
3576,
119,
1960,
21340,
1733,
149,
117,
149,
797,
1132,
1103,
1269,
1191,
1152,
4248,
1103,
1269,
2802,
1607,
1104,
14409,
2547,
1121,
1103,
3527,
9077,
1548,
21340,
1197,
119,
2994,
21340,
1197,
1145,
1144,
4954,
1295,
14516,
4426,
113,
149,
114,
1115,
1110,
1141,
3407,
1190,
1157,
6486,
21340,
1197,
112,
188,
4954,
1295,
119,
1109,
9077,
1548,
21340,
1197,
1144,
14516,
4426,
113,
149,
114,
134,
122,
119,
138,
21340,
1197,
149,
1110,
1687,
1118,
11892,
170,
4954,
1104,
14409,
157,
134,
164,
193,
1568,
117,
193,
1475,
117,
119,
119,
119,
166,
1106,
1157,
6486,
6486,
113,
149,
114,
2452,
1106,
1103,
11309,
2995,
119,
1960,
21340,
1733,
1336,
1138,
1103,
1269,
6486,
21340,
1197,
1105,
4954,
1295,
117,
1133,
11271,
1272,
1152,
3666,
1472,
14409,
119,
5322,
1463,
1115,
1103,
11309,
188,
25392,
9387,
1115,
1451,
1383,
1104,
14409,
1144,
170,
1260,
2083,
25685,
5668,
13649,
117,
1177,
1122,
1110,
1136,
1936,
1111,
1160,
5663,
15029,
1106,
6058,
1103,
1269,
14409,
1133,
1107,
170,
1472,
1546,
119,
1109,
15029,
10621,
1166,
170,
8536,
118,
1106,
118,
8536,
2443,
1134,
1144,
1185,
17421,
6796,
1114,
1103,
7414,
2162,
2401,
119,
1284,
2566,
7568,
1115,
1111,
1451,
14372,
21902,
1105,
1451,
14372,
153,
3361,
850,
7414,
2162,
1182,
117,
1175,
1110,
170,
10682,
16047,
2913,
3094,
1111,
21902,
1106,
3531,
124,
170,
172,
171,
174,
173,
176,
175,
178,
177,
179,
15982,
122,
131,
16409,
26671,
3496,
10873,
119,
1109,
11634,
7521,
4248,
1103,
7414,
2162,
1104,
14372,
21902,
119,
7416,
1121,
153,
3361,
119,
1706,
10407,
1216,
1126,
16047,
2913,
3094,
117,
1155,
7416,
1132,
5354,
6451,
9597,
2716,
1878,
1105,
22480,
1118,
21535,
119,
2994,
14372,
2745,
170,
1423,
4909,
12130,
3012,
117,
1134,
1165,
1270,
1121,
14372,
153,
3361,
10130,
1103,
1269,
3802,
1106,
1155,
15029,
21902,
1111,
1134,
153,
3361,
850,
7414,
2162,
1182,
119,
1130,
1103,
14975,
2756,
1107,
12647,
6696,
7231,
138,
117,
1195,
1329,
170,
7671,
3531,
12130,
1134,
1110,
1270,
1112,
27250,
8167,
23038,
1361,
1193,
1852,
1103,
1231,
27333,
1104,
170,
3012,
3802,
119,
1109,
9386,
1104,
161,
20336,
149,
13113,
1110,
1111,
170,
14372,
1106,
3106,
9221,
2193,
21340,
1733,
119,
138,
3106,
9221,
2913,
21340,
1197,
1110,
178,
11604,
24553
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0
] | [
"when",
"it",
"is",
"assumed",
".",
"For",
"any",
"node",
"Pi",
",",
"we",
"denote",
"ni",
"=",
"|",
"UN",
"##L",
"##i",
"|",
"and",
"define",
"the",
"q",
"##uo",
"##rum",
",",
"denoted",
"q",
"##i",
",",
"a",
"parameter",
"which",
"roughly",
"s",
"##pec",
"##ifies",
"the",
"minimum",
"number",
"of",
"agreeing",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"Pi",
"needs",
"to",
"hear",
"from",
"to",
"commit",
"to",
"a",
"decision",
".",
"Each",
"node",
"sets",
"q",
"##i",
"to",
"be",
"80",
"%",
"of",
"its",
"UN",
"##L",
"size",
",",
"or",
",",
"more",
"exactly",
",",
"q",
"##i",
"=",
"[UNK]",
"0",
".",
"8",
"##ni",
"[UNK]",
".",
"We",
"assume",
"at",
"most",
"t",
"##i",
"6",
"ni",
"β",
"q",
"##i",
"nodes",
"in",
"UN",
"##L",
"##i",
"may",
"be",
"Byzantine",
"fault",
"##y",
".",
"Let",
"L",
"represent",
"a",
"ledge",
"##r",
",",
"which",
"is",
"the",
"shared",
"state",
"of",
"the",
"system",
"and",
"includes",
"account",
"settings",
",",
"balance",
"##s",
",",
"order",
"books",
",",
"etc",
".",
"Two",
"ledge",
"##rs",
"L",
",",
"L",
"β²",
"are",
"the",
"same",
"if",
"they",
"represent",
"the",
"same",
"ordered",
"history",
"of",
"transactions",
"starting",
"from",
"the",
"unique",
"genes",
"##is",
"ledge",
"##r",
".",
"Each",
"ledge",
"##r",
"also",
"has",
"sequence",
"number",
"se",
"##q",
"(",
"L",
")",
"that",
"is",
"one",
"greater",
"than",
"its",
"parent",
"ledge",
"##r",
"'",
"s",
"sequence",
"number",
".",
"The",
"genes",
"##is",
"ledge",
"##r",
"has",
"se",
"##q",
"(",
"L",
")",
"=",
"1",
".",
"A",
"ledge",
"##r",
"L",
"is",
"created",
"by",
"applying",
"a",
"sequence",
"of",
"transactions",
"T",
"=",
"[",
"x",
"##0",
",",
"x",
"##1",
",",
".",
".",
".",
"]",
"to",
"its",
"parent",
"parent",
"(",
"L",
")",
"according",
"to",
"the",
"protocol",
"rules",
".",
"Two",
"ledge",
"##rs",
"may",
"have",
"the",
"same",
"parent",
"ledge",
"##r",
"and",
"sequence",
"number",
",",
"but",
"differ",
"because",
"they",
"applied",
"different",
"transactions",
".",
"Note",
"though",
"that",
"the",
"protocol",
"s",
"##pec",
"##ifies",
"that",
"every",
"set",
"of",
"transactions",
"has",
"a",
"de",
"##ter",
"##mini",
"##stic",
"ordering",
",",
"so",
"it",
"is",
"not",
"possible",
"for",
"two",
"correct",
"nodes",
"to",
"apply",
"the",
"same",
"transactions",
"but",
"in",
"a",
"different",
"order",
".",
"The",
"nodes",
"communicate",
"over",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
"which",
"has",
"no",
"prescribed",
"relation",
"with",
"the",
"UN",
"##L",
"structure",
".",
"We",
"simply",
"assume",
"that",
"for",
"every",
"node",
"Pi",
"and",
"every",
"node",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
",",
"there",
"is",
"a",
"reliable",
"authentic",
"##ated",
"channel",
"for",
"Pi",
"to",
"receive",
"3",
"a",
"c",
"b",
"e",
"d",
"g",
"f",
"i",
"h",
"j",
"Figure",
"1",
":",
"Ex",
"##ample",
"trust",
"graph",
".",
"The",
"highlighted",
"edges",
"represent",
"the",
"UN",
"##L",
"of",
"node",
"Pi",
".",
"messages",
"from",
"P",
"##j",
".",
"To",
"implement",
"such",
"an",
"authentic",
"##ated",
"channel",
",",
"all",
"messages",
"are",
"cry",
"##pt",
"##ographic",
"##ally",
"signed",
"and",
"verified",
"by",
"receivers",
".",
"Each",
"node",
"uses",
"a",
"single",
"communication",
"primitive",
"broadcast",
",",
"which",
"when",
"called",
"from",
"node",
"P",
"##j",
"sends",
"the",
"same",
"message",
"to",
"all",
"nodes",
"Pi",
"for",
"which",
"P",
"##j",
"β",
"UN",
"##L",
"##i",
".",
"In",
"the",
"algorithms",
"presented",
"in",
"app",
"##end",
"##ix",
"A",
",",
"we",
"use",
"a",
"corresponding",
"receive",
"primitive",
"which",
"is",
"called",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
"upon",
"the",
"re",
"##ceipt",
"of",
"a",
"broadcast",
"message",
".",
"The",
"outcome",
"of",
"X",
"##RP",
"L",
"##CP",
"is",
"for",
"a",
"node",
"to",
"fully",
"valid",
"##ate",
"ledge",
"##rs",
".",
"A",
"fully",
"valid",
"##ated",
"ledge",
"##r",
"is",
"i",
"##rre",
"##voc"
] | Analysis of the XRP Ledger Consensus Protocol | 158 |
ine fault tolerant consensus protocols have a rich history, but most
require preexisting agreement on the protocol participants [8, 3]. The distin-
guishing characteristic of XRP LCP is that it guarantees consistency with only
1
http://arxiv.org/abs/1802.07242v1
partial agreement on who participates, allowing a decentralized open network.
Compared to other decentralized consensus algorithms like proof-of-work [7] or
proof-of-stake [2], XRP LCP has since its inception provided lower transaction
latency | [
1895,
1105,
27355,
117,
1105,
11363,
14409,
4841,
118,
26410,
1906,
1118,
2443,
7550,
1105,
3134,
1118,
1103,
10923,
9932,
119,
8896,
1183,
191,
10584,
118,
4676,
170,
21340,
1197,
1145,
3106,
9221,
5430,
1155,
1104,
1157,
11005,
119,
1130,
1142,
5618,
117,
170,
13097,
1110,
170,
2820,
1107,
1134,
1160,
7345,
15029,
3106,
9221,
2193,
14255,
4487,
28113,
4649,
21340,
1733,
117,
178,
119,
174,
119,
117,
1472,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
119,
1109,
2443,
1110,
1163,
1106,
1129,
13097,
118,
2914,
1191,
1122,
1169,
1309,
13097,
1114,
170,
21073,
1181,
9566,
1104,
8377,
15029,
119,
1966,
161,
20336,
149,
13113,
1110,
3417,
3393,
1107,
2538,
1104,
1103,
3106,
9221,
2913,
4129,
1104,
21340,
1733,
117,
1290,
1296,
21340,
1197,
1107,
1103,
4129,
5149,
170,
1260,
2083,
25685,
5668,
2716,
118,
2802,
4954,
1104,
14409,
1122,
1145,
1169,
1129,
1737,
1112,
1126,
12861,
3012,
5250,
118,
1106,
2528,
1233,
1114,
15817,
1158,
1104,
14409,
1111,
8096,
119,
15075,
2716,
117,
1126,
12861,
3012,
11309,
1110,
1126,
9932,
1107,
1134,
170,
1383,
1104,
7550,
117,
170,
26281,
2875,
22190,
5264,
1242,
1104,
1134,
1336,
1129,
8377,
6088,
1183,
117,
1169,
3012,
14409,
117,
1105,
1296,
14372,
1169,
4392,
1199,
1104,
1343,
14409,
2452,
1106,
1103,
1378,
4625,
131,
122,
119,
5254,
118,
11225,
131,
1409,
170,
5663,
14372,
13749,
170,
13618,
1154,
170,
21340,
1197,
117,
1173,
2028,
1155,
5663,
15029,
4392,
1103,
13618,
1154,
170,
21340,
1197,
119,
125,
123,
119,
5254,
118,
2800,
7710,
3293,
5474,
131,
1409,
170,
5663,
14372,
13749,
13618,
193,
1196,
14715,
118,
2168,
193,
797,
117,
1173,
1155,
5663,
15029,
4392,
13618,
193,
1196,
193,
797,
119,
124,
119,
5254,
118,
24664,
27035,
1733,
3157,
118,
11336,
5053,
7174,
3633,
131,
1409,
170,
5663,
7230,
8737,
170,
9221,
14715,
7409,
118,
189,
1988,
193,
1106,
1155,
5663,
15029,
117,
193,
1209,
2028,
1129,
3134,
1118,
1155,
15029,
119,
1760,
12861,
3012,
9932,
1110,
1107,
2440,
170,
8120,
1104,
10923,
164,
125,
166,
119,
5322,
1115,
24664,
27035,
1733,
3157,
11336,
5053,
7174,
3633,
1110,
1103,
4698,
2200,
5754,
1104,
1977,
5070,
119,
1130,
2415,
117,
1103,
8536,
118,
1106,
118,
8536,
2443,
25772,
1116,
1103,
8875,
1115,
7550,
4841,
118,
26410,
1147,
13618,
1106,
1155,
5663,
15029,
117,
1290,
5663,
15029,
1209,
16278,
170,
4841,
118,
26410,
1906,
13618,
1106,
1296,
1168,
117,
9420,
1103,
2443,
1235,
1451,
14372,
7881,
1122,
119,
1130,
1546,
1106,
17459,
1103,
5663,
1757,
1104,
161,
20336,
149,
13113,
117,
1195,
2235,
1103,
8536,
118,
1106,
118,
8536,
2443,
1112,
1191,
1122,
1127,
4013,
1118,
170,
2443,
8050,
10704,
3113,
1115,
1169,
18492,
170,
26281,
2875,
22190,
5264,
119,
1109,
8050,
10704,
3113,
1110,
7451,
1103,
6779,
1546,
1104,
1155,
7416,
117,
1112,
1218,
1112,
1120,
1211,
189,
1182,
15029,
1107,
7414,
2162,
1182,
1111,
1251,
5663,
14372,
21902,
119,
1284,
7568,
1463,
1115,
1103,
8050,
10704,
3113,
1110,
19903,
1193,
10350,
132,
1107,
2440,
117,
1122,
1110,
3372,
1106,
2549,
2412,
3134,
5354,
6451,
9597,
19755,
119,
1109,
17409,
1104,
8377,
15029,
1132,
3655
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
9,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
23,
24,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
23,
24,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
22,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
9,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
23,
24,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
23,
24,
23,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##able",
"and",
"authoritative",
",",
"and",
"reflects",
"transactions",
"sub",
"-",
"mit",
"##ted",
"by",
"network",
"clients",
"and",
"accepted",
"by",
"the",
"consensus",
"algorithm",
".",
"Full",
"##y",
"v",
"##ali",
"-",
"dating",
"a",
"ledge",
"##r",
"also",
"fully",
"valid",
"##ates",
"all",
"of",
"its",
"ancestors",
".",
"In",
"this",
"context",
",",
"a",
"fork",
"is",
"a",
"situation",
"in",
"which",
"two",
"honest",
"nodes",
"fully",
"valid",
"##ate",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
",",
"i",
".",
"e",
".",
",",
"different",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
".",
"The",
"network",
"is",
"said",
"to",
"be",
"fork",
"-",
"safe",
"if",
"it",
"can",
"never",
"fork",
"with",
"a",
"tolerate",
"##d",
"configuration",
"of",
"Byzantine",
"nodes",
".",
"Although",
"X",
"##RP",
"L",
"##CP",
"is",
"typically",
"defined",
"in",
"terms",
"of",
"the",
"fully",
"valid",
"##ated",
"chain",
"of",
"ledge",
"##rs",
",",
"since",
"each",
"ledge",
"##r",
"in",
"the",
"chain",
"represents",
"a",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"-",
"ordered",
"sequence",
"of",
"transactions",
"it",
"also",
"can",
"be",
"considered",
"as",
"an",
"atomic",
"broadcast",
"pro",
"-",
"to",
"##co",
"##l",
"with",
"batch",
"##ing",
"of",
"transactions",
"for",
"efficiency",
".",
"Form",
"##ally",
",",
"an",
"atomic",
"broadcast",
"protocol",
"is",
"an",
"algorithm",
"in",
"which",
"a",
"set",
"of",
"clients",
",",
"a",
"##rb",
"##it",
"##rar",
"##ily",
"many",
"of",
"which",
"may",
"be",
"Byzantine",
"fault",
"##y",
",",
"can",
"broadcast",
"transactions",
",",
"and",
"each",
"node",
"can",
"accept",
"some",
"of",
"those",
"transactions",
"according",
"to",
"the",
"following",
"properties",
":",
"1",
".",
"ABC",
"-",
"Agreement",
":",
"If",
"a",
"correct",
"node",
"accepts",
"a",
"transaction",
"into",
"a",
"ledge",
"##r",
",",
"then",
"eventually",
"all",
"correct",
"nodes",
"accept",
"the",
"transaction",
"into",
"a",
"ledge",
"##r",
".",
"4",
"2",
".",
"ABC",
"-",
"Line",
"##ari",
"##za",
"##bility",
":",
"If",
"a",
"correct",
"node",
"accepts",
"transaction",
"x",
"before",
"trans",
"-",
"action",
"x",
"β²",
",",
"then",
"all",
"correct",
"nodes",
"accept",
"transaction",
"x",
"before",
"x",
"β²",
".",
"3",
".",
"ABC",
"-",
"Ce",
"##nso",
"##rs",
"##hip",
"-",
"Re",
"##si",
"##lie",
"##nce",
":",
"If",
"a",
"correct",
"client",
"broadcasts",
"a",
"valid",
"trans",
"##ac",
"-",
"t",
"##ion",
"x",
"to",
"all",
"correct",
"nodes",
",",
"x",
"will",
"eventually",
"be",
"accepted",
"by",
"all",
"nodes",
".",
"An",
"atomic",
"broadcast",
"algorithm",
"is",
"in",
"particular",
"a",
"variant",
"of",
"consensus",
"[",
"4",
"]",
".",
"Note",
"that",
"Ce",
"##nso",
"##rs",
"##hip",
"Re",
"##si",
"##lie",
"##nce",
"is",
"the",
"formal",
"##ized",
"definition",
"of",
"forward",
"progress",
".",
"In",
"practice",
",",
"the",
"peer",
"-",
"to",
"-",
"peer",
"network",
"weaken",
"##s",
"the",
"requirement",
"that",
"clients",
"sub",
"-",
"mit",
"their",
"transaction",
"to",
"all",
"correct",
"nodes",
",",
"since",
"correct",
"nodes",
"will",
"echo",
"a",
"sub",
"-",
"mit",
"##ted",
"transaction",
"to",
"each",
"other",
",",
"flooding",
"the",
"network",
"until",
"every",
"node",
"receives",
"it",
".",
"In",
"order",
"to",
"evaluate",
"the",
"correct",
"##ness",
"of",
"X",
"##RP",
"L",
"##CP",
",",
"we",
"model",
"the",
"peer",
"-",
"to",
"-",
"peer",
"network",
"as",
"if",
"it",
"were",
"controlled",
"by",
"a",
"network",
"ad",
"##vers",
"##ary",
"that",
"can",
"behave",
"a",
"##rb",
"##it",
"##rar",
"##ily",
".",
"The",
"ad",
"##vers",
"##ary",
"is",
"controls",
"the",
"delivery",
"order",
"of",
"all",
"messages",
",",
"as",
"well",
"as",
"at",
"most",
"t",
"##i",
"nodes",
"in",
"UN",
"##L",
"##i",
"for",
"any",
"correct",
"node",
"Pi",
".",
"We",
"assume",
"though",
"that",
"the",
"ad",
"##vers",
"##ary",
"is",
"computational",
"##ly",
"bounded",
";",
"in",
"particular",
",",
"it",
"is",
"unable",
"to",
"break",
"generally",
"accepted",
"cry",
"##pt",
"##ographic",
"protocols",
".",
"The",
"identities",
"of",
"Byzantine",
"nodes",
"are",
"unknown"
] | Analysis of the XRP Ledger Consensus Protocol | 159 |
ine fault tolerant consensus protocols have a rich history, but most
require preexisting agreement on the protocol participants [8, 3]. The distin-
guishing characteristic of XRP LCP is that it guarantees consistency with only
1
http://arxiv.org/abs/1802.07242v1
partial agreement on who participates, allowing a decentralized open network.
Compared to other decentralized consensus algorithms like proof-of-work [7] or
proof-of-stake [2], XRP LCP has since its inception provided lower transaction
latency | [
1895,
1105,
27355,
117,
1105,
11363,
14409,
4841,
118,
26410,
1906,
1118,
2443,
7550,
1105,
3134,
1118,
1103,
10923,
9932,
119,
8896,
1183,
191,
10584,
118,
4676,
170,
21340,
1197,
1145,
3106,
9221,
5430,
1155,
1104,
1157,
11005,
119,
1130,
1142,
5618,
117,
170,
13097,
1110,
170,
2820,
1107,
1134,
1160,
7345,
15029,
3106,
9221,
2193,
14255,
4487,
28113,
4649,
21340,
1733,
117,
178,
119,
174,
119,
117,
1472,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
119,
1109,
2443,
1110,
1163,
1106,
1129,
13097,
118,
2914,
1191,
1122,
1169,
1309,
13097,
1114,
170,
21073,
1181,
9566,
1104,
8377,
15029,
119,
1966,
161,
20336,
149,
13113,
1110,
3417,
3393,
1107,
2538,
1104,
1103,
3106,
9221,
2913,
4129,
1104,
21340,
1733,
117,
1290,
1296,
21340,
1197,
1107,
1103,
4129,
5149,
170,
1260,
2083,
25685,
5668,
2716,
118,
2802,
4954,
1104,
14409,
1122,
1145,
1169,
1129,
1737,
1112,
1126,
12861,
3012,
5250,
118,
1106,
2528,
1233,
1114,
15817,
1158,
1104,
14409,
1111,
8096,
119,
15075,
2716,
117,
1126,
12861,
3012,
11309,
1110,
1126,
9932,
1107,
1134,
170,
1383,
1104,
7550,
117,
170,
26281,
2875,
22190,
5264,
1242,
1104,
1134,
1336,
1129,
8377,
6088,
1183,
117,
1169,
3012,
14409,
117,
1105,
1296,
14372,
1169,
4392,
1199,
1104,
1343,
14409,
2452,
1106,
1103,
1378,
4625,
131,
122,
119,
5254,
118,
11225,
131,
1409,
170,
5663,
14372,
13749,
170,
13618,
1154,
170,
21340,
1197,
117,
1173,
2028,
1155,
5663,
15029,
4392,
1103,
13618,
1154,
170,
21340,
1197,
119,
125,
123,
119,
5254,
118,
2800,
7710,
3293,
5474,
131,
1409,
170,
5663,
14372,
13749,
13618,
193,
1196,
14715,
118,
2168,
193,
797,
117,
1173,
1155,
5663,
15029,
4392,
13618,
193,
1196,
193,
797,
119,
124,
119,
5254,
118,
24664,
27035,
1733,
3157,
118,
11336,
5053,
7174,
3633,
131,
1409,
170,
5663,
7230,
8737,
170,
9221,
14715,
7409,
118,
189,
1988,
193,
1106,
1155,
5663,
15029,
117,
193,
1209,
2028,
1129,
3134,
1118,
1155,
15029,
119,
1760,
12861,
3012,
9932,
1110,
1107,
2440,
170,
8120,
1104,
10923,
164,
125,
166,
119,
5322,
1115,
24664,
27035,
1733,
3157,
11336,
5053,
7174,
3633,
1110,
1103,
4698,
2200,
5754,
1104,
1977,
5070,
119,
1130,
2415,
117,
1103,
8536,
118,
1106,
118,
8536,
2443,
25772,
1116,
1103,
8875,
1115,
7550,
4841,
118,
26410,
1147,
13618,
1106,
1155,
5663,
15029,
117,
1290,
5663,
15029,
1209,
16278,
170,
4841,
118,
26410,
1906,
13618,
1106,
1296,
1168,
117,
9420,
1103,
2443,
1235,
1451,
14372,
7881,
1122,
119,
1130,
1546,
1106,
17459,
1103,
5663,
1757,
1104,
161,
20336,
149,
13113,
117,
1195,
2235,
1103,
8536,
118,
1106,
118,
8536,
2443,
1112,
1191,
1122,
1127,
4013,
1118,
170,
2443,
8050,
10704,
3113,
1115,
1169,
18492,
170,
26281,
2875,
22190,
5264,
119,
1109,
8050,
10704,
3113,
1110,
7451,
1103,
6779,
1546,
1104,
1155,
7416,
117,
1112,
1218,
1112,
1120,
1211,
189,
1182,
15029,
1107,
7414,
2162,
1182,
1111,
1251,
5663,
14372,
21902,
119,
1284,
7568,
1463,
1115,
1103,
8050,
10704,
3113,
1110,
19903,
1193,
10350,
132,
1107,
2440,
117,
1122,
1110,
3372,
1106,
2549,
2412,
3134,
5354,
6451,
9597,
19755,
119,
1109,
17409,
1104,
8377,
15029,
1132,
3655
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"##able",
"and",
"authoritative",
",",
"and",
"reflects",
"transactions",
"sub",
"-",
"mit",
"##ted",
"by",
"network",
"clients",
"and",
"accepted",
"by",
"the",
"consensus",
"algorithm",
".",
"Full",
"##y",
"v",
"##ali",
"-",
"dating",
"a",
"ledge",
"##r",
"also",
"fully",
"valid",
"##ates",
"all",
"of",
"its",
"ancestors",
".",
"In",
"this",
"context",
",",
"a",
"fork",
"is",
"a",
"situation",
"in",
"which",
"two",
"honest",
"nodes",
"fully",
"valid",
"##ate",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
",",
"i",
".",
"e",
".",
",",
"different",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
".",
"The",
"network",
"is",
"said",
"to",
"be",
"fork",
"-",
"safe",
"if",
"it",
"can",
"never",
"fork",
"with",
"a",
"tolerate",
"##d",
"configuration",
"of",
"Byzantine",
"nodes",
".",
"Although",
"X",
"##RP",
"L",
"##CP",
"is",
"typically",
"defined",
"in",
"terms",
"of",
"the",
"fully",
"valid",
"##ated",
"chain",
"of",
"ledge",
"##rs",
",",
"since",
"each",
"ledge",
"##r",
"in",
"the",
"chain",
"represents",
"a",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"-",
"ordered",
"sequence",
"of",
"transactions",
"it",
"also",
"can",
"be",
"considered",
"as",
"an",
"atomic",
"broadcast",
"pro",
"-",
"to",
"##co",
"##l",
"with",
"batch",
"##ing",
"of",
"transactions",
"for",
"efficiency",
".",
"Form",
"##ally",
",",
"an",
"atomic",
"broadcast",
"protocol",
"is",
"an",
"algorithm",
"in",
"which",
"a",
"set",
"of",
"clients",
",",
"a",
"##rb",
"##it",
"##rar",
"##ily",
"many",
"of",
"which",
"may",
"be",
"Byzantine",
"fault",
"##y",
",",
"can",
"broadcast",
"transactions",
",",
"and",
"each",
"node",
"can",
"accept",
"some",
"of",
"those",
"transactions",
"according",
"to",
"the",
"following",
"properties",
":",
"1",
".",
"ABC",
"-",
"Agreement",
":",
"If",
"a",
"correct",
"node",
"accepts",
"a",
"transaction",
"into",
"a",
"ledge",
"##r",
",",
"then",
"eventually",
"all",
"correct",
"nodes",
"accept",
"the",
"transaction",
"into",
"a",
"ledge",
"##r",
".",
"4",
"2",
".",
"ABC",
"-",
"Line",
"##ari",
"##za",
"##bility",
":",
"If",
"a",
"correct",
"node",
"accepts",
"transaction",
"x",
"before",
"trans",
"-",
"action",
"x",
"β²",
",",
"then",
"all",
"correct",
"nodes",
"accept",
"transaction",
"x",
"before",
"x",
"β²",
".",
"3",
".",
"ABC",
"-",
"Ce",
"##nso",
"##rs",
"##hip",
"-",
"Re",
"##si",
"##lie",
"##nce",
":",
"If",
"a",
"correct",
"client",
"broadcasts",
"a",
"valid",
"trans",
"##ac",
"-",
"t",
"##ion",
"x",
"to",
"all",
"correct",
"nodes",
",",
"x",
"will",
"eventually",
"be",
"accepted",
"by",
"all",
"nodes",
".",
"An",
"atomic",
"broadcast",
"algorithm",
"is",
"in",
"particular",
"a",
"variant",
"of",
"consensus",
"[",
"4",
"]",
".",
"Note",
"that",
"Ce",
"##nso",
"##rs",
"##hip",
"Re",
"##si",
"##lie",
"##nce",
"is",
"the",
"formal",
"##ized",
"definition",
"of",
"forward",
"progress",
".",
"In",
"practice",
",",
"the",
"peer",
"-",
"to",
"-",
"peer",
"network",
"weaken",
"##s",
"the",
"requirement",
"that",
"clients",
"sub",
"-",
"mit",
"their",
"transaction",
"to",
"all",
"correct",
"nodes",
",",
"since",
"correct",
"nodes",
"will",
"echo",
"a",
"sub",
"-",
"mit",
"##ted",
"transaction",
"to",
"each",
"other",
",",
"flooding",
"the",
"network",
"until",
"every",
"node",
"receives",
"it",
".",
"In",
"order",
"to",
"evaluate",
"the",
"correct",
"##ness",
"of",
"X",
"##RP",
"L",
"##CP",
",",
"we",
"model",
"the",
"peer",
"-",
"to",
"-",
"peer",
"network",
"as",
"if",
"it",
"were",
"controlled",
"by",
"a",
"network",
"ad",
"##vers",
"##ary",
"that",
"can",
"behave",
"a",
"##rb",
"##it",
"##rar",
"##ily",
".",
"The",
"ad",
"##vers",
"##ary",
"is",
"controls",
"the",
"delivery",
"order",
"of",
"all",
"messages",
",",
"as",
"well",
"as",
"at",
"most",
"t",
"##i",
"nodes",
"in",
"UN",
"##L",
"##i",
"for",
"any",
"correct",
"node",
"Pi",
".",
"We",
"assume",
"though",
"that",
"the",
"ad",
"##vers",
"##ary",
"is",
"computational",
"##ly",
"bounded",
";",
"in",
"particular",
",",
"it",
"is",
"unable",
"to",
"break",
"generally",
"accepted",
"cry",
"##pt",
"##ographic",
"protocols",
".",
"The",
"identities",
"of",
"Byzantine",
"nodes",
"are",
"unknown"
] | Analysis of the XRP Ledger Consensus Protocol | 160 |
and higher throughput for its users. However, without uniform agree-
ment on the network participants, users still need a way to determine whether
their choice of network peers will lead to a consistent network state. In this
setting, each user individually defines a unique node list or UNL, which is
the set of nodes whose messages it will listen to when making decisions about
the network state. It is the intersection of any pair of correct nodes' UNLs that
determines network safety. As described in the | [
1107,
4657,
1118,
7345,
15029,
1107,
1103,
2443,
119,
1967,
12861,
3012,
1110,
170,
8120,
1104,
10923,
117,
1118,
1103,
23485,
2101,
1871,
164,
126,
166,
1195,
2834,
11865,
1977,
5070,
1107,
1103,
2915,
1104,
16439,
1112,
27250,
8167,
10031,
1105,
6088,
1183,
15029,
119,
3743,
117,
1195,
7568,
170,
1532,
1104,
107,
4780,
1112,
27250,
8167,
10031,
107,
131,
3429,
1431,
2080,
1223,
16439,
1112,
27250,
8167,
10031,
117,
1133,
18125,
1231,
5053,
7174,
3633,
1110,
1178,
13008,
1106,
2080,
1223,
1103,
13457,
1115,
1103,
2443,
1110,
2028,
2987,
117,
2764,
1115,
7416,
1132,
4653,
1439,
1199,
11309,
118,
9467,
4177,
8513,
4930,
1105,
1185,
15029,
1132,
6088,
1183,
119,
1130,
1546,
1106,
1494,
17542,
1103,
10350,
8513,
1107,
1103,
161,
20336,
21340,
1197,
24034,
14183,
1424,
118,
27629,
2116,
117,
1317,
1119,
26900,
1116,
1132,
1215,
1106,
6183,
2495,
10932,
15029,
117,
3843,
12177,
9420,
1104,
7416,
1105,
2438,
3404,
1194,
1103,
2443,
119,
17580,
11934,
1145,
9410,
4177,
15308,
1113,
1472,
9373,
7416,
1107,
1126,
2661,
1106,
4256,
1686,
1757,
119,
1966,
1195,
8429,
1292,
4068,
1106,
27466,
8223,
22881,
1103,
8685,
2071,
117,
1195,
6600,
1115,
1152,
1132,
1696,
6691,
19069,
1107,
1103,
4315,
24034,
14183,
1424,
118,
27629,
2116,
1105,
1654,
1103,
1842,
1362,
2099,
1104,
1103,
9932,
119,
1109,
1864,
1115,
161,
20336,
149,
13113,
1110,
1178,
19057,
1112,
27250,
8167,
23038,
1361,
1105,
1157,
2099,
9113,
1113,
1292,
11934,
1110,
170,
26802,
1104,
1103,
9932,
119,
3291,
26443,
117,
1103,
3000,
4174,
9932,
1106,
161,
20336,
149,
13113,
117,
1674,
1136,
1138,
1292,
13004,
119,
1135,
2745,
5354,
6451,
9597,
7091,
1757,
1106,
174,
27923,
1103,
23485,
2101,
1871,
1105,
24512,
1977,
5070,
1256,
1114,
1103,
12477,
23984,
1295,
1104,
21073,
1181,
6088,
1183,
15029,
1105,
8362,
8346,
1174,
1112,
27250,
8167,
10031,
164,
127,
166,
119,
11389,
122,
7584,
7317,
9534,
1412,
16049,
117,
1259,
1199,
1115,
1209,
1129,
3716,
1107,
4194,
4886,
119,
124,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
2923,
1104,
1210,
2425,
5644,
131,
794,
9352,
24851,
1891,
117,
1107,
1134,
15029,
1122,
21126,
1193,
17794,
170,
13618,
1383,
1106,
6058,
1106,
170,
2988,
21340,
1197,
117,
1359,
1113,
10698,
1460,
1121,
1168,
9373,
126,
21902,
138,
14372,
1107,
1103,
2443,
7414,
2162,
1182,
1109,
3527,
14372,
2190,
113,
7414,
2162,
114,
2700,
1118,
21902,
11437,
117,
186,
1182,
117,
189,
1182,
1109,
2060,
117,
9221,
1891,
186,
11848,
5697,
1105,
4177,
8377,
21688,
1104,
7414,
2162,
1182,
149,
138,
21340,
1197,
14516,
4426,
113,
149,
114,
22087,
25113,
1295,
1104,
21340,
1197,
149,
100,
8896,
1183,
9221,
2913,
21340,
1197,
1114,
2026,
4954,
1295,
113,
1103,
3106,
9221,
2913,
5580,
21340,
1197,
114,
149,
28311,
9493,
1684,
21340,
1197,
1104,
3687,
24851,
1891,
157,
134,
196,
193,
1568,
117,
193,
1475,
117,
119,
119,
119,
198,
138,
1383,
1104,
14409,
22216,
117,
187,
117,
149,
117,
178,
1302,
2007,
21902,
112,
188,
187,
118,
24438,
3687,
24851,
1891,
5835,
1104,
14409,
157,
1106,
6058,
1106,
149
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
23,
24,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
23,
24,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"in",
"advance",
"by",
"honest",
"nodes",
"in",
"the",
"network",
".",
"Since",
"atomic",
"broadcast",
"is",
"a",
"variant",
"of",
"consensus",
",",
"by",
"the",
"FL",
"##P",
"result",
"[",
"5",
"]",
"we",
"cannot",
"guarantee",
"forward",
"progress",
"in",
"the",
"presence",
"of",
"arbitrary",
"as",
"##ync",
"##hr",
"##ony",
"and",
"fault",
"##y",
"nodes",
".",
"Instead",
",",
"we",
"assume",
"a",
"form",
"of",
"\"",
"weak",
"as",
"##ync",
"##hr",
"##ony",
"\"",
":",
"safety",
"should",
"hold",
"under",
"arbitrary",
"as",
"##ync",
"##hr",
"##ony",
",",
"but",
"censorship",
"re",
"##si",
"##lie",
"##nce",
"is",
"only",
"guaranteed",
"to",
"hold",
"under",
"the",
"assumption",
"that",
"the",
"network",
"is",
"eventually",
"civil",
",",
"meaning",
"that",
"messages",
"are",
"delivered",
"within",
"some",
"protocol",
"-",
"specified",
"maximum",
"delay",
"bound",
"and",
"no",
"nodes",
"are",
"fault",
"##y",
".",
"In",
"order",
"to",
"help",
"enforce",
"the",
"bounded",
"delay",
"in",
"the",
"X",
"##RP",
"ledge",
"##r",
"imp",
"##lem",
"##en",
"-",
"ta",
"##tion",
",",
"several",
"he",
"##uristic",
"##s",
"are",
"used",
"to",
"identify",
"la",
"##gging",
"nodes",
",",
"prevent",
"excessive",
"flooding",
"of",
"messages",
"and",
"route",
"traffic",
"through",
"the",
"network",
".",
"Protocol",
"parameters",
"also",
"define",
"maximum",
"delays",
"on",
"different",
"trusted",
"messages",
"in",
"an",
"attempt",
"to",
"aid",
"live",
"##ness",
".",
"Although",
"we",
"ignore",
"these",
"details",
"to",
"si",
"##mp",
"##lify",
"the",
"presentation",
"below",
",",
"we",
"stress",
"that",
"they",
"are",
"important",
"practical",
"considerations",
"in",
"the",
"actual",
"imp",
"##lem",
"##en",
"-",
"ta",
"##tion",
"and",
"control",
"the",
"real",
"world",
"performance",
"of",
"the",
"algorithm",
".",
"The",
"fact",
"that",
"X",
"##RP",
"L",
"##CP",
"is",
"only",
"weakly",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"and",
"its",
"performance",
"depends",
"on",
"these",
"parameters",
"is",
"a",
"limitation",
"of",
"the",
"algorithm",
".",
"Co",
"##balt",
",",
"the",
"proposed",
"alternative",
"algorithm",
"to",
"X",
"##RP",
"L",
"##CP",
",",
"does",
"not",
"have",
"these",
"limitations",
".",
"It",
"uses",
"cry",
"##pt",
"##ographic",
"random",
"##ness",
"to",
"e",
"##vade",
"the",
"FL",
"##P",
"result",
"and",
"guarantees",
"forward",
"progress",
"even",
"with",
"the",
"ma",
"##ximal",
"number",
"of",
"tolerate",
"##d",
"fault",
"##y",
"nodes",
"and",
"un",
"##bound",
"##ed",
"as",
"##ync",
"##hr",
"##ony",
"[",
"6",
"]",
".",
"Table",
"1",
"sum",
"##mar",
"##izes",
"our",
"notation",
",",
"including",
"some",
"that",
"will",
"be",
"explained",
"in",
"subsequent",
"sections",
".",
"3",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"consists",
"of",
"three",
"primary",
"components",
":",
"β’",
"Del",
"##iber",
"##ation",
",",
"in",
"which",
"nodes",
"it",
"##erative",
"##ly",
"propose",
"a",
"transaction",
"set",
"to",
"apply",
"to",
"a",
"prior",
"ledge",
"##r",
",",
"based",
"on",
"proposals",
"received",
"from",
"other",
"trusted",
"5",
"Pi",
"A",
"node",
"in",
"the",
"network",
"UN",
"##L",
"##i",
"The",
"unique",
"node",
"list",
"(",
"UN",
"##L",
")",
"selected",
"by",
"Pi",
"ni",
",",
"q",
"##i",
",",
"t",
"##i",
"The",
"size",
",",
"valid",
"##ation",
"q",
"##uo",
"##rum",
"and",
"maximum",
"Byzantine",
"faults",
"of",
"UN",
"##L",
"##i",
"L",
"A",
"ledge",
"##r",
"se",
"##q",
"(",
"L",
")",
"Se",
"##quence",
"number",
"of",
"ledge",
"##r",
"L",
"[UNK]",
"Full",
"##y",
"valid",
"##ated",
"ledge",
"##r",
"with",
"largest",
"sequence",
"number",
"(",
"the",
"fully",
"valid",
"##ated",
"tip",
"ledge",
"##r",
")",
"L",
"##Μ",
"Current",
"working",
"ledge",
"##r",
"of",
"del",
"##iber",
"##ation",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
",",
".",
".",
".",
"}",
"A",
"set",
"of",
"transactions",
"PT",
",",
"r",
",",
"L",
",",
"i",
"No",
"##de",
"Pi",
"'",
"s",
"r",
"-",
"th",
"del",
"##iber",
"##ation",
"proposal",
"of",
"transactions",
"T",
"to",
"apply",
"to",
"L"
] | Analysis of the XRP Ledger Consensus Protocol | 161 |
and higher throughput for its users. However, without uniform agree-
ment on the network participants, users still need a way to determine whether
their choice of network peers will lead to a consistent network state. In this
setting, each user individually defines a unique node list or UNL, which is
the set of nodes whose messages it will listen to when making decisions about
the network state. It is the intersection of any pair of correct nodes' UNLs that
determines network safety. As described in the | [
1107,
4657,
1118,
7345,
15029,
1107,
1103,
2443,
119,
1967,
12861,
3012,
1110,
170,
8120,
1104,
10923,
117,
1118,
1103,
23485,
2101,
1871,
164,
126,
166,
1195,
2834,
11865,
1977,
5070,
1107,
1103,
2915,
1104,
16439,
1112,
27250,
8167,
10031,
1105,
6088,
1183,
15029,
119,
3743,
117,
1195,
7568,
170,
1532,
1104,
107,
4780,
1112,
27250,
8167,
10031,
107,
131,
3429,
1431,
2080,
1223,
16439,
1112,
27250,
8167,
10031,
117,
1133,
18125,
1231,
5053,
7174,
3633,
1110,
1178,
13008,
1106,
2080,
1223,
1103,
13457,
1115,
1103,
2443,
1110,
2028,
2987,
117,
2764,
1115,
7416,
1132,
4653,
1439,
1199,
11309,
118,
9467,
4177,
8513,
4930,
1105,
1185,
15029,
1132,
6088,
1183,
119,
1130,
1546,
1106,
1494,
17542,
1103,
10350,
8513,
1107,
1103,
161,
20336,
21340,
1197,
24034,
14183,
1424,
118,
27629,
2116,
117,
1317,
1119,
26900,
1116,
1132,
1215,
1106,
6183,
2495,
10932,
15029,
117,
3843,
12177,
9420,
1104,
7416,
1105,
2438,
3404,
1194,
1103,
2443,
119,
17580,
11934,
1145,
9410,
4177,
15308,
1113,
1472,
9373,
7416,
1107,
1126,
2661,
1106,
4256,
1686,
1757,
119,
1966,
1195,
8429,
1292,
4068,
1106,
27466,
8223,
22881,
1103,
8685,
2071,
117,
1195,
6600,
1115,
1152,
1132,
1696,
6691,
19069,
1107,
1103,
4315,
24034,
14183,
1424,
118,
27629,
2116,
1105,
1654,
1103,
1842,
1362,
2099,
1104,
1103,
9932,
119,
1109,
1864,
1115,
161,
20336,
149,
13113,
1110,
1178,
19057,
1112,
27250,
8167,
23038,
1361,
1105,
1157,
2099,
9113,
1113,
1292,
11934,
1110,
170,
26802,
1104,
1103,
9932,
119,
3291,
26443,
117,
1103,
3000,
4174,
9932,
1106,
161,
20336,
149,
13113,
117,
1674,
1136,
1138,
1292,
13004,
119,
1135,
2745,
5354,
6451,
9597,
7091,
1757,
1106,
174,
27923,
1103,
23485,
2101,
1871,
1105,
24512,
1977,
5070,
1256,
1114,
1103,
12477,
23984,
1295,
1104,
21073,
1181,
6088,
1183,
15029,
1105,
8362,
8346,
1174,
1112,
27250,
8167,
10031,
164,
127,
166,
119,
11389,
122,
7584,
7317,
9534,
1412,
16049,
117,
1259,
1199,
1115,
1209,
1129,
3716,
1107,
4194,
4886,
119,
124,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
1109,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
2923,
1104,
1210,
2425,
5644,
131,
794,
9352,
24851,
1891,
117,
1107,
1134,
15029,
1122,
21126,
1193,
17794,
170,
13618,
1383,
1106,
6058,
1106,
170,
2988,
21340,
1197,
117,
1359,
1113,
10698,
1460,
1121,
1168,
9373,
126,
21902,
138,
14372,
1107,
1103,
2443,
7414,
2162,
1182,
1109,
3527,
14372,
2190,
113,
7414,
2162,
114,
2700,
1118,
21902,
11437,
117,
186,
1182,
117,
189,
1182,
1109,
2060,
117,
9221,
1891,
186,
11848,
5697,
1105,
4177,
8377,
21688,
1104,
7414,
2162,
1182,
149,
138,
21340,
1197,
14516,
4426,
113,
149,
114,
22087,
25113,
1295,
1104,
21340,
1197,
149,
100,
8896,
1183,
9221,
2913,
21340,
1197,
1114,
2026,
4954,
1295,
113,
1103,
3106,
9221,
2913,
5580,
21340,
1197,
114,
149,
28311,
9493,
1684,
21340,
1197,
1104,
3687,
24851,
1891,
157,
134,
196,
193,
1568,
117,
193,
1475,
117,
119,
119,
119,
198,
138,
1383,
1104,
14409,
22216,
117,
187,
117,
149,
117,
178,
1302,
2007,
21902,
112,
188,
187,
118,
24438,
3687,
24851,
1891,
5835,
1104,
14409,
157,
1106,
6058,
1106,
149
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"in",
"advance",
"by",
"honest",
"nodes",
"in",
"the",
"network",
".",
"Since",
"atomic",
"broadcast",
"is",
"a",
"variant",
"of",
"consensus",
",",
"by",
"the",
"FL",
"##P",
"result",
"[",
"5",
"]",
"we",
"cannot",
"guarantee",
"forward",
"progress",
"in",
"the",
"presence",
"of",
"arbitrary",
"as",
"##ync",
"##hr",
"##ony",
"and",
"fault",
"##y",
"nodes",
".",
"Instead",
",",
"we",
"assume",
"a",
"form",
"of",
"\"",
"weak",
"as",
"##ync",
"##hr",
"##ony",
"\"",
":",
"safety",
"should",
"hold",
"under",
"arbitrary",
"as",
"##ync",
"##hr",
"##ony",
",",
"but",
"censorship",
"re",
"##si",
"##lie",
"##nce",
"is",
"only",
"guaranteed",
"to",
"hold",
"under",
"the",
"assumption",
"that",
"the",
"network",
"is",
"eventually",
"civil",
",",
"meaning",
"that",
"messages",
"are",
"delivered",
"within",
"some",
"protocol",
"-",
"specified",
"maximum",
"delay",
"bound",
"and",
"no",
"nodes",
"are",
"fault",
"##y",
".",
"In",
"order",
"to",
"help",
"enforce",
"the",
"bounded",
"delay",
"in",
"the",
"X",
"##RP",
"ledge",
"##r",
"imp",
"##lem",
"##en",
"-",
"ta",
"##tion",
",",
"several",
"he",
"##uristic",
"##s",
"are",
"used",
"to",
"identify",
"la",
"##gging",
"nodes",
",",
"prevent",
"excessive",
"flooding",
"of",
"messages",
"and",
"route",
"traffic",
"through",
"the",
"network",
".",
"Protocol",
"parameters",
"also",
"define",
"maximum",
"delays",
"on",
"different",
"trusted",
"messages",
"in",
"an",
"attempt",
"to",
"aid",
"live",
"##ness",
".",
"Although",
"we",
"ignore",
"these",
"details",
"to",
"si",
"##mp",
"##lify",
"the",
"presentation",
"below",
",",
"we",
"stress",
"that",
"they",
"are",
"important",
"practical",
"considerations",
"in",
"the",
"actual",
"imp",
"##lem",
"##en",
"-",
"ta",
"##tion",
"and",
"control",
"the",
"real",
"world",
"performance",
"of",
"the",
"algorithm",
".",
"The",
"fact",
"that",
"X",
"##RP",
"L",
"##CP",
"is",
"only",
"weakly",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"and",
"its",
"performance",
"depends",
"on",
"these",
"parameters",
"is",
"a",
"limitation",
"of",
"the",
"algorithm",
".",
"Co",
"##balt",
",",
"the",
"proposed",
"alternative",
"algorithm",
"to",
"X",
"##RP",
"L",
"##CP",
",",
"does",
"not",
"have",
"these",
"limitations",
".",
"It",
"uses",
"cry",
"##pt",
"##ographic",
"random",
"##ness",
"to",
"e",
"##vade",
"the",
"FL",
"##P",
"result",
"and",
"guarantees",
"forward",
"progress",
"even",
"with",
"the",
"ma",
"##ximal",
"number",
"of",
"tolerate",
"##d",
"fault",
"##y",
"nodes",
"and",
"un",
"##bound",
"##ed",
"as",
"##ync",
"##hr",
"##ony",
"[",
"6",
"]",
".",
"Table",
"1",
"sum",
"##mar",
"##izes",
"our",
"notation",
",",
"including",
"some",
"that",
"will",
"be",
"explained",
"in",
"subsequent",
"sections",
".",
"3",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"The",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
"consists",
"of",
"three",
"primary",
"components",
":",
"β’",
"Del",
"##iber",
"##ation",
",",
"in",
"which",
"nodes",
"it",
"##erative",
"##ly",
"propose",
"a",
"transaction",
"set",
"to",
"apply",
"to",
"a",
"prior",
"ledge",
"##r",
",",
"based",
"on",
"proposals",
"received",
"from",
"other",
"trusted",
"5",
"Pi",
"A",
"node",
"in",
"the",
"network",
"UN",
"##L",
"##i",
"The",
"unique",
"node",
"list",
"(",
"UN",
"##L",
")",
"selected",
"by",
"Pi",
"ni",
",",
"q",
"##i",
",",
"t",
"##i",
"The",
"size",
",",
"valid",
"##ation",
"q",
"##uo",
"##rum",
"and",
"maximum",
"Byzantine",
"faults",
"of",
"UN",
"##L",
"##i",
"L",
"A",
"ledge",
"##r",
"se",
"##q",
"(",
"L",
")",
"Se",
"##quence",
"number",
"of",
"ledge",
"##r",
"L",
"[UNK]",
"Full",
"##y",
"valid",
"##ated",
"ledge",
"##r",
"with",
"largest",
"sequence",
"number",
"(",
"the",
"fully",
"valid",
"##ated",
"tip",
"ledge",
"##r",
")",
"L",
"##Μ",
"Current",
"working",
"ledge",
"##r",
"of",
"del",
"##iber",
"##ation",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
",",
".",
".",
".",
"}",
"A",
"set",
"of",
"transactions",
"PT",
",",
"r",
",",
"L",
",",
"i",
"No",
"##de",
"Pi",
"'",
"s",
"r",
"-",
"th",
"del",
"##iber",
"##ation",
"proposal",
"of",
"transactions",
"T",
"to",
"apply",
"to",
"L"
] | Analysis of the XRP Ledger Consensus Protocol | 162 |
original whitepaper [10], the
minimum overlap requirement was originally believed to be roughly 20% of the
UNL. An independent analysis later suggested the correct bound was instead
roughly > 40% [1].
Given this confusion, our goal in this work is to give a clear and detailed
explanation of XRP LCP and derive the necessary conditions on UNL overlap
for consistency and liveness. We will not discuss the transactional semantics
of XRP's ledger or XRP's benefits as a digital currency, but instead view the
al | [
159,
2162,
117,
178,
1302,
2007,
21902,
112,
188,
9221,
1891,
1104,
21340,
1197,
149,
28117,
8661,
27961,
113,
149,
114,
117,
28117,
8661,
6766,
11273,
113,
149,
114,
157,
9717,
1105,
3392,
1619,
1104,
170,
21340,
1197,
149,
8362,
8178,
9084,
1906,
113,
188,
114,
12118,
8178,
9084,
1906,
1619,
1120,
4954,
1295,
188,
439,
113,
149,
117,
149,
797,
114,
2864,
1158,
3053,
1115,
1110,
122,
1191,
149,
135,
149,
797,
113,
1118,
1144,
1324,
114,
1105,
121,
4303,
11389,
122,
131,
15463,
12917,
1616,
1104,
16049,
15029,
119,
1332,
170,
14372,
6616,
1536,
10698,
5340,
117,
1122,
12175,
1103,
1884,
11604,
118,
188,
5674,
17038,
14409,
1106,
1103,
2988,
21340,
1197,
2452,
1106,
1103,
21340,
1197,
11309,
2995,
119,
1135,
1173,
2492,
170,
9221,
1891,
1111,
1103,
6455,
21340,
1197,
119,
794,
12226,
6859,
2116,
117,
1107,
1134,
15029,
4958,
2480,
1106,
3106,
9221,
2193,
170,
21340,
1197,
117,
1359,
1113,
1103,
9221,
6006,
3010,
1118,
9373,
15029,
119,
2857,
170,
186,
11848,
5697,
1104,
191,
1348,
118,
25021,
6006,
1111,
1103,
1269,
21340,
1197,
1110,
1680,
117,
1115,
21340,
1197,
1105,
1157,
11005,
1132,
8012,
3106,
9221,
2913,
1105,
1157,
1352,
1110,
27355,
1105,
178,
11604,
24553,
1895,
119,
794,
11689,
26025,
6541,
117,
1107,
1134,
15029,
4959,
1103,
6349,
1684,
3392,
1104,
21340,
1197,
1607,
119,
1130,
1551,
1104,
1112,
27250,
8167,
10031,
117,
2443,
7262,
117,
1137,
8377,
4290,
117,
15029,
1336,
1136,
2786,
9221,
2193,
1103,
1269,
21340,
1197,
1111,
170,
1549,
4954,
1295,
119,
1130,
1546,
1106,
1294,
1977,
5070,
1105,
3106,
191,
10584,
118,
2236,
1224,
21340,
1733,
117,
15029,
1329,
1103,
21340,
1197,
11626,
1104,
9373,
9221,
6006,
1106,
14926,
3687,
24851,
3798,
1113,
1103,
2443,
112,
188,
6349,
21340,
1197,
119,
1130,
1603,
117,
1111,
1296,
4954,
1295,
188,
117,
1296,
8536,
21902,
2492,
170,
9221,
1891,
159,
2162,
117,
178,
1111,
1103,
21340,
1197,
149,
1114,
188,
134,
14516,
4426,
113,
149,
114,
1115,
1122,
27402,
1209,
1129,
3106,
9221,
2913,
1118,
9221,
1891,
119,
2831,
2987,
26107,
117,
1103,
3687,
24851,
1891,
1965,
2228,
1122,
3023,
2620,
1103,
9221,
2913,
21340,
1197,
1209,
1801,
1103,
21340,
1197,
9221,
2913,
1118,
1157,
9373,
14097,
119,
1130,
2740,
1165,
1103,
2443,
1110,
1136,
1684,
5156,
117,
6349,
3392,
23613,
14097,
8247,
170,
1887,
3392,
1216,
1115,
15029,
1209,
1224,
3106,
9221,
2193,
1103,
1269,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
188,
119,
1188,
1160,
118,
2585,
4954,
1104,
3687,
24851,
1891,
1105,
9221,
1891,
1110,
1861,
1106,
1103,
6777,
1104,
8219,
1509,
1785,
176,
3556,
16609,
3055,
2234,
1118,
1252,
9866,
1179,
1105,
14672,
164,
123,
166,
119,
10364,
117,
1103,
6349,
3392,
11309,
6117,
170,
1887,
6708,
1114,
1103,
144,
3048,
9025,
1942,
3013,
1104,
1573,
24729,
17828,
3781,
1105,
163,
10559,
1813,
164,
1429,
166,
119,
127,
100,
149,
28311,
6058,
113,
157,
117,
149,
28311,
114,
149,
797,
12226,
6859,
2116,
11689,
26025,
6541,
9352,
24851,
1891,
14516,
4426,
113,
149,
114,
188,
188,
116,
122,
188,
116,
123,
188
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
9,
10,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
23,
24,
24,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
13,
14,
14,
14,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
9,
10,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
23,
24,
24,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
13,
14,
14,
14,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"V",
"##L",
",",
"i",
"No",
"##de",
"Pi",
"'",
"s",
"valid",
"##ation",
"of",
"ledge",
"##r",
"L",
"su",
"##pp",
"##tip",
"(",
"L",
")",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
")",
"T",
"##ip",
"and",
"branch",
"support",
"of",
"a",
"ledge",
"##r",
"L",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
"Un",
"##com",
"##mit",
"##ted",
"support",
"at",
"sequence",
"number",
"s",
"Ο",
"(",
"L",
",",
"L",
"β²",
")",
"Order",
"##ing",
"function",
"that",
"is",
"1",
"if",
"L",
">",
"L",
"β²",
"(",
"by",
"has",
"##h",
")",
"and",
"0",
"otherwise",
"Table",
"1",
":",
"Su",
"##mma",
"##ry",
"of",
"notation",
"nodes",
".",
"When",
"a",
"node",
"believes",
"enough",
"proposals",
"agree",
",",
"it",
"applies",
"the",
"co",
"##rre",
"-",
"s",
"##po",
"##nding",
"transactions",
"to",
"the",
"prior",
"ledge",
"##r",
"according",
"to",
"the",
"ledge",
"##r",
"protocol",
"rules",
".",
"It",
"then",
"issues",
"a",
"valid",
"##ation",
"for",
"the",
"generated",
"ledge",
"##r",
".",
"β’",
"Val",
"##ida",
"##tion",
",",
"in",
"which",
"nodes",
"decide",
"whether",
"to",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
",",
"based",
"on",
"the",
"valid",
"##ations",
"issued",
"by",
"trusted",
"nodes",
".",
"Once",
"a",
"q",
"##uo",
"##rum",
"of",
"v",
"##al",
"-",
"id",
"##ations",
"for",
"the",
"same",
"ledge",
"##r",
"is",
"reached",
",",
"that",
"ledge",
"##r",
"and",
"its",
"ancestors",
"are",
"deemed",
"fully",
"valid",
"##ated",
"and",
"its",
"state",
"is",
"authoritative",
"and",
"i",
"##rre",
"##voc",
"##able",
".",
"β’",
"Pre",
"##ferred",
"Branch",
",",
"in",
"which",
"nodes",
"determine",
"the",
"preferred",
"working",
"branch",
"of",
"ledge",
"##r",
"history",
".",
"In",
"times",
"of",
"as",
"##ync",
"##hr",
"##ony",
",",
"network",
"difficulty",
",",
"or",
"Byzantine",
"failure",
",",
"nodes",
"may",
"not",
"initially",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
"for",
"a",
"given",
"sequence",
"number",
".",
"In",
"order",
"to",
"make",
"forward",
"progress",
"and",
"fully",
"v",
"##ali",
"-",
"date",
"later",
"ledge",
"##rs",
",",
"nodes",
"use",
"the",
"ledge",
"##r",
"ancestry",
"of",
"trusted",
"valid",
"##ations",
"to",
"resume",
"del",
"##iber",
"##ating",
"on",
"the",
"network",
"'",
"s",
"preferred",
"ledge",
"##r",
".",
"In",
"short",
",",
"for",
"each",
"sequence",
"number",
"s",
",",
"each",
"peer",
"Pi",
"issues",
"a",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"s",
"=",
"se",
"##q",
"(",
"L",
")",
"that",
"it",
"expects",
"will",
"be",
"fully",
"valid",
"##ated",
"by",
"valid",
"##ation",
".",
"Under",
"civil",
"executions",
",",
"the",
"del",
"##iber",
"##ation",
"process",
"makes",
"it",
"highly",
"likely",
"the",
"valid",
"##ated",
"ledge",
"##r",
"will",
"match",
"the",
"ledge",
"##r",
"valid",
"##ated",
"by",
"its",
"trusted",
"peers",
".",
"In",
"cases",
"when",
"the",
"network",
"is",
"not",
"working",
"normally",
",",
"preferred",
"branch",
"ensures",
"peers",
"select",
"a",
"common",
"branch",
"such",
"that",
"nodes",
"will",
"later",
"fully",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"s",
".",
"This",
"two",
"-",
"step",
"sequence",
"of",
"del",
"##iber",
"##ation",
"and",
"valid",
"##ation",
"is",
"similar",
"to",
"the",
"proof",
"of",
"stake",
"final",
"##ity",
"g",
"##ad",
"##get",
"recently",
"introduced",
"by",
"But",
"##eri",
"##n",
"and",
"Griffith",
"[",
"2",
"]",
".",
"Indeed",
",",
"the",
"preferred",
"branch",
"protocol",
"shares",
"a",
"common",
"principle",
"with",
"the",
"G",
"##H",
"##OS",
"##T",
"rule",
"of",
"So",
"##mpo",
"##lins",
"##ky",
"and",
"Z",
"##oh",
"##ar",
"[",
"11",
"]",
".",
"6",
"[UNK]",
"L",
"##Μ",
"apply",
"(",
"T",
",",
"L",
"##Μ",
")",
"L",
"β²",
"Val",
"##ida",
"##tion",
"Pre",
"##ferred",
"Branch",
"Del",
"##iber",
"##ation",
"se",
"##q",
"(",
"L",
")",
"s",
"s",
"+",
"1",
"s",
"+",
"2",
"s"
] | Analysis of the XRP Ledger Consensus Protocol | 163 |
original whitepaper [10], the
minimum overlap requirement was originally believed to be roughly 20% of the
UNL. An independent analysis later suggested the correct bound was instead
roughly > 40% [1].
Given this confusion, our goal in this work is to give a clear and detailed
explanation of XRP LCP and derive the necessary conditions on UNL overlap
for consistency and liveness. We will not discuss the transactional semantics
of XRP's ledger or XRP's benefits as a digital currency, but instead view the
al | [
159,
2162,
117,
178,
1302,
2007,
21902,
112,
188,
9221,
1891,
1104,
21340,
1197,
149,
28117,
8661,
27961,
113,
149,
114,
117,
28117,
8661,
6766,
11273,
113,
149,
114,
157,
9717,
1105,
3392,
1619,
1104,
170,
21340,
1197,
149,
8362,
8178,
9084,
1906,
113,
188,
114,
12118,
8178,
9084,
1906,
1619,
1120,
4954,
1295,
188,
439,
113,
149,
117,
149,
797,
114,
2864,
1158,
3053,
1115,
1110,
122,
1191,
149,
135,
149,
797,
113,
1118,
1144,
1324,
114,
1105,
121,
4303,
11389,
122,
131,
15463,
12917,
1616,
1104,
16049,
15029,
119,
1332,
170,
14372,
6616,
1536,
10698,
5340,
117,
1122,
12175,
1103,
1884,
11604,
118,
188,
5674,
17038,
14409,
1106,
1103,
2988,
21340,
1197,
2452,
1106,
1103,
21340,
1197,
11309,
2995,
119,
1135,
1173,
2492,
170,
9221,
1891,
1111,
1103,
6455,
21340,
1197,
119,
794,
12226,
6859,
2116,
117,
1107,
1134,
15029,
4958,
2480,
1106,
3106,
9221,
2193,
170,
21340,
1197,
117,
1359,
1113,
1103,
9221,
6006,
3010,
1118,
9373,
15029,
119,
2857,
170,
186,
11848,
5697,
1104,
191,
1348,
118,
25021,
6006,
1111,
1103,
1269,
21340,
1197,
1110,
1680,
117,
1115,
21340,
1197,
1105,
1157,
11005,
1132,
8012,
3106,
9221,
2913,
1105,
1157,
1352,
1110,
27355,
1105,
178,
11604,
24553,
1895,
119,
794,
11689,
26025,
6541,
117,
1107,
1134,
15029,
4959,
1103,
6349,
1684,
3392,
1104,
21340,
1197,
1607,
119,
1130,
1551,
1104,
1112,
27250,
8167,
10031,
117,
2443,
7262,
117,
1137,
8377,
4290,
117,
15029,
1336,
1136,
2786,
9221,
2193,
1103,
1269,
21340,
1197,
1111,
170,
1549,
4954,
1295,
119,
1130,
1546,
1106,
1294,
1977,
5070,
1105,
3106,
191,
10584,
118,
2236,
1224,
21340,
1733,
117,
15029,
1329,
1103,
21340,
1197,
11626,
1104,
9373,
9221,
6006,
1106,
14926,
3687,
24851,
3798,
1113,
1103,
2443,
112,
188,
6349,
21340,
1197,
119,
1130,
1603,
117,
1111,
1296,
4954,
1295,
188,
117,
1296,
8536,
21902,
2492,
170,
9221,
1891,
159,
2162,
117,
178,
1111,
1103,
21340,
1197,
149,
1114,
188,
134,
14516,
4426,
113,
149,
114,
1115,
1122,
27402,
1209,
1129,
3106,
9221,
2913,
1118,
9221,
1891,
119,
2831,
2987,
26107,
117,
1103,
3687,
24851,
1891,
1965,
2228,
1122,
3023,
2620,
1103,
9221,
2913,
21340,
1197,
1209,
1801,
1103,
21340,
1197,
9221,
2913,
1118,
1157,
9373,
14097,
119,
1130,
2740,
1165,
1103,
2443,
1110,
1136,
1684,
5156,
117,
6349,
3392,
23613,
14097,
8247,
170,
1887,
3392,
1216,
1115,
15029,
1209,
1224,
3106,
9221,
2193,
1103,
1269,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
188,
119,
1188,
1160,
118,
2585,
4954,
1104,
3687,
24851,
1891,
1105,
9221,
1891,
1110,
1861,
1106,
1103,
6777,
1104,
8219,
1509,
1785,
176,
3556,
16609,
3055,
2234,
1118,
1252,
9866,
1179,
1105,
14672,
164,
123,
166,
119,
10364,
117,
1103,
6349,
3392,
11309,
6117,
170,
1887,
6708,
1114,
1103,
144,
3048,
9025,
1942,
3013,
1104,
1573,
24729,
17828,
3781,
1105,
163,
10559,
1813,
164,
1429,
166,
119,
127,
100,
149,
28311,
6058,
113,
157,
117,
149,
28311,
114,
149,
797,
12226,
6859,
2116,
11689,
26025,
6541,
9352,
24851,
1891,
14516,
4426,
113,
149,
114,
188,
188,
116,
122,
188,
116,
123,
188
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"V",
"##L",
",",
"i",
"No",
"##de",
"Pi",
"'",
"s",
"valid",
"##ation",
"of",
"ledge",
"##r",
"L",
"su",
"##pp",
"##tip",
"(",
"L",
")",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
")",
"T",
"##ip",
"and",
"branch",
"support",
"of",
"a",
"ledge",
"##r",
"L",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
"Un",
"##com",
"##mit",
"##ted",
"support",
"at",
"sequence",
"number",
"s",
"Ο",
"(",
"L",
",",
"L",
"β²",
")",
"Order",
"##ing",
"function",
"that",
"is",
"1",
"if",
"L",
">",
"L",
"β²",
"(",
"by",
"has",
"##h",
")",
"and",
"0",
"otherwise",
"Table",
"1",
":",
"Su",
"##mma",
"##ry",
"of",
"notation",
"nodes",
".",
"When",
"a",
"node",
"believes",
"enough",
"proposals",
"agree",
",",
"it",
"applies",
"the",
"co",
"##rre",
"-",
"s",
"##po",
"##nding",
"transactions",
"to",
"the",
"prior",
"ledge",
"##r",
"according",
"to",
"the",
"ledge",
"##r",
"protocol",
"rules",
".",
"It",
"then",
"issues",
"a",
"valid",
"##ation",
"for",
"the",
"generated",
"ledge",
"##r",
".",
"β’",
"Val",
"##ida",
"##tion",
",",
"in",
"which",
"nodes",
"decide",
"whether",
"to",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
",",
"based",
"on",
"the",
"valid",
"##ations",
"issued",
"by",
"trusted",
"nodes",
".",
"Once",
"a",
"q",
"##uo",
"##rum",
"of",
"v",
"##al",
"-",
"id",
"##ations",
"for",
"the",
"same",
"ledge",
"##r",
"is",
"reached",
",",
"that",
"ledge",
"##r",
"and",
"its",
"ancestors",
"are",
"deemed",
"fully",
"valid",
"##ated",
"and",
"its",
"state",
"is",
"authoritative",
"and",
"i",
"##rre",
"##voc",
"##able",
".",
"β’",
"Pre",
"##ferred",
"Branch",
",",
"in",
"which",
"nodes",
"determine",
"the",
"preferred",
"working",
"branch",
"of",
"ledge",
"##r",
"history",
".",
"In",
"times",
"of",
"as",
"##ync",
"##hr",
"##ony",
",",
"network",
"difficulty",
",",
"or",
"Byzantine",
"failure",
",",
"nodes",
"may",
"not",
"initially",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
"for",
"a",
"given",
"sequence",
"number",
".",
"In",
"order",
"to",
"make",
"forward",
"progress",
"and",
"fully",
"v",
"##ali",
"-",
"date",
"later",
"ledge",
"##rs",
",",
"nodes",
"use",
"the",
"ledge",
"##r",
"ancestry",
"of",
"trusted",
"valid",
"##ations",
"to",
"resume",
"del",
"##iber",
"##ating",
"on",
"the",
"network",
"'",
"s",
"preferred",
"ledge",
"##r",
".",
"In",
"short",
",",
"for",
"each",
"sequence",
"number",
"s",
",",
"each",
"peer",
"Pi",
"issues",
"a",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"s",
"=",
"se",
"##q",
"(",
"L",
")",
"that",
"it",
"expects",
"will",
"be",
"fully",
"valid",
"##ated",
"by",
"valid",
"##ation",
".",
"Under",
"civil",
"executions",
",",
"the",
"del",
"##iber",
"##ation",
"process",
"makes",
"it",
"highly",
"likely",
"the",
"valid",
"##ated",
"ledge",
"##r",
"will",
"match",
"the",
"ledge",
"##r",
"valid",
"##ated",
"by",
"its",
"trusted",
"peers",
".",
"In",
"cases",
"when",
"the",
"network",
"is",
"not",
"working",
"normally",
",",
"preferred",
"branch",
"ensures",
"peers",
"select",
"a",
"common",
"branch",
"such",
"that",
"nodes",
"will",
"later",
"fully",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"s",
".",
"This",
"two",
"-",
"step",
"sequence",
"of",
"del",
"##iber",
"##ation",
"and",
"valid",
"##ation",
"is",
"similar",
"to",
"the",
"proof",
"of",
"stake",
"final",
"##ity",
"g",
"##ad",
"##get",
"recently",
"introduced",
"by",
"But",
"##eri",
"##n",
"and",
"Griffith",
"[",
"2",
"]",
".",
"Indeed",
",",
"the",
"preferred",
"branch",
"protocol",
"shares",
"a",
"common",
"principle",
"with",
"the",
"G",
"##H",
"##OS",
"##T",
"rule",
"of",
"So",
"##mpo",
"##lins",
"##ky",
"and",
"Z",
"##oh",
"##ar",
"[",
"11",
"]",
".",
"6",
"[UNK]",
"L",
"##Μ",
"apply",
"(",
"T",
",",
"L",
"##Μ",
")",
"L",
"β²",
"Val",
"##ida",
"##tion",
"Pre",
"##ferred",
"Branch",
"Del",
"##iber",
"##ation",
"se",
"##q",
"(",
"L",
")",
"s",
"s",
"+",
"1",
"s",
"+",
"2",
"s"
] | Analysis of the XRP Ledger Consensus Protocol | 164 |
gorithm as a general consensus protocol. We re-evaluate the two prior overlap
results and provide a single corrected bound which is partway between the
bounds of [10] and [1]. We also show that under a more general fault model which
was not considered in the original whitepaper but is canonically used in the
research literature, the minimum overlap is actually roughly > 90% of the UNL.
Finally, we show that during the present stages of diversifying trusted network
operators [12], the XRP network is both s | [
116,
124,
15982,
123,
131,
3291,
24729,
21222,
1116,
1104,
161,
20336,
149,
13113,
119,
2994,
7982,
1231,
5822,
4993,
1513,
1110,
170,
21340,
1197,
1114,
1126,
11473,
6903,
1106,
1157,
6486,
119,
15982,
123,
1110,
170,
188,
4386,
10734,
2458,
1104,
21340,
1197,
1607,
1105,
2196,
1293,
1292,
3254,
5674,
118,
24928,
5240,
12254,
1106,
4657,
1103,
21340,
1197,
1352,
1121,
1103,
7281,
1104,
170,
1423,
14372,
119,
2614,
5611,
1106,
1103,
1268,
117,
1114,
1103,
1160,
5583,
21340,
1733,
1113,
1103,
1286,
13682,
1103,
3106,
9221,
2913,
1105,
27355,
21340,
1197,
4129,
1114,
5580,
21340,
1197,
100,
119,
1109,
19647,
21340,
1197,
1113,
1103,
1268,
5149,
1103,
3687,
24851,
1891,
13638,
117,
1107,
1134,
1103,
14372,
1110,
1971,
21262,
1114,
1157,
9373,
15029,
1113,
1134,
14409,
1106,
6058,
2019,
1103,
1397,
21340,
1197,
119,
1109,
8362,
18591,
1174,
21340,
1733,
4248,
1160,
21776,
21340,
1733,
149,
28311,
117,
149,
797,
1115,
1138,
1151,
9221,
2913,
1118,
1472,
15029,
117,
1133,
1134,
1138,
1136,
1460,
170,
186,
11848,
5697,
1106,
3106,
9221,
2193,
119,
1130,
1142,
188,
4386,
10734,
117,
6349,
3392,
3552,
1103,
3105,
21340,
1197,
149,
28311,
1110,
1211,
2620,
1106,
1129,
3106,
9221,
2913,
117,
1177,
1115,
1110,
1103,
1684,
6486,
21340,
1197,
1111,
1142,
14372,
112,
188,
2327,
3687,
24851,
1891,
1668,
119,
124,
119,
122,
9352,
24851,
1891,
9352,
24851,
1891,
1110,
1103,
6552,
1104,
155,
9717,
7136,
10923,
1107,
1134,
15029,
2661,
1106,
5340,
1113,
1103,
1383,
1104,
14409,
1106,
6058,
2019,
21340,
1733,
1152,
9221,
2193,
119,
140,
19526,
1116,
12295,
14409,
1106,
1141,
1137,
1167,
15029,
1107,
1103,
2443,
117,
1150,
1107,
1885,
3012,
1103,
13618,
1106,
1103,
1832,
1104,
1103,
2443,
119,
2994,
14372,
9032,
170,
1383,
1104,
1292,
15498,
14409,
1115,
1138,
1136,
1151,
1529,
1107,
170,
21340,
1197,
119,
8955,
1121,
1142,
1383,
117,
170,
14372,
1122,
21126,
1193,
18381,
1207,
13618,
3741,
1359,
1113,
1103,
1619,
1104,
2510,
14409,
1621,
1103,
3741,
3000,
1118,
15029,
1107,
1157,
7414,
2162,
119,
2994,
5835,
22216,
117,
187,
117,
149,
117,
178,
1110,
170,
189,
4455,
1513,
1104,
794,
157,
117,
1103,
24637,
14372,
112,
188,
1954,
3319,
1104,
1103,
10923,
13618,
1383,
119,
794,
187,
117,
1103,
1668,
1295,
1104,
1142,
5835,
5236,
1106,
1103,
1168,
10698,
1121,
21902,
1359,
1113,
2988,
21340,
1197,
149,
119,
794,
149,
117,
1103,
2988,
21340,
1197,
1292,
14409,
1209,
6058,
1106,
119,
128,
1838,
11984,
11984,
11984,
153,
1568,
117,
178,
153,
1475,
117,
178,
153,
1477,
117,
178,
153,
1568,
117,
180,
153,
1568,
117,
179,
153,
1475,
117,
180,
153,
1475,
117,
179,
153,
1477,
117,
179,
6058,
159,
1182,
15982,
124,
131,
3278,
7334,
1104,
3687,
24851,
1891,
1121,
1103,
7281,
1104,
21902,
119,
1109,
16031,
1132,
10698,
1137,
9221,
6006,
117,
1114,
1155,
1133,
1103,
3687,
24851,
1891,
1668,
1105,
14372,
25021,
3452,
17792,
4841,
1116,
20506,
2856,
1111,
9304,
25769,
119,
794,
178,
117,
1103,
25021,
3452,
17792,
1104,
1103,
14372,
21902,
1115,
8737,
1142,
5835,
119,
1332,
1536,
15029,
1107,
1157,
7414,
2162,
17794,
1103,
1269
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
5,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
5,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"+",
"3",
"Figure",
"2",
":",
"Co",
"##mpo",
"##nent",
"##s",
"of",
"X",
"##RP",
"L",
"##CP",
".",
"Each",
"rounded",
"re",
"##ct",
"##ang",
"##le",
"is",
"a",
"ledge",
"##r",
"with",
"an",
"arrow",
"pointing",
"to",
"its",
"parent",
".",
"Figure",
"2",
"is",
"a",
"s",
"##che",
"##matic",
"view",
"of",
"ledge",
"##r",
"history",
"and",
"shows",
"how",
"these",
"com",
"##po",
"-",
"ne",
"##nts",
"interact",
"to",
"advance",
"the",
"ledge",
"##r",
"state",
"from",
"the",
"perspective",
"of",
"a",
"single",
"node",
".",
"Time",
"flows",
"to",
"the",
"right",
",",
"with",
"the",
"two",
"grey",
"ledge",
"##rs",
"on",
"the",
"left",
"defining",
"the",
"fully",
"valid",
"##ated",
"and",
"authoritative",
"ledge",
"##r",
"chain",
"with",
"tip",
"ledge",
"##r",
"[UNK]",
".",
"The",
"dashed",
"ledge",
"##r",
"on",
"the",
"right",
"represents",
"the",
"del",
"##iber",
"##ation",
"frontier",
",",
"in",
"which",
"the",
"node",
"is",
"currently",
"negotiating",
"with",
"its",
"trusted",
"nodes",
"on",
"which",
"transactions",
"to",
"apply",
"towards",
"the",
"next",
"ledge",
"##r",
".",
"The",
"un",
"##fill",
"##ed",
"ledge",
"##rs",
"represent",
"two",
"conflicting",
"ledge",
"##rs",
"L",
"##Μ",
",",
"L",
"β²",
"that",
"have",
"been",
"valid",
"##ated",
"by",
"different",
"nodes",
",",
"but",
"which",
"have",
"not",
"received",
"a",
"q",
"##uo",
"##rum",
"to",
"fully",
"valid",
"##ate",
".",
"In",
"this",
"s",
"##che",
"##matic",
",",
"preferred",
"branch",
"determined",
"the",
"upper",
"ledge",
"##r",
"L",
"##Μ",
"is",
"most",
"likely",
"to",
"be",
"fully",
"valid",
"##ated",
",",
"so",
"that",
"is",
"the",
"working",
"parent",
"ledge",
"##r",
"for",
"this",
"node",
"'",
"s",
"active",
"del",
"##iber",
"##ation",
"round",
".",
"3",
".",
"1",
"Del",
"##iber",
"##ation",
"Del",
"##iber",
"##ation",
"is",
"the",
"component",
"of",
"R",
"##ip",
"##ple",
"consensus",
"in",
"which",
"nodes",
"attempt",
"to",
"agree",
"on",
"the",
"set",
"of",
"transactions",
"to",
"apply",
"towards",
"ledge",
"##rs",
"they",
"valid",
"##ate",
".",
"C",
"##lient",
"##s",
"submit",
"transactions",
"to",
"one",
"or",
"more",
"nodes",
"in",
"the",
"network",
",",
"who",
"in",
"turn",
"broadcast",
"the",
"transaction",
"to",
"the",
"rest",
"of",
"the",
"network",
".",
"Each",
"node",
"maintains",
"a",
"set",
"of",
"these",
"pending",
"transactions",
"that",
"have",
"not",
"been",
"included",
"in",
"a",
"ledge",
"##r",
".",
"Starting",
"from",
"this",
"set",
",",
"a",
"node",
"it",
"##erative",
"##ly",
"proposes",
"new",
"transaction",
"sets",
"based",
"on",
"the",
"support",
"of",
"individual",
"transactions",
"among",
"the",
"sets",
"proposed",
"by",
"nodes",
"in",
"its",
"UN",
"##L",
".",
"Each",
"proposal",
"PT",
",",
"r",
",",
"L",
",",
"i",
"is",
"a",
"t",
"##up",
"##le",
"of",
"β’",
"T",
",",
"the",
"proposing",
"node",
"'",
"s",
"current",
"guess",
"of",
"the",
"consensus",
"transaction",
"set",
".",
"β’",
"r",
",",
"the",
"round",
"number",
"of",
"this",
"proposal",
"relative",
"to",
"the",
"other",
"proposals",
"from",
"Pi",
"based",
"on",
"prior",
"ledge",
"##r",
"L",
".",
"β’",
"L",
",",
"the",
"prior",
"ledge",
"##r",
"these",
"transactions",
"will",
"apply",
"to",
".",
"7",
"start",
"update",
"update",
"update",
"P",
"##0",
",",
"i",
"P",
"##1",
",",
"i",
"P",
"##2",
",",
"i",
"P",
"##0",
",",
"k",
"P",
"##0",
",",
"j",
"P",
"##1",
",",
"k",
"P",
"##1",
",",
"j",
"P",
"##2",
",",
"j",
"apply",
"V",
"##i",
"Figure",
"3",
":",
"Over",
"##view",
"of",
"del",
"##iber",
"##ation",
"from",
"the",
"perspective",
"of",
"Pi",
".",
"The",
"diamonds",
"are",
"proposals",
"or",
"valid",
"##ations",
",",
"with",
"all",
"but",
"the",
"del",
"##iber",
"##ation",
"round",
"and",
"node",
"id",
"##ent",
"##ifier",
"sub",
"##s",
"##cripts",
"removed",
"for",
"br",
"##evity",
".",
"β’",
"i",
",",
"the",
"id",
"##ent",
"##ifier",
"of",
"the",
"node",
"Pi",
"that",
"broadcasts",
"this",
"proposal",
".",
"When",
"enough",
"nodes",
"in",
"its",
"UN",
"##L",
"propose",
"the",
"same"
] | Analysis of the XRP Ledger Consensus Protocol | 165 |
gorithm as a general consensus protocol. We re-evaluate the two prior overlap
results and provide a single corrected bound which is partway between the
bounds of [10] and [1]. We also show that under a more general fault model which
was not considered in the original whitepaper but is canonically used in the
research literature, the minimum overlap is actually roughly > 90% of the UNL.
Finally, we show that during the present stages of diversifying trusted network
operators [12], the XRP network is both s | [
116,
124,
15982,
123,
131,
3291,
24729,
21222,
1116,
1104,
161,
20336,
149,
13113,
119,
2994,
7982,
1231,
5822,
4993,
1513,
1110,
170,
21340,
1197,
1114,
1126,
11473,
6903,
1106,
1157,
6486,
119,
15982,
123,
1110,
170,
188,
4386,
10734,
2458,
1104,
21340,
1197,
1607,
1105,
2196,
1293,
1292,
3254,
5674,
118,
24928,
5240,
12254,
1106,
4657,
1103,
21340,
1197,
1352,
1121,
1103,
7281,
1104,
170,
1423,
14372,
119,
2614,
5611,
1106,
1103,
1268,
117,
1114,
1103,
1160,
5583,
21340,
1733,
1113,
1103,
1286,
13682,
1103,
3106,
9221,
2913,
1105,
27355,
21340,
1197,
4129,
1114,
5580,
21340,
1197,
100,
119,
1109,
19647,
21340,
1197,
1113,
1103,
1268,
5149,
1103,
3687,
24851,
1891,
13638,
117,
1107,
1134,
1103,
14372,
1110,
1971,
21262,
1114,
1157,
9373,
15029,
1113,
1134,
14409,
1106,
6058,
2019,
1103,
1397,
21340,
1197,
119,
1109,
8362,
18591,
1174,
21340,
1733,
4248,
1160,
21776,
21340,
1733,
149,
28311,
117,
149,
797,
1115,
1138,
1151,
9221,
2913,
1118,
1472,
15029,
117,
1133,
1134,
1138,
1136,
1460,
170,
186,
11848,
5697,
1106,
3106,
9221,
2193,
119,
1130,
1142,
188,
4386,
10734,
117,
6349,
3392,
3552,
1103,
3105,
21340,
1197,
149,
28311,
1110,
1211,
2620,
1106,
1129,
3106,
9221,
2913,
117,
1177,
1115,
1110,
1103,
1684,
6486,
21340,
1197,
1111,
1142,
14372,
112,
188,
2327,
3687,
24851,
1891,
1668,
119,
124,
119,
122,
9352,
24851,
1891,
9352,
24851,
1891,
1110,
1103,
6552,
1104,
155,
9717,
7136,
10923,
1107,
1134,
15029,
2661,
1106,
5340,
1113,
1103,
1383,
1104,
14409,
1106,
6058,
2019,
21340,
1733,
1152,
9221,
2193,
119,
140,
19526,
1116,
12295,
14409,
1106,
1141,
1137,
1167,
15029,
1107,
1103,
2443,
117,
1150,
1107,
1885,
3012,
1103,
13618,
1106,
1103,
1832,
1104,
1103,
2443,
119,
2994,
14372,
9032,
170,
1383,
1104,
1292,
15498,
14409,
1115,
1138,
1136,
1151,
1529,
1107,
170,
21340,
1197,
119,
8955,
1121,
1142,
1383,
117,
170,
14372,
1122,
21126,
1193,
18381,
1207,
13618,
3741,
1359,
1113,
1103,
1619,
1104,
2510,
14409,
1621,
1103,
3741,
3000,
1118,
15029,
1107,
1157,
7414,
2162,
119,
2994,
5835,
22216,
117,
187,
117,
149,
117,
178,
1110,
170,
189,
4455,
1513,
1104,
794,
157,
117,
1103,
24637,
14372,
112,
188,
1954,
3319,
1104,
1103,
10923,
13618,
1383,
119,
794,
187,
117,
1103,
1668,
1295,
1104,
1142,
5835,
5236,
1106,
1103,
1168,
10698,
1121,
21902,
1359,
1113,
2988,
21340,
1197,
149,
119,
794,
149,
117,
1103,
2988,
21340,
1197,
1292,
14409,
1209,
6058,
1106,
119,
128,
1838,
11984,
11984,
11984,
153,
1568,
117,
178,
153,
1475,
117,
178,
153,
1477,
117,
178,
153,
1568,
117,
180,
153,
1568,
117,
179,
153,
1475,
117,
180,
153,
1475,
117,
179,
153,
1477,
117,
179,
6058,
159,
1182,
15982,
124,
131,
3278,
7334,
1104,
3687,
24851,
1891,
1121,
1103,
7281,
1104,
21902,
119,
1109,
16031,
1132,
10698,
1137,
9221,
6006,
117,
1114,
1155,
1133,
1103,
3687,
24851,
1891,
1668,
1105,
14372,
25021,
3452,
17792,
4841,
1116,
20506,
2856,
1111,
9304,
25769,
119,
794,
178,
117,
1103,
25021,
3452,
17792,
1104,
1103,
14372,
21902,
1115,
8737,
1142,
5835,
119,
1332,
1536,
15029,
1107,
1157,
7414,
2162,
17794,
1103,
1269
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"+",
"3",
"Figure",
"2",
":",
"Co",
"##mpo",
"##nent",
"##s",
"of",
"X",
"##RP",
"L",
"##CP",
".",
"Each",
"rounded",
"re",
"##ct",
"##ang",
"##le",
"is",
"a",
"ledge",
"##r",
"with",
"an",
"arrow",
"pointing",
"to",
"its",
"parent",
".",
"Figure",
"2",
"is",
"a",
"s",
"##che",
"##matic",
"view",
"of",
"ledge",
"##r",
"history",
"and",
"shows",
"how",
"these",
"com",
"##po",
"-",
"ne",
"##nts",
"interact",
"to",
"advance",
"the",
"ledge",
"##r",
"state",
"from",
"the",
"perspective",
"of",
"a",
"single",
"node",
".",
"Time",
"flows",
"to",
"the",
"right",
",",
"with",
"the",
"two",
"grey",
"ledge",
"##rs",
"on",
"the",
"left",
"defining",
"the",
"fully",
"valid",
"##ated",
"and",
"authoritative",
"ledge",
"##r",
"chain",
"with",
"tip",
"ledge",
"##r",
"[UNK]",
".",
"The",
"dashed",
"ledge",
"##r",
"on",
"the",
"right",
"represents",
"the",
"del",
"##iber",
"##ation",
"frontier",
",",
"in",
"which",
"the",
"node",
"is",
"currently",
"negotiating",
"with",
"its",
"trusted",
"nodes",
"on",
"which",
"transactions",
"to",
"apply",
"towards",
"the",
"next",
"ledge",
"##r",
".",
"The",
"un",
"##fill",
"##ed",
"ledge",
"##rs",
"represent",
"two",
"conflicting",
"ledge",
"##rs",
"L",
"##Μ",
",",
"L",
"β²",
"that",
"have",
"been",
"valid",
"##ated",
"by",
"different",
"nodes",
",",
"but",
"which",
"have",
"not",
"received",
"a",
"q",
"##uo",
"##rum",
"to",
"fully",
"valid",
"##ate",
".",
"In",
"this",
"s",
"##che",
"##matic",
",",
"preferred",
"branch",
"determined",
"the",
"upper",
"ledge",
"##r",
"L",
"##Μ",
"is",
"most",
"likely",
"to",
"be",
"fully",
"valid",
"##ated",
",",
"so",
"that",
"is",
"the",
"working",
"parent",
"ledge",
"##r",
"for",
"this",
"node",
"'",
"s",
"active",
"del",
"##iber",
"##ation",
"round",
".",
"3",
".",
"1",
"Del",
"##iber",
"##ation",
"Del",
"##iber",
"##ation",
"is",
"the",
"component",
"of",
"R",
"##ip",
"##ple",
"consensus",
"in",
"which",
"nodes",
"attempt",
"to",
"agree",
"on",
"the",
"set",
"of",
"transactions",
"to",
"apply",
"towards",
"ledge",
"##rs",
"they",
"valid",
"##ate",
".",
"C",
"##lient",
"##s",
"submit",
"transactions",
"to",
"one",
"or",
"more",
"nodes",
"in",
"the",
"network",
",",
"who",
"in",
"turn",
"broadcast",
"the",
"transaction",
"to",
"the",
"rest",
"of",
"the",
"network",
".",
"Each",
"node",
"maintains",
"a",
"set",
"of",
"these",
"pending",
"transactions",
"that",
"have",
"not",
"been",
"included",
"in",
"a",
"ledge",
"##r",
".",
"Starting",
"from",
"this",
"set",
",",
"a",
"node",
"it",
"##erative",
"##ly",
"proposes",
"new",
"transaction",
"sets",
"based",
"on",
"the",
"support",
"of",
"individual",
"transactions",
"among",
"the",
"sets",
"proposed",
"by",
"nodes",
"in",
"its",
"UN",
"##L",
".",
"Each",
"proposal",
"PT",
",",
"r",
",",
"L",
",",
"i",
"is",
"a",
"t",
"##up",
"##le",
"of",
"β’",
"T",
",",
"the",
"proposing",
"node",
"'",
"s",
"current",
"guess",
"of",
"the",
"consensus",
"transaction",
"set",
".",
"β’",
"r",
",",
"the",
"round",
"number",
"of",
"this",
"proposal",
"relative",
"to",
"the",
"other",
"proposals",
"from",
"Pi",
"based",
"on",
"prior",
"ledge",
"##r",
"L",
".",
"β’",
"L",
",",
"the",
"prior",
"ledge",
"##r",
"these",
"transactions",
"will",
"apply",
"to",
".",
"7",
"start",
"update",
"update",
"update",
"P",
"##0",
",",
"i",
"P",
"##1",
",",
"i",
"P",
"##2",
",",
"i",
"P",
"##0",
",",
"k",
"P",
"##0",
",",
"j",
"P",
"##1",
",",
"k",
"P",
"##1",
",",
"j",
"P",
"##2",
",",
"j",
"apply",
"V",
"##i",
"Figure",
"3",
":",
"Over",
"##view",
"of",
"del",
"##iber",
"##ation",
"from",
"the",
"perspective",
"of",
"Pi",
".",
"The",
"diamonds",
"are",
"proposals",
"or",
"valid",
"##ations",
",",
"with",
"all",
"but",
"the",
"del",
"##iber",
"##ation",
"round",
"and",
"node",
"id",
"##ent",
"##ifier",
"sub",
"##s",
"##cripts",
"removed",
"for",
"br",
"##evity",
".",
"β’",
"i",
",",
"the",
"id",
"##ent",
"##ifier",
"of",
"the",
"node",
"Pi",
"that",
"broadcasts",
"this",
"proposal",
".",
"When",
"enough",
"nodes",
"in",
"its",
"UN",
"##L",
"propose",
"the",
"same"
] | Analysis of the XRP Ledger Consensus Protocol | 166 |
afe and cannot become "stuck" making
no forward progress.
This research provides a definitive result about the safety of XRP Ledger in
its current state. However, to encourage greater flexibility in choosing UNLs in
the future, we would prefer an algorithm that gets closer to the original expected
overlap bounds. In a sibling paper [6], we present a novel alternative consensus
algorithm called Cobalt that lowers the overlap bound to only > 60% in the
general fault model, cannot get stuck in any network t | [
13618,
1383,
117,
170,
14372,
2492,
170,
9221,
1891,
1359,
1113,
1115,
1383,
1105,
3471,
1103,
1397,
1668,
1104,
3687,
24851,
1891,
119,
15982,
124,
1110,
170,
1344,
118,
1634,
24431,
1104,
3687,
24851,
1891,
117,
2756,
5708,
1107,
2393,
2758,
118,
187,
7088,
1306,
122,
119,
138,
14372,
2786,
3675,
1838,
1106,
3295,
170,
1207,
3687,
24851,
1891,
1668,
1105,
17794,
1157,
3288,
2458,
1104,
1103,
10923,
14409,
119,
1135,
1112,
27250,
8167,
23038,
1361,
1193,
5250,
118,
172,
5800,
1279,
1207,
10698,
1121,
9373,
15029,
117,
8338,
1103,
1383,
1104,
1211,
2793,
10698,
1121,
1296,
119,
5096,
5674,
11794,
1116,
1132,
1178,
1737,
1191,
1152,
1132,
1111,
1103,
1269,
2988,
21340,
1197,
149,
28311,
119,
1109,
14372,
4857,
15549,
1157,
3000,
10923,
13618,
1383,
1107,
2593,
1106,
3599,
1460,
14372,
10698,
117,
1178,
1259,
14409,
1675,
1107,
1120,
1655,
11810,
113,
187,
114,
1104,
1103,
1211,
3055,
1460,
10698,
1121,
1157,
9373,
15029,
119,
1109,
11810,
3816,
1112,
170,
3014,
2656,
1104,
1103,
15029,
1107,
1103,
7414,
2162,
117,
1133,
11631,
17374,
1116,
1146,
1112,
3687,
24851,
1891,
5720,
10980,
119,
1188,
23613,
3345,
15029,
1169,
112,
189,
3843,
10923,
14255,
4121,
3375,
119,
1130,
1103,
161,
20336,
18657,
2895,
7249,
117,
1103,
11810,
2947,
121,
119,
126,
28740,
121,
119,
2625,
28740,
121,
119,
3102,
28740,
121,
119,
4573,
1112,
187,
6986,
119,
2994,
14372,
21902,
20651,
10923,
1680,
1165,
1122,
5302,
1103,
186,
11848,
5697,
186,
1182,
1104,
1157,
9373,
15029,
5340,
1113,
1103,
13618,
1383,
119,
1135,
1173,
12175,
1103,
10923,
14409,
1106,
9509,
1103,
1397,
21340,
1197,
149,
117,
8737,
1157,
9221,
1891,
159,
2162,
117,
178,
1105,
3471,
170,
1207,
1668,
1104,
3687,
24851,
1891,
119,
1135,
1110,
1696,
1106,
3805,
1115,
170,
14372,
1336,
1178,
9221,
2193,
1141,
21340,
1197,
1114,
170,
1549,
4954,
1295,
119,
1130,
1864,
117,
1103,
27289,
1110,
1111,
14372,
21902,
1106,
1178,
2486,
170,
9221,
1891,
159,
2162,
117,
178,
1111,
170,
21340,
1197,
149,
1191,
14516,
4426,
113,
149,
114,
1110,
3407,
1190,
1115,
1104,
1251,
21340,
1197,
2331,
9221,
2913,
1118,
21902,
119,
4516,
1191,
1219,
3687,
24851,
1891,
117,
170,
14372,
17579,
1122,
1110,
1136,
1684,
1113,
1103,
6349,
3392,
117,
1122,
1209,
6878,
1106,
1250,
1113,
1103,
6349,
21340,
1197,
1133,
1209,
1136,
2486,
170,
9221,
1891,
1235,
1122,
1144,
2347,
1171,
1146,
1106,
1103,
4954,
1295,
1122,
1108,
1113,
1196,
12806,
119,
1130,
1103,
161,
20336,
18657,
2895,
7249,
1104,
3687,
24851,
1891,
117,
11309,
11491,
18311,
1306,
118,
129,
3084,
1468,
4959,
1103,
188,
27250,
8167,
11153,
8569,
5420,
1104,
14372,
10698,
1105,
14255,
118,
4267,
6126,
1111,
3830,
3687,
24851,
1891,
119,
8154,
2613,
6461,
1206,
12877,
1104,
3687,
24851,
1891,
5233,
1103,
1194,
16156,
1105,
1523,
7232,
1104,
13618,
6165,
1112,
1218,
1112,
1103,
2443,
9008,
1104,
6731,
10698,
1105,
13618,
3741,
119,
1247,
1132,
1145,
11309,
2995,
1115,
4959,
1134,
14409,
1132,
1107,
1103,
1107,
1182,
118,
189,
2916,
5835,
1105,
1293,
14409,
1115,
2604,
1106,
1129,
1529,
1132,
1231,
19091,
1174,
1107,
4194,
3687,
24851,
6006,
119
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
23,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
23,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"transaction",
"set",
",",
"a",
"node",
"issues",
"a",
"valid",
"##ation",
"based",
"on",
"that",
"set",
"and",
"begins",
"the",
"next",
"round",
"of",
"del",
"##iber",
"##ation",
".",
"Figure",
"3",
"is",
"a",
"high",
"-",
"level",
"overview",
"of",
"del",
"##iber",
"##ation",
",",
"presented",
"formally",
"in",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
"1",
".",
"A",
"node",
"initially",
"calls",
"start",
"to",
"begin",
"a",
"new",
"del",
"##iber",
"##ation",
"round",
"and",
"propose",
"its",
"initial",
"view",
"of",
"the",
"consensus",
"transactions",
".",
"It",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
"pro",
"-",
"c",
"##ess",
"##es",
"new",
"proposals",
"from",
"trusted",
"nodes",
",",
"maintaining",
"the",
"set",
"of",
"most",
"recent",
"proposals",
"from",
"each",
".",
"Pro",
"##po",
"##sal",
"##s",
"are",
"only",
"considered",
"if",
"they",
"are",
"for",
"the",
"same",
"prior",
"ledge",
"##r",
"L",
"##Μ",
".",
"The",
"node",
"regularly",
"updates",
"its",
"proposed",
"consensus",
"transaction",
"set",
"in",
"response",
"to",
"newly",
"received",
"node",
"proposals",
",",
"only",
"including",
"transactions",
"present",
"in",
"at",
"least",
"threshold",
"(",
"r",
")",
"of",
"the",
"most",
"recently",
"received",
"proposals",
"from",
"its",
"trusted",
"nodes",
".",
"The",
"threshold",
"starts",
"as",
"a",
"simple",
"majority",
"of",
"the",
"nodes",
"in",
"the",
"UN",
"##L",
",",
"but",
"rat",
"##chet",
"##s",
"up",
"as",
"del",
"##iber",
"##ation",
"rounds",
"proceed",
".",
"This",
"ensures",
"slow",
"nodes",
"can",
"'",
"t",
"prevent",
"consensus",
"con",
"##ver",
"##ging",
".",
"In",
"the",
"X",
"##RP",
"Led",
"##ger",
"implementation",
",",
"the",
"threshold",
"goes",
"0",
".",
"5",
"##β",
"0",
".",
"65",
"##β",
"0",
".",
"70",
"##β",
"0",
".",
"95",
"as",
"r",
"increases",
".",
"Each",
"node",
"Pi",
"declares",
"consensus",
"reached",
"when",
"it",
"sees",
"the",
"q",
"##uo",
"##rum",
"q",
"##i",
"of",
"its",
"trusted",
"nodes",
"agree",
"on",
"the",
"transaction",
"set",
".",
"It",
"then",
"applies",
"the",
"consensus",
"transactions",
"to",
"generate",
"the",
"next",
"ledge",
"##r",
"L",
",",
"broadcasts",
"its",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"and",
"begins",
"a",
"new",
"round",
"of",
"del",
"##iber",
"##ation",
".",
"It",
"is",
"important",
"to",
"note",
"that",
"a",
"node",
"may",
"only",
"valid",
"##ate",
"one",
"ledge",
"##r",
"with",
"a",
"given",
"sequence",
"number",
".",
"In",
"fact",
",",
"the",
"invariant",
"is",
"for",
"node",
"Pi",
"to",
"only",
"issue",
"a",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"for",
"a",
"ledge",
"##r",
"L",
"if",
"se",
"##q",
"(",
"L",
")",
"is",
"greater",
"than",
"that",
"of",
"any",
"ledge",
"##r",
"previously",
"valid",
"##ated",
"by",
"Pi",
".",
"Thus",
"if",
"during",
"del",
"##iber",
"##ation",
",",
"a",
"node",
"determines",
"it",
"is",
"not",
"working",
"on",
"the",
"preferred",
"branch",
",",
"it",
"will",
"switch",
"to",
"work",
"on",
"the",
"preferred",
"ledge",
"##r",
"but",
"will",
"not",
"issue",
"a",
"valid",
"##ation",
"until",
"it",
"has",
"caught",
"back",
"up",
"to",
"the",
"sequence",
"number",
"it",
"was",
"on",
"before",
"switching",
".",
"In",
"the",
"X",
"##RP",
"Led",
"##ger",
"implementation",
"of",
"del",
"##iber",
"##ation",
",",
"protocol",
"timing",
"para",
"##m",
"-",
"8",
"et",
"##ers",
"determine",
"the",
"s",
"##ync",
"##hr",
"##oni",
"##zation",
"requirements",
"of",
"node",
"proposals",
"and",
"con",
"-",
"di",
"##tions",
"for",
"ending",
"del",
"##iber",
"##ation",
".",
"Additional",
"waiting",
"periods",
"between",
"phases",
"of",
"del",
"##iber",
"##ation",
"balance",
"the",
"through",
"##put",
"and",
"late",
"##ncy",
"of",
"transaction",
"processing",
"as",
"well",
"as",
"the",
"network",
"overhead",
"of",
"broadcasting",
"proposals",
"and",
"transaction",
"sets",
".",
"There",
"are",
"also",
"protocol",
"rules",
"that",
"determine",
"which",
"transactions",
"are",
"in",
"the",
"in",
"##i",
"-",
"t",
"##ial",
"proposal",
"and",
"how",
"transactions",
"that",
"failed",
"to",
"be",
"included",
"are",
"re",
"##tri",
"##ed",
"in",
"subsequent",
"del",
"##iber",
"##ations",
"."
] | Analysis of the XRP Ledger Consensus Protocol | 167 |
afe and cannot become "stuck" making
no forward progress.
This research provides a definitive result about the safety of XRP Ledger in
its current state. However, to encourage greater flexibility in choosing UNLs in
the future, we would prefer an algorithm that gets closer to the original expected
overlap bounds. In a sibling paper [6], we present a novel alternative consensus
algorithm called Cobalt that lowers the overlap bound to only > 60% in the
general fault model, cannot get stuck in any network t | [
13618,
1383,
117,
170,
14372,
2492,
170,
9221,
1891,
1359,
1113,
1115,
1383,
1105,
3471,
1103,
1397,
1668,
1104,
3687,
24851,
1891,
119,
15982,
124,
1110,
170,
1344,
118,
1634,
24431,
1104,
3687,
24851,
1891,
117,
2756,
5708,
1107,
2393,
2758,
118,
187,
7088,
1306,
122,
119,
138,
14372,
2786,
3675,
1838,
1106,
3295,
170,
1207,
3687,
24851,
1891,
1668,
1105,
17794,
1157,
3288,
2458,
1104,
1103,
10923,
14409,
119,
1135,
1112,
27250,
8167,
23038,
1361,
1193,
5250,
118,
172,
5800,
1279,
1207,
10698,
1121,
9373,
15029,
117,
8338,
1103,
1383,
1104,
1211,
2793,
10698,
1121,
1296,
119,
5096,
5674,
11794,
1116,
1132,
1178,
1737,
1191,
1152,
1132,
1111,
1103,
1269,
2988,
21340,
1197,
149,
28311,
119,
1109,
14372,
4857,
15549,
1157,
3000,
10923,
13618,
1383,
1107,
2593,
1106,
3599,
1460,
14372,
10698,
117,
1178,
1259,
14409,
1675,
1107,
1120,
1655,
11810,
113,
187,
114,
1104,
1103,
1211,
3055,
1460,
10698,
1121,
1157,
9373,
15029,
119,
1109,
11810,
3816,
1112,
170,
3014,
2656,
1104,
1103,
15029,
1107,
1103,
7414,
2162,
117,
1133,
11631,
17374,
1116,
1146,
1112,
3687,
24851,
1891,
5720,
10980,
119,
1188,
23613,
3345,
15029,
1169,
112,
189,
3843,
10923,
14255,
4121,
3375,
119,
1130,
1103,
161,
20336,
18657,
2895,
7249,
117,
1103,
11810,
2947,
121,
119,
126,
28740,
121,
119,
2625,
28740,
121,
119,
3102,
28740,
121,
119,
4573,
1112,
187,
6986,
119,
2994,
14372,
21902,
20651,
10923,
1680,
1165,
1122,
5302,
1103,
186,
11848,
5697,
186,
1182,
1104,
1157,
9373,
15029,
5340,
1113,
1103,
13618,
1383,
119,
1135,
1173,
12175,
1103,
10923,
14409,
1106,
9509,
1103,
1397,
21340,
1197,
149,
117,
8737,
1157,
9221,
1891,
159,
2162,
117,
178,
1105,
3471,
170,
1207,
1668,
1104,
3687,
24851,
1891,
119,
1135,
1110,
1696,
1106,
3805,
1115,
170,
14372,
1336,
1178,
9221,
2193,
1141,
21340,
1197,
1114,
170,
1549,
4954,
1295,
119,
1130,
1864,
117,
1103,
27289,
1110,
1111,
14372,
21902,
1106,
1178,
2486,
170,
9221,
1891,
159,
2162,
117,
178,
1111,
170,
21340,
1197,
149,
1191,
14516,
4426,
113,
149,
114,
1110,
3407,
1190,
1115,
1104,
1251,
21340,
1197,
2331,
9221,
2913,
1118,
21902,
119,
4516,
1191,
1219,
3687,
24851,
1891,
117,
170,
14372,
17579,
1122,
1110,
1136,
1684,
1113,
1103,
6349,
3392,
117,
1122,
1209,
6878,
1106,
1250,
1113,
1103,
6349,
21340,
1197,
1133,
1209,
1136,
2486,
170,
9221,
1891,
1235,
1122,
1144,
2347,
1171,
1146,
1106,
1103,
4954,
1295,
1122,
1108,
1113,
1196,
12806,
119,
1130,
1103,
161,
20336,
18657,
2895,
7249,
1104,
3687,
24851,
1891,
117,
11309,
11491,
18311,
1306,
118,
129,
3084,
1468,
4959,
1103,
188,
27250,
8167,
11153,
8569,
5420,
1104,
14372,
10698,
1105,
14255,
118,
4267,
6126,
1111,
3830,
3687,
24851,
1891,
119,
8154,
2613,
6461,
1206,
12877,
1104,
3687,
24851,
1891,
5233,
1103,
1194,
16156,
1105,
1523,
7232,
1104,
13618,
6165,
1112,
1218,
1112,
1103,
2443,
9008,
1104,
6731,
10698,
1105,
13618,
3741,
119,
1247,
1132,
1145,
11309,
2995,
1115,
4959,
1134,
14409,
1132,
1107,
1103,
1107,
1182,
118,
189,
2916,
5835,
1105,
1293,
14409,
1115,
2604,
1106,
1129,
1529,
1132,
1231,
19091,
1174,
1107,
4194,
3687,
24851,
6006,
119
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"transaction",
"set",
",",
"a",
"node",
"issues",
"a",
"valid",
"##ation",
"based",
"on",
"that",
"set",
"and",
"begins",
"the",
"next",
"round",
"of",
"del",
"##iber",
"##ation",
".",
"Figure",
"3",
"is",
"a",
"high",
"-",
"level",
"overview",
"of",
"del",
"##iber",
"##ation",
",",
"presented",
"formally",
"in",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
"1",
".",
"A",
"node",
"initially",
"calls",
"start",
"to",
"begin",
"a",
"new",
"del",
"##iber",
"##ation",
"round",
"and",
"propose",
"its",
"initial",
"view",
"of",
"the",
"consensus",
"transactions",
".",
"It",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
"pro",
"-",
"c",
"##ess",
"##es",
"new",
"proposals",
"from",
"trusted",
"nodes",
",",
"maintaining",
"the",
"set",
"of",
"most",
"recent",
"proposals",
"from",
"each",
".",
"Pro",
"##po",
"##sal",
"##s",
"are",
"only",
"considered",
"if",
"they",
"are",
"for",
"the",
"same",
"prior",
"ledge",
"##r",
"L",
"##Μ",
".",
"The",
"node",
"regularly",
"updates",
"its",
"proposed",
"consensus",
"transaction",
"set",
"in",
"response",
"to",
"newly",
"received",
"node",
"proposals",
",",
"only",
"including",
"transactions",
"present",
"in",
"at",
"least",
"threshold",
"(",
"r",
")",
"of",
"the",
"most",
"recently",
"received",
"proposals",
"from",
"its",
"trusted",
"nodes",
".",
"The",
"threshold",
"starts",
"as",
"a",
"simple",
"majority",
"of",
"the",
"nodes",
"in",
"the",
"UN",
"##L",
",",
"but",
"rat",
"##chet",
"##s",
"up",
"as",
"del",
"##iber",
"##ation",
"rounds",
"proceed",
".",
"This",
"ensures",
"slow",
"nodes",
"can",
"'",
"t",
"prevent",
"consensus",
"con",
"##ver",
"##ging",
".",
"In",
"the",
"X",
"##RP",
"Led",
"##ger",
"implementation",
",",
"the",
"threshold",
"goes",
"0",
".",
"5",
"##β",
"0",
".",
"65",
"##β",
"0",
".",
"70",
"##β",
"0",
".",
"95",
"as",
"r",
"increases",
".",
"Each",
"node",
"Pi",
"declares",
"consensus",
"reached",
"when",
"it",
"sees",
"the",
"q",
"##uo",
"##rum",
"q",
"##i",
"of",
"its",
"trusted",
"nodes",
"agree",
"on",
"the",
"transaction",
"set",
".",
"It",
"then",
"applies",
"the",
"consensus",
"transactions",
"to",
"generate",
"the",
"next",
"ledge",
"##r",
"L",
",",
"broadcasts",
"its",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"and",
"begins",
"a",
"new",
"round",
"of",
"del",
"##iber",
"##ation",
".",
"It",
"is",
"important",
"to",
"note",
"that",
"a",
"node",
"may",
"only",
"valid",
"##ate",
"one",
"ledge",
"##r",
"with",
"a",
"given",
"sequence",
"number",
".",
"In",
"fact",
",",
"the",
"invariant",
"is",
"for",
"node",
"Pi",
"to",
"only",
"issue",
"a",
"valid",
"##ation",
"V",
"##L",
",",
"i",
"for",
"a",
"ledge",
"##r",
"L",
"if",
"se",
"##q",
"(",
"L",
")",
"is",
"greater",
"than",
"that",
"of",
"any",
"ledge",
"##r",
"previously",
"valid",
"##ated",
"by",
"Pi",
".",
"Thus",
"if",
"during",
"del",
"##iber",
"##ation",
",",
"a",
"node",
"determines",
"it",
"is",
"not",
"working",
"on",
"the",
"preferred",
"branch",
",",
"it",
"will",
"switch",
"to",
"work",
"on",
"the",
"preferred",
"ledge",
"##r",
"but",
"will",
"not",
"issue",
"a",
"valid",
"##ation",
"until",
"it",
"has",
"caught",
"back",
"up",
"to",
"the",
"sequence",
"number",
"it",
"was",
"on",
"before",
"switching",
".",
"In",
"the",
"X",
"##RP",
"Led",
"##ger",
"implementation",
"of",
"del",
"##iber",
"##ation",
",",
"protocol",
"timing",
"para",
"##m",
"-",
"8",
"et",
"##ers",
"determine",
"the",
"s",
"##ync",
"##hr",
"##oni",
"##zation",
"requirements",
"of",
"node",
"proposals",
"and",
"con",
"-",
"di",
"##tions",
"for",
"ending",
"del",
"##iber",
"##ation",
".",
"Additional",
"waiting",
"periods",
"between",
"phases",
"of",
"del",
"##iber",
"##ation",
"balance",
"the",
"through",
"##put",
"and",
"late",
"##ncy",
"of",
"transaction",
"processing",
"as",
"well",
"as",
"the",
"network",
"overhead",
"of",
"broadcasting",
"proposals",
"and",
"transaction",
"sets",
".",
"There",
"are",
"also",
"protocol",
"rules",
"that",
"determine",
"which",
"transactions",
"are",
"in",
"the",
"in",
"##i",
"-",
"t",
"##ial",
"proposal",
"and",
"how",
"transactions",
"that",
"failed",
"to",
"be",
"included",
"are",
"re",
"##tri",
"##ed",
"in",
"subsequent",
"del",
"##iber",
"##ations",
"."
] | Analysis of the XRP Ledger Consensus Protocol | 168 |
hat satisfies the overlap
bound, and has several other properties that make it suitable for eventually
replacing XRP LCP. This paper thus serves primarily to show that the XRP
Ledger is safe in the interim while transitioning to Cobalt, and the relatively
strict requirements on UNL configurations under XRP LCP should be viewed
in light of this planned transition.
Section 2 defines the network model and defines the consensus problem. Sec-
tion 3 is a detailed description of the Ripple consensus algorithm. | [
1966,
1142,
1260,
7137,
3052,
1121,
1103,
11108,
9932,
2756,
1107,
1142,
2526,
117,
1195,
2059,
1103,
2607,
1178,
15574,
1103,
8685,
1104,
1103,
9932,
1105,
1169,
1129,
6497,
1112,
1126,
25161,
1111,
4138,
13618,
1194,
16156,
119,
2082,
16246,
117,
1103,
3429,
1105,
1686,
1757,
2686,
1107,
2237,
125,
1202,
1136,
12864,
1113,
1292,
4068,
1104,
3687,
24851,
1891,
119,
124,
119,
123,
12226,
6859,
2116,
12226,
6859,
2116,
1110,
1103,
23565,
1104,
1103,
1210,
5644,
1105,
1110,
25172,
1107,
2393,
2758,
118,
187,
7088,
1306,
123,
119,
1302,
4704,
1107,
1103,
2443,
2566,
5113,
1111,
9221,
6006,
1121,
9373,
15029,
119,
1409,
170,
14372,
21902,
5302,
170,
186,
11848,
5697,
186,
1182,
1104,
9221,
6006,
1111,
170,
21340,
1197,
149,
117,
1173,
1122,
3741,
1103,
1207,
3106,
9221,
2913,
5580,
21340,
1197,
100,
1106,
149,
119,
124,
119,
124,
11689,
26025,
6541,
12226,
6859,
5067,
5156,
9221,
2193,
170,
3014,
4129,
1104,
21340,
1733,
117,
174,
119,
176,
119,
10722,
845,
149,
2064,
845,
149,
1658,
119,
119,
119,
119,
1438,
117,
1219,
1551,
1104,
1112,
27250,
8167,
10031,
117,
2443,
7262,
117,
1137,
5335,
8377,
4290,
1219,
3687,
24851,
1891,
117,
1136,
1155,
5663,
15029,
1336,
1322,
1146,
4172,
1536,
9221,
6006,
1111,
1251,
2510,
21340,
1197,
1106,
3106,
9221,
2193,
119,
1332,
2756,
1114,
14255,
118,
22593,
17882,
1158,
21340,
1733,
117,
6349,
3392,
1110,
1103,
5564,
1134,
17579,
1103,
6349,
4129,
1104,
21340,
1733,
1106,
6878,
1106,
1107,
1546,
1106,
2760,
1543,
1977,
5070,
119,
1135,
1110,
1359,
1113,
1103,
3416,
11626,
1104,
1103,
1211,
2793,
9221,
2913,
21340,
1733,
117,
1314,
2559,
2393,
1116,
117,
1105,
1103,
1378,
12709,
131,
122,
119,
1109,
5580,
1619,
1104,
170,
21340,
1197,
149,
117,
1134,
1110,
1103,
1295,
1104,
9373,
15029,
2133,
1211,
2793,
9221,
2913,
21340,
1197,
1110,
149,
117,
28117,
8661,
27961,
113,
149,
114,
134,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
149,
134,
149,
797,
198,
197,
119,
113,
122,
114,
123,
119,
1109,
3392,
1619,
1104,
170,
21340,
1197,
149,
117,
1134,
1110,
1103,
1295,
1104,
9373,
15029,
2133,
1211,
3055,
9221,
2913,
21340,
1197,
1110,
1719,
149,
1137,
1110,
9026,
1121,
149,
117,
28117,
8661,
6766,
11273,
113,
149,
114,
134,
28117,
8661,
27961,
113,
149,
114,
116,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
149,
850,
11005,
113,
149,
797,
114,
198,
197,
117,
113,
123,
114,
1187,
11005,
113,
149,
797,
114,
1110,
1103,
1383,
1104,
11005,
1104,
149,
797,
117,
178,
119,
174,
119,
1103,
6486,
117,
5372,
118,
6486,
117,
1632,
118,
5372,
17482,
3452,
117,
3576,
119,
117,
1155,
1103,
1236,
1171,
1106,
1103,
9077,
1548,
21340,
1197,
119,
124,
119,
1109,
8362,
8178,
9084,
1906,
1619,
1113,
170,
4954,
1295,
188,
117,
1134,
1110,
1103,
183,
1818,
118,
1129,
1197,
1104,
9373,
15029,
2133,
1211,
2793,
9221,
2913,
21340,
1197,
1110,
1111,
170,
21340,
1197,
1114,
1719,
4954,
2211,
1190,
188,
1137,
1114,
4954,
2211,
1190,
1115,
1104,
1103,
2026,
21340,
1197,
149
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
23,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
9,
10,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
23,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
9,
10,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"Although",
"this",
"de",
"##via",
"##tes",
"from",
"the",
"abstract",
"algorithm",
"presented",
"in",
"this",
"paper",
",",
"we",
"believe",
"the",
"changes",
"only",
"obscure",
"the",
"presentation",
"of",
"the",
"algorithm",
"and",
"can",
"be",
"viewed",
"as",
"an",
"optimization",
"for",
"increasing",
"transaction",
"through",
"##put",
".",
"Most",
"importantly",
",",
"the",
"safety",
"and",
"live",
"##ness",
"results",
"in",
"section",
"4",
"do",
"not",
"depend",
"on",
"these",
"details",
"of",
"del",
"##iber",
"##ation",
".",
"3",
".",
"2",
"Val",
"##ida",
"##tion",
"Val",
"##ida",
"##tion",
"is",
"the",
"simplest",
"of",
"the",
"three",
"components",
"and",
"is",
"summarized",
"in",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
"2",
".",
"No",
"##des",
"in",
"the",
"network",
"simply",
"listen",
"for",
"valid",
"##ations",
"from",
"trusted",
"nodes",
".",
"If",
"a",
"node",
"Pi",
"sees",
"a",
"q",
"##uo",
"##rum",
"q",
"##i",
"of",
"valid",
"##ations",
"for",
"a",
"ledge",
"##r",
"L",
",",
"then",
"it",
"sets",
"the",
"new",
"fully",
"valid",
"##ated",
"tip",
"ledge",
"##r",
"[UNK]",
"to",
"L",
".",
"3",
".",
"3",
"Pre",
"##ferred",
"Branch",
"Val",
"##ida",
"##tors",
"normally",
"valid",
"##ate",
"a",
"simple",
"chain",
"of",
"ledge",
"##rs",
",",
"e",
".",
"g",
".",
"LA",
"β",
"L",
"##B",
"β",
"L",
"##C",
".",
".",
".",
".",
"However",
",",
"during",
"times",
"of",
"as",
"##ync",
"##hr",
"##ony",
",",
"network",
"difficulty",
",",
"or",
"temporary",
"Byzantine",
"failure",
"during",
"del",
"##iber",
"##ation",
",",
"not",
"all",
"correct",
"nodes",
"may",
"end",
"up",
"receiving",
"enough",
"valid",
"##ations",
"for",
"any",
"individual",
"ledge",
"##r",
"to",
"fully",
"valid",
"##ate",
".",
"When",
"presented",
"with",
"con",
"-",
"fl",
"##ict",
"##ing",
"ledge",
"##rs",
",",
"preferred",
"branch",
"is",
"the",
"strategy",
"which",
"determines",
"the",
"preferred",
"chain",
"of",
"ledge",
"##rs",
"to",
"switch",
"to",
"in",
"order",
"to",
"continue",
"making",
"forward",
"progress",
".",
"It",
"is",
"based",
"on",
"the",
"shared",
"ancestry",
"of",
"the",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##rs",
",",
"last",
"##V",
"al",
"##s",
",",
"and",
"the",
"following",
"quantities",
":",
"1",
".",
"The",
"tip",
"support",
"of",
"a",
"ledge",
"##r",
"L",
",",
"which",
"is",
"the",
"number",
"of",
"trusted",
"nodes",
"whose",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##r",
"is",
"L",
",",
"su",
"##pp",
"##tip",
"(",
"L",
")",
"=",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"L",
"=",
"L",
"β²",
"}",
"|",
".",
"(",
"1",
")",
"2",
".",
"The",
"branch",
"support",
"of",
"a",
"ledge",
"##r",
"L",
",",
"which",
"is",
"the",
"number",
"of",
"trusted",
"nodes",
"whose",
"most",
"recently",
"valid",
"##ated",
"ledge",
"##r",
"is",
"either",
"L",
"or",
"is",
"descended",
"from",
"L",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
")",
"=",
"su",
"##pp",
"##tip",
"(",
"L",
")",
"+",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"L",
"β",
"ancestors",
"(",
"L",
"β²",
")",
"}",
"|",
",",
"(",
"2",
")",
"where",
"ancestors",
"(",
"L",
"β²",
")",
"is",
"the",
"set",
"of",
"ancestors",
"of",
"L",
"β²",
",",
"i",
".",
"e",
".",
"the",
"parent",
",",
"grand",
"-",
"parent",
",",
"great",
"-",
"grand",
"##par",
"##ent",
",",
"etc",
".",
",",
"all",
"the",
"way",
"back",
"to",
"the",
"genes",
"##is",
"ledge",
"##r",
".",
"3",
".",
"The",
"un",
"##com",
"##mit",
"##ted",
"support",
"on",
"a",
"sequence",
"number",
"s",
",",
"which",
"is",
"the",
"n",
"##um",
"-",
"be",
"##r",
"of",
"trusted",
"nodes",
"whose",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##r",
"is",
"for",
"a",
"ledge",
"##r",
"with",
"either",
"sequence",
"lower",
"than",
"s",
"or",
"with",
"sequence",
"lower",
"than",
"that",
"of",
"the",
"largest",
"ledge",
"##r",
"L"
] | Analysis of the XRP Ledger Consensus Protocol | 169 |
hat satisfies the overlap
bound, and has several other properties that make it suitable for eventually
replacing XRP LCP. This paper thus serves primarily to show that the XRP
Ledger is safe in the interim while transitioning to Cobalt, and the relatively
strict requirements on UNL configurations under XRP LCP should be viewed
in light of this planned transition.
Section 2 defines the network model and defines the consensus problem. Sec-
tion 3 is a detailed description of the Ripple consensus algorithm. | [
1966,
1142,
1260,
7137,
3052,
1121,
1103,
11108,
9932,
2756,
1107,
1142,
2526,
117,
1195,
2059,
1103,
2607,
1178,
15574,
1103,
8685,
1104,
1103,
9932,
1105,
1169,
1129,
6497,
1112,
1126,
25161,
1111,
4138,
13618,
1194,
16156,
119,
2082,
16246,
117,
1103,
3429,
1105,
1686,
1757,
2686,
1107,
2237,
125,
1202,
1136,
12864,
1113,
1292,
4068,
1104,
3687,
24851,
1891,
119,
124,
119,
123,
12226,
6859,
2116,
12226,
6859,
2116,
1110,
1103,
23565,
1104,
1103,
1210,
5644,
1105,
1110,
25172,
1107,
2393,
2758,
118,
187,
7088,
1306,
123,
119,
1302,
4704,
1107,
1103,
2443,
2566,
5113,
1111,
9221,
6006,
1121,
9373,
15029,
119,
1409,
170,
14372,
21902,
5302,
170,
186,
11848,
5697,
186,
1182,
1104,
9221,
6006,
1111,
170,
21340,
1197,
149,
117,
1173,
1122,
3741,
1103,
1207,
3106,
9221,
2913,
5580,
21340,
1197,
100,
1106,
149,
119,
124,
119,
124,
11689,
26025,
6541,
12226,
6859,
5067,
5156,
9221,
2193,
170,
3014,
4129,
1104,
21340,
1733,
117,
174,
119,
176,
119,
10722,
845,
149,
2064,
845,
149,
1658,
119,
119,
119,
119,
1438,
117,
1219,
1551,
1104,
1112,
27250,
8167,
10031,
117,
2443,
7262,
117,
1137,
5335,
8377,
4290,
1219,
3687,
24851,
1891,
117,
1136,
1155,
5663,
15029,
1336,
1322,
1146,
4172,
1536,
9221,
6006,
1111,
1251,
2510,
21340,
1197,
1106,
3106,
9221,
2193,
119,
1332,
2756,
1114,
14255,
118,
22593,
17882,
1158,
21340,
1733,
117,
6349,
3392,
1110,
1103,
5564,
1134,
17579,
1103,
6349,
4129,
1104,
21340,
1733,
1106,
6878,
1106,
1107,
1546,
1106,
2760,
1543,
1977,
5070,
119,
1135,
1110,
1359,
1113,
1103,
3416,
11626,
1104,
1103,
1211,
2793,
9221,
2913,
21340,
1733,
117,
1314,
2559,
2393,
1116,
117,
1105,
1103,
1378,
12709,
131,
122,
119,
1109,
5580,
1619,
1104,
170,
21340,
1197,
149,
117,
1134,
1110,
1103,
1295,
1104,
9373,
15029,
2133,
1211,
2793,
9221,
2913,
21340,
1197,
1110,
149,
117,
28117,
8661,
27961,
113,
149,
114,
134,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
149,
134,
149,
797,
198,
197,
119,
113,
122,
114,
123,
119,
1109,
3392,
1619,
1104,
170,
21340,
1197,
149,
117,
1134,
1110,
1103,
1295,
1104,
9373,
15029,
2133,
1211,
3055,
9221,
2913,
21340,
1197,
1110,
1719,
149,
1137,
1110,
9026,
1121,
149,
117,
28117,
8661,
6766,
11273,
113,
149,
114,
134,
28117,
8661,
27961,
113,
149,
114,
116,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
149,
850,
11005,
113,
149,
797,
114,
198,
197,
117,
113,
123,
114,
1187,
11005,
113,
149,
797,
114,
1110,
1103,
1383,
1104,
11005,
1104,
149,
797,
117,
178,
119,
174,
119,
1103,
6486,
117,
5372,
118,
6486,
117,
1632,
118,
5372,
17482,
3452,
117,
3576,
119,
117,
1155,
1103,
1236,
1171,
1106,
1103,
9077,
1548,
21340,
1197,
119,
124,
119,
1109,
8362,
8178,
9084,
1906,
1619,
1113,
170,
4954,
1295,
188,
117,
1134,
1110,
1103,
183,
1818,
118,
1129,
1197,
1104,
9373,
15029,
2133,
1211,
2793,
9221,
2913,
21340,
1197,
1110,
1111,
170,
21340,
1197,
1114,
1719,
4954,
2211,
1190,
188,
1137,
1114,
4954,
2211,
1190,
1115,
1104,
1103,
2026,
21340,
1197,
149
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"Although",
"this",
"de",
"##via",
"##tes",
"from",
"the",
"abstract",
"algorithm",
"presented",
"in",
"this",
"paper",
",",
"we",
"believe",
"the",
"changes",
"only",
"obscure",
"the",
"presentation",
"of",
"the",
"algorithm",
"and",
"can",
"be",
"viewed",
"as",
"an",
"optimization",
"for",
"increasing",
"transaction",
"through",
"##put",
".",
"Most",
"importantly",
",",
"the",
"safety",
"and",
"live",
"##ness",
"results",
"in",
"section",
"4",
"do",
"not",
"depend",
"on",
"these",
"details",
"of",
"del",
"##iber",
"##ation",
".",
"3",
".",
"2",
"Val",
"##ida",
"##tion",
"Val",
"##ida",
"##tion",
"is",
"the",
"simplest",
"of",
"the",
"three",
"components",
"and",
"is",
"summarized",
"in",
"al",
"##go",
"-",
"r",
"##ith",
"##m",
"2",
".",
"No",
"##des",
"in",
"the",
"network",
"simply",
"listen",
"for",
"valid",
"##ations",
"from",
"trusted",
"nodes",
".",
"If",
"a",
"node",
"Pi",
"sees",
"a",
"q",
"##uo",
"##rum",
"q",
"##i",
"of",
"valid",
"##ations",
"for",
"a",
"ledge",
"##r",
"L",
",",
"then",
"it",
"sets",
"the",
"new",
"fully",
"valid",
"##ated",
"tip",
"ledge",
"##r",
"[UNK]",
"to",
"L",
".",
"3",
".",
"3",
"Pre",
"##ferred",
"Branch",
"Val",
"##ida",
"##tors",
"normally",
"valid",
"##ate",
"a",
"simple",
"chain",
"of",
"ledge",
"##rs",
",",
"e",
".",
"g",
".",
"LA",
"β",
"L",
"##B",
"β",
"L",
"##C",
".",
".",
".",
".",
"However",
",",
"during",
"times",
"of",
"as",
"##ync",
"##hr",
"##ony",
",",
"network",
"difficulty",
",",
"or",
"temporary",
"Byzantine",
"failure",
"during",
"del",
"##iber",
"##ation",
",",
"not",
"all",
"correct",
"nodes",
"may",
"end",
"up",
"receiving",
"enough",
"valid",
"##ations",
"for",
"any",
"individual",
"ledge",
"##r",
"to",
"fully",
"valid",
"##ate",
".",
"When",
"presented",
"with",
"con",
"-",
"fl",
"##ict",
"##ing",
"ledge",
"##rs",
",",
"preferred",
"branch",
"is",
"the",
"strategy",
"which",
"determines",
"the",
"preferred",
"chain",
"of",
"ledge",
"##rs",
"to",
"switch",
"to",
"in",
"order",
"to",
"continue",
"making",
"forward",
"progress",
".",
"It",
"is",
"based",
"on",
"the",
"shared",
"ancestry",
"of",
"the",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##rs",
",",
"last",
"##V",
"al",
"##s",
",",
"and",
"the",
"following",
"quantities",
":",
"1",
".",
"The",
"tip",
"support",
"of",
"a",
"ledge",
"##r",
"L",
",",
"which",
"is",
"the",
"number",
"of",
"trusted",
"nodes",
"whose",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##r",
"is",
"L",
",",
"su",
"##pp",
"##tip",
"(",
"L",
")",
"=",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"L",
"=",
"L",
"β²",
"}",
"|",
".",
"(",
"1",
")",
"2",
".",
"The",
"branch",
"support",
"of",
"a",
"ledge",
"##r",
"L",
",",
"which",
"is",
"the",
"number",
"of",
"trusted",
"nodes",
"whose",
"most",
"recently",
"valid",
"##ated",
"ledge",
"##r",
"is",
"either",
"L",
"or",
"is",
"descended",
"from",
"L",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
")",
"=",
"su",
"##pp",
"##tip",
"(",
"L",
")",
"+",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"L",
"β",
"ancestors",
"(",
"L",
"β²",
")",
"}",
"|",
",",
"(",
"2",
")",
"where",
"ancestors",
"(",
"L",
"β²",
")",
"is",
"the",
"set",
"of",
"ancestors",
"of",
"L",
"β²",
",",
"i",
".",
"e",
".",
"the",
"parent",
",",
"grand",
"-",
"parent",
",",
"great",
"-",
"grand",
"##par",
"##ent",
",",
"etc",
".",
",",
"all",
"the",
"way",
"back",
"to",
"the",
"genes",
"##is",
"ledge",
"##r",
".",
"3",
".",
"The",
"un",
"##com",
"##mit",
"##ted",
"support",
"on",
"a",
"sequence",
"number",
"s",
",",
"which",
"is",
"the",
"n",
"##um",
"-",
"be",
"##r",
"of",
"trusted",
"nodes",
"whose",
"most",
"recent",
"valid",
"##ated",
"ledge",
"##r",
"is",
"for",
"a",
"ledge",
"##r",
"with",
"either",
"sequence",
"lower",
"than",
"s",
"or",
"with",
"sequence",
"lower",
"than",
"that",
"of",
"the",
"largest",
"ledge",
"##r",
"L"
] | Analysis of the XRP Ledger Consensus Protocol | 170 |
In section 4,
we prove the network conditions needed to guarantee correctness of the algo-
rithm. Finally, section 5 concludes with a discussion of the results and directions
for improvement.
2
2 Network Model and Problem Definition
Let Pi be a node in the network with unique identifier i, such as a cryptographic
public key. Each node Pi is free to choose a unique node list UNLi, which is
the set of nodes (possibly including itself) whose messages Pi will listen to as
part of the XRP LCP. The UNL re | [
9221,
1891,
1115,
1195,
7572,
1138,
3012,
1174,
131,
8362,
8178,
9084,
1906,
113,
188,
114,
134,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
14516,
4426,
113,
149,
797,
114,
133,
12477,
1775,
113,
188,
117,
14516,
4426,
113,
149,
114,
114,
119,
113,
124,
114,
130,
10722,
131,
113,
121,
117,
126,
117,
121,
114,
149,
2064,
131,
113,
122,
117,
124,
117,
121,
114,
149,
2137,
131,
113,
122,
117,
123,
117,
122,
114,
149,
2036,
131,
113,
122,
117,
122,
117,
125,
114,
149,
1658,
131,
113,
121,
117,
123,
117,
121,
114,
149,
2271,
131,
113,
123,
117,
123,
117,
122,
114,
15982,
125,
131,
18657,
2895,
11626,
1126,
12512,
2913,
1114,
189,
4455,
1513,
1104,
28117,
8661,
27961,
117,
28117,
8661,
6766,
11273,
117,
1105,
8362,
8178,
9084,
1906,
114,
1121,
1103,
7281,
1104,
1103,
14372,
1115,
1314,
9221,
2913,
149,
2271,
119,
18657,
2895,
149,
2137,
1110,
6349,
119,
15982,
125,
2196,
170,
182,
3329,
19012,
1859,
117,
1187,
1296,
21340,
1197,
1110,
1126,
12512,
2913,
1114,
1103,
189,
4455,
1513,
1104,
113,
28117,
8661,
27961,
117,
28117,
8661,
6766,
11273,
117,
8362,
8178,
9084,
1906,
114,
1121,
1103,
7281,
1104,
170,
14372,
1115,
1314,
9221,
2913,
149,
2271,
119,
1247,
1132,
126,
9373,
15029,
117,
1160,
1115,
1314,
9221,
2913,
149,
2271,
1105,
1141,
1296,
9221,
3798,
149,
2064,
117,
149,
2137,
1105,
149,
2036,
119,
1109,
6349,
3392,
5564,
17579,
1115,
149,
2137,
1110,
6349,
119,
1109,
6349,
3392,
11309,
1110,
2136,
1107,
2586,
18791,
7088,
1306,
124,
119,
1130,
7926,
8588,
1193,
117,
1103,
1911,
1110,
1111,
1296,
14372,
1106,
1129,
6588,
1105,
1178,
6878,
1106,
170,
1472,
3392,
1165,
1122,
3520,
1536,
15029,
1138,
4762,
1106,
1115,
4129,
1104,
21340,
1733,
1216,
1115,
1126,
4174,
4129,
2834,
1138,
1167,
1619,
119,
1109,
6349,
21340,
1197,
1110,
1276,
1118,
3179,
1103,
11626,
2780,
117,
2547,
1121,
1103,
21340,
1197,
149,
1115,
1110,
1103,
1887,
13596,
21340,
1197,
1104,
1103,
1211,
3055,
9221,
2913,
21340,
1733,
119,
1284,
1173,
8247,
1103,
2027,
21340,
1197,
149,
797,
850,
1482,
113,
149,
114,
1114,
2439,
28117,
8661,
6766,
11273,
113,
149,
797,
114,
117,
1115,
1156,
1253,
1138,
1103,
1211,
1619,
1256,
1191,
1155,
8362,
8178,
9084,
1906,
113,
14516,
4426,
113,
149,
797,
114,
114,
3015,
170,
21776,
26563,
21340,
1197,
119,
1409,
1195,
2834,
8247,
170,
2027,
1104,
149,
18330,
1142,
8875,
117,
1173,
149,
1110,
1103,
6349,
21340,
1197,
119,
1409,
1195,
1169,
1525,
170,
6349,
2027,
149,
797,
117,
1173,
1195,
9488,
1103,
1965,
1113,
1103,
1482,
1104,
149,
797,
119,
1130,
1546,
1106,
4989,
170,
1703,
13649,
1113,
21340,
1733,
1105,
2549,
7057,
1206,
26563,
21340,
1733,
117,
1195,
11235,
1113,
170,
3053,
439,
113,
149,
797,
117,
149,
797,
797,
114,
117,
1134,
1110,
122,
1191,
1103,
1144,
1324,
1104,
149,
797,
135,
149,
797,
797,
1105,
1110,
121,
4303,
119,
1409,
1103,
21340,
1197,
1276,
1110,
1126,
13596,
1104,
1412,
1954,
1684,
21340,
1197,
149,
28311,
117,
1195,
1712,
149,
28311
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"valid",
"##ation",
"that",
"we",
"personally",
"have",
"broadcast",
"##ed",
":",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
"=",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"se",
"##q",
"(",
"L",
"β²",
")",
"<",
"ma",
"##x",
"(",
"s",
",",
"se",
"##q",
"(",
"L",
")",
")",
".",
"(",
"3",
")",
"9",
"LA",
":",
"(",
"0",
",",
"5",
",",
"0",
")",
"L",
"##B",
":",
"(",
"1",
",",
"3",
",",
"0",
")",
"L",
"##D",
":",
"(",
"1",
",",
"2",
",",
"1",
")",
"L",
"##E",
":",
"(",
"1",
",",
"1",
",",
"4",
")",
"L",
"##C",
":",
"(",
"0",
",",
"2",
",",
"0",
")",
"L",
"##F",
":",
"(",
"2",
",",
"2",
",",
"1",
")",
"Figure",
"4",
":",
"Led",
"##ger",
"ancestry",
"an",
"##not",
"##ated",
"with",
"t",
"##up",
"##le",
"of",
"su",
"##pp",
"##tip",
",",
"su",
"##pp",
"##bra",
"##nch",
",",
"and",
"un",
"##com",
"##mit",
"##ted",
")",
"from",
"the",
"perspective",
"of",
"the",
"node",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
".",
"Led",
"##ger",
"L",
"##D",
"is",
"preferred",
".",
"Figure",
"4",
"shows",
"a",
"m",
"##ot",
"##ivating",
"example",
",",
"where",
"each",
"ledge",
"##r",
"is",
"an",
"##not",
"##ated",
"with",
"the",
"t",
"##up",
"##le",
"of",
"(",
"su",
"##pp",
"##tip",
",",
"su",
"##pp",
"##bra",
"##nch",
",",
"un",
"##com",
"##mit",
"##ted",
")",
"from",
"the",
"perspective",
"of",
"a",
"node",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
".",
"There",
"are",
"5",
"trusted",
"nodes",
",",
"two",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
"and",
"one",
"each",
"valid",
"##ating",
"L",
"##B",
",",
"L",
"##D",
"and",
"L",
"##E",
".",
"The",
"preferred",
"branch",
"strategy",
"determines",
"that",
"L",
"##D",
"is",
"preferred",
".",
"The",
"preferred",
"branch",
"protocol",
"is",
"provided",
"in",
"Al",
"##gor",
"##ith",
"##m",
"3",
".",
"In",
"##tu",
"##itive",
"##ly",
",",
"the",
"idea",
"is",
"for",
"each",
"node",
"to",
"be",
"conservative",
"and",
"only",
"switch",
"to",
"a",
"different",
"branch",
"when",
"it",
"knows",
"enough",
"nodes",
"have",
"committed",
"to",
"that",
"chain",
"of",
"ledge",
"##rs",
"such",
"that",
"an",
"alternative",
"chain",
"cannot",
"have",
"more",
"support",
".",
"The",
"preferred",
"ledge",
"##r",
"is",
"found",
"by",
"walking",
"the",
"ancestry",
"tree",
",",
"starting",
"from",
"the",
"ledge",
"##r",
"L",
"that",
"is",
"the",
"common",
"ancestor",
"ledge",
"##r",
"of",
"the",
"most",
"recently",
"valid",
"##ated",
"ledge",
"##rs",
".",
"We",
"then",
"select",
"the",
"child",
"ledge",
"##r",
"L",
"β²",
"β",
"children",
"(",
"L",
")",
"with",
"highest",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
"β²",
")",
",",
"that",
"would",
"still",
"have",
"the",
"most",
"support",
"even",
"if",
"all",
"un",
"##com",
"##mit",
"##ted",
"(",
"se",
"##q",
"(",
"L",
"β²",
")",
")",
"picked",
"a",
"conflicting",
"sibling",
"ledge",
"##r",
".",
"If",
"we",
"cannot",
"select",
"a",
"child",
"of",
"L",
"satisfying",
"this",
"requirement",
",",
"then",
"L",
"is",
"the",
"preferred",
"ledge",
"##r",
".",
"If",
"we",
"can",
"find",
"a",
"preferred",
"child",
"L",
"β²",
",",
"then",
"we",
"repeat",
"the",
"process",
"on",
"the",
"children",
"of",
"L",
"β²",
".",
"In",
"order",
"to",
"ensure",
"a",
"total",
"ordering",
"on",
"ledge",
"##rs",
"and",
"break",
"ties",
"between",
"sibling",
"ledge",
"##rs",
",",
"we",
"rely",
"on",
"a",
"function",
"Ο",
"(",
"L",
"β²",
",",
"L",
"β²",
"β²",
")",
",",
"which",
"is",
"1",
"if",
"the",
"has",
"##h",
"of",
"L",
"β²",
">",
"L",
"β²",
"β²",
"and",
"is",
"0",
"otherwise",
".",
"If",
"the",
"ledge",
"##r",
"found",
"is",
"an",
"ancestor",
"of",
"our",
"current",
"working",
"ledge",
"##r",
"L",
"##Μ",
",",
"we",
"keep",
"L",
"##Μ"
] | Analysis of the XRP Ledger Consensus Protocol | 171 |
In section 4,
we prove the network conditions needed to guarantee correctness of the algo-
rithm. Finally, section 5 concludes with a discussion of the results and directions
for improvement.
2
2 Network Model and Problem Definition
Let Pi be a node in the network with unique identifier i, such as a cryptographic
public key. Each node Pi is free to choose a unique node list UNLi, which is
the set of nodes (possibly including itself) whose messages Pi will listen to as
part of the XRP LCP. The UNL re | [
9221,
1891,
1115,
1195,
7572,
1138,
3012,
1174,
131,
8362,
8178,
9084,
1906,
113,
188,
114,
134,
197,
196,
159,
2162,
797,
117,
178,
850,
1314,
2559,
2393,
1116,
131,
14516,
4426,
113,
149,
797,
114,
133,
12477,
1775,
113,
188,
117,
14516,
4426,
113,
149,
114,
114,
119,
113,
124,
114,
130,
10722,
131,
113,
121,
117,
126,
117,
121,
114,
149,
2064,
131,
113,
122,
117,
124,
117,
121,
114,
149,
2137,
131,
113,
122,
117,
123,
117,
122,
114,
149,
2036,
131,
113,
122,
117,
122,
117,
125,
114,
149,
1658,
131,
113,
121,
117,
123,
117,
121,
114,
149,
2271,
131,
113,
123,
117,
123,
117,
122,
114,
15982,
125,
131,
18657,
2895,
11626,
1126,
12512,
2913,
1114,
189,
4455,
1513,
1104,
28117,
8661,
27961,
117,
28117,
8661,
6766,
11273,
117,
1105,
8362,
8178,
9084,
1906,
114,
1121,
1103,
7281,
1104,
1103,
14372,
1115,
1314,
9221,
2913,
149,
2271,
119,
18657,
2895,
149,
2137,
1110,
6349,
119,
15982,
125,
2196,
170,
182,
3329,
19012,
1859,
117,
1187,
1296,
21340,
1197,
1110,
1126,
12512,
2913,
1114,
1103,
189,
4455,
1513,
1104,
113,
28117,
8661,
27961,
117,
28117,
8661,
6766,
11273,
117,
8362,
8178,
9084,
1906,
114,
1121,
1103,
7281,
1104,
170,
14372,
1115,
1314,
9221,
2913,
149,
2271,
119,
1247,
1132,
126,
9373,
15029,
117,
1160,
1115,
1314,
9221,
2913,
149,
2271,
1105,
1141,
1296,
9221,
3798,
149,
2064,
117,
149,
2137,
1105,
149,
2036,
119,
1109,
6349,
3392,
5564,
17579,
1115,
149,
2137,
1110,
6349,
119,
1109,
6349,
3392,
11309,
1110,
2136,
1107,
2586,
18791,
7088,
1306,
124,
119,
1130,
7926,
8588,
1193,
117,
1103,
1911,
1110,
1111,
1296,
14372,
1106,
1129,
6588,
1105,
1178,
6878,
1106,
170,
1472,
3392,
1165,
1122,
3520,
1536,
15029,
1138,
4762,
1106,
1115,
4129,
1104,
21340,
1733,
1216,
1115,
1126,
4174,
4129,
2834,
1138,
1167,
1619,
119,
1109,
6349,
21340,
1197,
1110,
1276,
1118,
3179,
1103,
11626,
2780,
117,
2547,
1121,
1103,
21340,
1197,
149,
1115,
1110,
1103,
1887,
13596,
21340,
1197,
1104,
1103,
1211,
3055,
9221,
2913,
21340,
1733,
119,
1284,
1173,
8247,
1103,
2027,
21340,
1197,
149,
797,
850,
1482,
113,
149,
114,
1114,
2439,
28117,
8661,
6766,
11273,
113,
149,
797,
114,
117,
1115,
1156,
1253,
1138,
1103,
1211,
1619,
1256,
1191,
1155,
8362,
8178,
9084,
1906,
113,
14516,
4426,
113,
149,
797,
114,
114,
3015,
170,
21776,
26563,
21340,
1197,
119,
1409,
1195,
2834,
8247,
170,
2027,
1104,
149,
18330,
1142,
8875,
117,
1173,
149,
1110,
1103,
6349,
21340,
1197,
119,
1409,
1195,
1169,
1525,
170,
6349,
2027,
149,
797,
117,
1173,
1195,
9488,
1103,
1965,
1113,
1103,
1482,
1104,
149,
797,
119,
1130,
1546,
1106,
4989,
170,
1703,
13649,
1113,
21340,
1733,
1105,
2549,
7057,
1206,
26563,
21340,
1733,
117,
1195,
11235,
1113,
170,
3053,
439,
113,
149,
797,
117,
149,
797,
797,
114,
117,
1134,
1110,
122,
1191,
1103,
1144,
1324,
1104,
149,
797,
135,
149,
797,
797,
1105,
1110,
121,
4303,
119,
1409,
1103,
21340,
1197,
1276,
1110,
1126,
13596,
1104,
1412,
1954,
1684,
21340,
1197,
149,
28311,
117,
1195,
1712,
149,
28311
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"valid",
"##ation",
"that",
"we",
"personally",
"have",
"broadcast",
"##ed",
":",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
"=",
"|",
"{",
"V",
"##L",
"β²",
",",
"i",
"β",
"last",
"##V",
"al",
"##s",
":",
"se",
"##q",
"(",
"L",
"β²",
")",
"<",
"ma",
"##x",
"(",
"s",
",",
"se",
"##q",
"(",
"L",
")",
")",
".",
"(",
"3",
")",
"9",
"LA",
":",
"(",
"0",
",",
"5",
",",
"0",
")",
"L",
"##B",
":",
"(",
"1",
",",
"3",
",",
"0",
")",
"L",
"##D",
":",
"(",
"1",
",",
"2",
",",
"1",
")",
"L",
"##E",
":",
"(",
"1",
",",
"1",
",",
"4",
")",
"L",
"##C",
":",
"(",
"0",
",",
"2",
",",
"0",
")",
"L",
"##F",
":",
"(",
"2",
",",
"2",
",",
"1",
")",
"Figure",
"4",
":",
"Led",
"##ger",
"ancestry",
"an",
"##not",
"##ated",
"with",
"t",
"##up",
"##le",
"of",
"su",
"##pp",
"##tip",
",",
"su",
"##pp",
"##bra",
"##nch",
",",
"and",
"un",
"##com",
"##mit",
"##ted",
")",
"from",
"the",
"perspective",
"of",
"the",
"node",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
".",
"Led",
"##ger",
"L",
"##D",
"is",
"preferred",
".",
"Figure",
"4",
"shows",
"a",
"m",
"##ot",
"##ivating",
"example",
",",
"where",
"each",
"ledge",
"##r",
"is",
"an",
"##not",
"##ated",
"with",
"the",
"t",
"##up",
"##le",
"of",
"(",
"su",
"##pp",
"##tip",
",",
"su",
"##pp",
"##bra",
"##nch",
",",
"un",
"##com",
"##mit",
"##ted",
")",
"from",
"the",
"perspective",
"of",
"a",
"node",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
".",
"There",
"are",
"5",
"trusted",
"nodes",
",",
"two",
"that",
"last",
"valid",
"##ated",
"L",
"##F",
"and",
"one",
"each",
"valid",
"##ating",
"L",
"##B",
",",
"L",
"##D",
"and",
"L",
"##E",
".",
"The",
"preferred",
"branch",
"strategy",
"determines",
"that",
"L",
"##D",
"is",
"preferred",
".",
"The",
"preferred",
"branch",
"protocol",
"is",
"provided",
"in",
"Al",
"##gor",
"##ith",
"##m",
"3",
".",
"In",
"##tu",
"##itive",
"##ly",
",",
"the",
"idea",
"is",
"for",
"each",
"node",
"to",
"be",
"conservative",
"and",
"only",
"switch",
"to",
"a",
"different",
"branch",
"when",
"it",
"knows",
"enough",
"nodes",
"have",
"committed",
"to",
"that",
"chain",
"of",
"ledge",
"##rs",
"such",
"that",
"an",
"alternative",
"chain",
"cannot",
"have",
"more",
"support",
".",
"The",
"preferred",
"ledge",
"##r",
"is",
"found",
"by",
"walking",
"the",
"ancestry",
"tree",
",",
"starting",
"from",
"the",
"ledge",
"##r",
"L",
"that",
"is",
"the",
"common",
"ancestor",
"ledge",
"##r",
"of",
"the",
"most",
"recently",
"valid",
"##ated",
"ledge",
"##rs",
".",
"We",
"then",
"select",
"the",
"child",
"ledge",
"##r",
"L",
"β²",
"β",
"children",
"(",
"L",
")",
"with",
"highest",
"su",
"##pp",
"##bra",
"##nch",
"(",
"L",
"β²",
")",
",",
"that",
"would",
"still",
"have",
"the",
"most",
"support",
"even",
"if",
"all",
"un",
"##com",
"##mit",
"##ted",
"(",
"se",
"##q",
"(",
"L",
"β²",
")",
")",
"picked",
"a",
"conflicting",
"sibling",
"ledge",
"##r",
".",
"If",
"we",
"cannot",
"select",
"a",
"child",
"of",
"L",
"satisfying",
"this",
"requirement",
",",
"then",
"L",
"is",
"the",
"preferred",
"ledge",
"##r",
".",
"If",
"we",
"can",
"find",
"a",
"preferred",
"child",
"L",
"β²",
",",
"then",
"we",
"repeat",
"the",
"process",
"on",
"the",
"children",
"of",
"L",
"β²",
".",
"In",
"order",
"to",
"ensure",
"a",
"total",
"ordering",
"on",
"ledge",
"##rs",
"and",
"break",
"ties",
"between",
"sibling",
"ledge",
"##rs",
",",
"we",
"rely",
"on",
"a",
"function",
"Ο",
"(",
"L",
"β²",
",",
"L",
"β²",
"β²",
")",
",",
"which",
"is",
"1",
"if",
"the",
"has",
"##h",
"of",
"L",
"β²",
">",
"L",
"β²",
"β²",
"and",
"is",
"0",
"otherwise",
".",
"If",
"the",
"ledge",
"##r",
"found",
"is",
"an",
"ancestor",
"of",
"our",
"current",
"working",
"ledge",
"##r",
"L",
"##Μ",
",",
"we",
"keep",
"L",
"##Μ"
] | Analysis of the XRP Ledger Consensus Protocol | 172 |
presents a subset of the network which, when
taken collectively, is trusted by Pi to not collude in an attempt to defraud the
network (see [10] for the motivation of this name). The UNLs give structure to
the network, with a node that is present in more UNLs implicitly having more
influence. An individual node has complete discretion in the choice of their
UNL, although we show in section 4 that minimum overlap with other UNLs
is necessary for consistency and liveness with other honest nodes. We do not
as | [
1110,
1103,
6349,
21340,
1197,
117,
1290,
1195,
1202,
1136,
1870,
1221,
1195,
1132,
1113,
1103,
2488,
3392,
119,
5322,
1115,
1107,
2740,
1104,
6122,
1112,
27250,
8167,
10031,
117,
170,
3392,
1336,
1178,
1129,
2786,
2726,
1118,
170,
1423,
14372,
1165,
1122,
3316,
6349,
119,
1337,
2086,
1168,
15029,
1538,
23073,
1103,
11309,
27289,
1116,
1104,
1115,
21340,
1197,
1196,
12806,
1106,
16170,
1113,
1122,
119,
125,
12504,
5823,
1758,
1103,
161,
20336,
149,
13113,
1121,
170,
11309,
7281,
117,
1195,
1208,
5708,
5424,
2686,
1164,
1157,
3429,
1105,
1686,
1757,
119,
1275,
125,
119,
122,
9218,
1130,
1142,
2237,
1195,
1209,
5424,
2975,
1113,
1103,
2443,
9566,
1115,
176,
6718,
1197,
118,
22904,
3051,
1472,
15029,
1919,
1103,
161,
20336,
149,
13113,
1209,
3118,
8080,
119,
1130,
1103,
1378,
3622,
117,
1195,
1525,
1122,
14785,
1106,
7568,
1115,
3106,
9221,
3798,
170,
21340,
1197,
1674,
1136,
3106,
9221,
2193,
1157,
11005,
119,
1249,
1195,
1209,
1525,
117,
1122,
3587,
1115,
1122,
1336,
1129,
1936,
1107,
1199,
25209,
1111,
1160,
15029,
1106,
3106,
9221,
2193,
14255,
4487,
28113,
4649,
21340,
1733,
1114,
1472,
4954,
2849,
1256,
1191,
3106,
9221,
3798,
14255,
4487,
28113,
4649,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
1110,
4763,
119,
1109,
1393,
1110,
1198,
1112,
20405,
1112,
1103,
2985,
117,
1133,
1195,
1525,
1122,
14785,
1106,
2767,
1149,
1103,
1160,
4290,
3322,
1105,
5424,
2975,
10878,
1172,
10380,
119,
1370,
1103,
3288,
3622,
117,
1195,
1294,
170,
27466,
8223,
22881,
1158,
13457,
119,
2611,
1107,
1103,
2526,
1195,
1209,
1231,
3906,
1193,
3171,
1103,
2463,
1443,
1292,
19129,
119,
1109,
13457,
1195,
1294,
1110,
1115,
170,
8377,
6088,
1183,
14372,
2834,
7627,
1160,
7345,
15029,
1115,
1122,
9221,
2913,
1472,
21340,
1733,
119,
1188,
13457,
1108,
1215,
1107,
1103,
1560,
1653,
26311,
164,
1275,
166,
1105,
1110,
12478,
2200,
1118,
1103,
1911,
1115,
1155,
4909,
1110,
1694,
1194,
13179,
4321,
8305,
1166,
170,
8536,
118,
1106,
118,
8536,
2443,
117,
1177,
1115,
1103,
107,
24390,
107,
1104,
1160,
14255,
4487,
28113,
4649,
7416,
1156,
1129,
3535,
1107,
1159,
1111,
1103,
3802,
1106,
1129,
5794,
117,
1290,
1103,
7416,
1132,
1878,
119,
7595,
1142,
13457,
1674,
1136,
2080,
1107,
170,
3106,
1112,
27250,
8167,
23038,
1361,
2443,
117,
1290,
170,
2443,
16416,
1180,
14516,
1403,
1874,
4948,
1103,
14255,
4487,
28113,
4649,
7416,
1263,
1536,
1111,
3290,
1106,
4467,
119,
1284,
1840,
1142,
13457,
8377,
3300,
6328,
117,
1105,
1209,
1579,
3835,
1165,
1195,
1132,
1606,
1122,
1112,
1126,
13457,
119,
1249,
19951,
8377,
3300,
6328,
3486,
117,
1195,
1208,
19774,
1165,
1122,
1110,
1936,
1111,
1160,
15029,
1106,
3106,
9221,
2193,
1472,
21340,
1733,
1107,
170,
1423,
1668,
1104,
10923,
119,
12556,
3309,
16877,
1103,
16049,
2776,
117,
1103,
3879,
3228,
1107,
1103,
1653,
26311,
164,
1275,
166,
1108,
1115,
1160,
15029,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
21776,
21340,
1733,
1191,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
12477,
1775,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
119,
1556,
186,
11848,
5697,
1116,
1104
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
23,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0
] | [
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
22,
22,
0,
0,
0,
23,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0
] | [
"is",
"the",
"preferred",
"ledge",
"##r",
",",
"since",
"we",
"do",
"not",
"yet",
"know",
"we",
"are",
"on",
"the",
"wrong",
"branch",
".",
"Note",
"that",
"in",
"cases",
"of",
"extreme",
"as",
"##ync",
"##hr",
"##ony",
",",
"a",
"branch",
"may",
"only",
"be",
"initially",
"supported",
"by",
"a",
"single",
"node",
"when",
"it",
"becomes",
"preferred",
".",
"That",
"means",
"other",
"nodes",
"must",
"verify",
"the",
"protocol",
"invariant",
"##s",
"of",
"that",
"ledge",
"##r",
"before",
"switching",
"to",
"deliberate",
"on",
"it",
".",
"4",
"Analysis",
"Having",
"described",
"the",
"X",
"##RP",
"L",
"##CP",
"from",
"a",
"protocol",
"perspective",
",",
"we",
"now",
"formally",
"prove",
"results",
"about",
"its",
"safety",
"and",
"live",
"##ness",
".",
"10",
"4",
".",
"1",
"Safety",
"In",
"this",
"section",
"we",
"will",
"prove",
"conditions",
"on",
"the",
"network",
"configuration",
"that",
"g",
"##ua",
"##r",
"-",
"ant",
"##ee",
"different",
"nodes",
"running",
"the",
"X",
"##RP",
"L",
"##CP",
"will",
"remain",
"consistent",
".",
"In",
"the",
"following",
"analysis",
",",
"we",
"find",
"it",
"convenient",
"to",
"assume",
"that",
"fully",
"valid",
"##ating",
"a",
"ledge",
"##r",
"does",
"not",
"fully",
"valid",
"##ate",
"its",
"ancestors",
".",
"As",
"we",
"will",
"find",
",",
"it",
"turns",
"that",
"it",
"may",
"be",
"possible",
"in",
"some",
"configurations",
"for",
"two",
"nodes",
"to",
"fully",
"valid",
"##ate",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
"with",
"different",
"sequence",
"numbers",
"even",
"if",
"fully",
"valid",
"##ating",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
"is",
"impossible",
".",
"The",
"former",
"is",
"just",
"as",
"problematic",
"as",
"the",
"latter",
",",
"but",
"we",
"find",
"it",
"convenient",
"to",
"separate",
"out",
"the",
"two",
"failure",
"types",
"and",
"prove",
"conditions",
"preventing",
"them",
"separately",
".",
"For",
"the",
"initial",
"analysis",
",",
"we",
"make",
"a",
"si",
"##mp",
"##lify",
"##ing",
"assumption",
".",
"Later",
"in",
"the",
"paper",
"we",
"will",
"re",
"##ana",
"##ly",
"##ze",
"the",
"problem",
"without",
"these",
"assumptions",
".",
"The",
"assumption",
"we",
"make",
"is",
"that",
"a",
"Byzantine",
"fault",
"##y",
"node",
"cannot",
"convince",
"two",
"honest",
"nodes",
"that",
"it",
"valid",
"##ated",
"different",
"ledge",
"##rs",
".",
"This",
"assumption",
"was",
"used",
"in",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
"and",
"is",
"rational",
"##ized",
"by",
"the",
"idea",
"that",
"all",
"communication",
"is",
"done",
"through",
"generic",
"multi",
"##cast",
"over",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
",",
"so",
"that",
"the",
"\"",
"echoes",
"\"",
"of",
"two",
"con",
"##tra",
"##dict",
"##ory",
"messages",
"would",
"be",
"noticed",
"in",
"time",
"for",
"the",
"message",
"to",
"be",
"ignored",
",",
"since",
"the",
"messages",
"are",
"signed",
".",
"Unfortunately",
"this",
"assumption",
"does",
"not",
"hold",
"in",
"a",
"fully",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"network",
",",
"since",
"a",
"network",
"partition",
"could",
"se",
"##g",
"##re",
"##gate",
"the",
"con",
"##tra",
"##dict",
"##ory",
"messages",
"long",
"enough",
"for",
"damage",
"to",
"occur",
".",
"We",
"call",
"this",
"assumption",
"Byzantine",
"account",
"##ability",
",",
"and",
"will",
"always",
"reference",
"when",
"we",
"are",
"using",
"it",
"as",
"an",
"assumption",
".",
"As",
"##suming",
"Byzantine",
"account",
"##ability",
"holds",
",",
"we",
"now",
"analyze",
"when",
"it",
"is",
"possible",
"for",
"two",
"nodes",
"to",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"in",
"a",
"single",
"round",
"of",
"consensus",
".",
"Mo",
"##di",
"##fying",
"the",
"notation",
"slightly",
",",
"the",
"condition",
"suggested",
"in",
"the",
"white",
"##paper",
"[",
"10",
"]",
"was",
"that",
"two",
"nodes",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"conflicting",
"ledge",
"##rs",
"if",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ma",
"##x",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
".",
"With",
"q",
"##uo",
"##rum",
"##s",
"of"
] | Analysis of the XRP Ledger Consensus Protocol | 173 |
presents a subset of the network which, when
taken collectively, is trusted by Pi to not collude in an attempt to defraud the
network (see [10] for the motivation of this name). The UNLs give structure to
the network, with a node that is present in more UNLs implicitly having more
influence. An individual node has complete discretion in the choice of their
UNL, although we show in section 4 that minimum overlap with other UNLs
is necessary for consistency and liveness with other honest nodes. We do not
as | [
1110,
1103,
6349,
21340,
1197,
117,
1290,
1195,
1202,
1136,
1870,
1221,
1195,
1132,
1113,
1103,
2488,
3392,
119,
5322,
1115,
1107,
2740,
1104,
6122,
1112,
27250,
8167,
10031,
117,
170,
3392,
1336,
1178,
1129,
2786,
2726,
1118,
170,
1423,
14372,
1165,
1122,
3316,
6349,
119,
1337,
2086,
1168,
15029,
1538,
23073,
1103,
11309,
27289,
1116,
1104,
1115,
21340,
1197,
1196,
12806,
1106,
16170,
1113,
1122,
119,
125,
12504,
5823,
1758,
1103,
161,
20336,
149,
13113,
1121,
170,
11309,
7281,
117,
1195,
1208,
5708,
5424,
2686,
1164,
1157,
3429,
1105,
1686,
1757,
119,
1275,
125,
119,
122,
9218,
1130,
1142,
2237,
1195,
1209,
5424,
2975,
1113,
1103,
2443,
9566,
1115,
176,
6718,
1197,
118,
22904,
3051,
1472,
15029,
1919,
1103,
161,
20336,
149,
13113,
1209,
3118,
8080,
119,
1130,
1103,
1378,
3622,
117,
1195,
1525,
1122,
14785,
1106,
7568,
1115,
3106,
9221,
3798,
170,
21340,
1197,
1674,
1136,
3106,
9221,
2193,
1157,
11005,
119,
1249,
1195,
1209,
1525,
117,
1122,
3587,
1115,
1122,
1336,
1129,
1936,
1107,
1199,
25209,
1111,
1160,
15029,
1106,
3106,
9221,
2193,
14255,
4487,
28113,
4649,
21340,
1733,
1114,
1472,
4954,
2849,
1256,
1191,
3106,
9221,
3798,
14255,
4487,
28113,
4649,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
1110,
4763,
119,
1109,
1393,
1110,
1198,
1112,
20405,
1112,
1103,
2985,
117,
1133,
1195,
1525,
1122,
14785,
1106,
2767,
1149,
1103,
1160,
4290,
3322,
1105,
5424,
2975,
10878,
1172,
10380,
119,
1370,
1103,
3288,
3622,
117,
1195,
1294,
170,
27466,
8223,
22881,
1158,
13457,
119,
2611,
1107,
1103,
2526,
1195,
1209,
1231,
3906,
1193,
3171,
1103,
2463,
1443,
1292,
19129,
119,
1109,
13457,
1195,
1294,
1110,
1115,
170,
8377,
6088,
1183,
14372,
2834,
7627,
1160,
7345,
15029,
1115,
1122,
9221,
2913,
1472,
21340,
1733,
119,
1188,
13457,
1108,
1215,
1107,
1103,
1560,
1653,
26311,
164,
1275,
166,
1105,
1110,
12478,
2200,
1118,
1103,
1911,
1115,
1155,
4909,
1110,
1694,
1194,
13179,
4321,
8305,
1166,
170,
8536,
118,
1106,
118,
8536,
2443,
117,
1177,
1115,
1103,
107,
24390,
107,
1104,
1160,
14255,
4487,
28113,
4649,
7416,
1156,
1129,
3535,
1107,
1159,
1111,
1103,
3802,
1106,
1129,
5794,
117,
1290,
1103,
7416,
1132,
1878,
119,
7595,
1142,
13457,
1674,
1136,
2080,
1107,
170,
3106,
1112,
27250,
8167,
23038,
1361,
2443,
117,
1290,
170,
2443,
16416,
1180,
14516,
1403,
1874,
4948,
1103,
14255,
4487,
28113,
4649,
7416,
1263,
1536,
1111,
3290,
1106,
4467,
119,
1284,
1840,
1142,
13457,
8377,
3300,
6328,
117,
1105,
1209,
1579,
3835,
1165,
1195,
1132,
1606,
1122,
1112,
1126,
13457,
119,
1249,
19951,
8377,
3300,
6328,
3486,
117,
1195,
1208,
19774,
1165,
1122,
1110,
1936,
1111,
1160,
15029,
1106,
3106,
9221,
2193,
1472,
21340,
1733,
1107,
170,
1423,
1668,
1104,
10923,
119,
12556,
3309,
16877,
1103,
16049,
2776,
117,
1103,
3879,
3228,
1107,
1103,
1653,
26311,
164,
1275,
166,
1108,
1115,
1160,
15029,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
21776,
21340,
1733,
1191,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
12477,
1775,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
119,
1556,
186,
11848,
5697,
1116,
1104
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"is",
"the",
"preferred",
"ledge",
"##r",
",",
"since",
"we",
"do",
"not",
"yet",
"know",
"we",
"are",
"on",
"the",
"wrong",
"branch",
".",
"Note",
"that",
"in",
"cases",
"of",
"extreme",
"as",
"##ync",
"##hr",
"##ony",
",",
"a",
"branch",
"may",
"only",
"be",
"initially",
"supported",
"by",
"a",
"single",
"node",
"when",
"it",
"becomes",
"preferred",
".",
"That",
"means",
"other",
"nodes",
"must",
"verify",
"the",
"protocol",
"invariant",
"##s",
"of",
"that",
"ledge",
"##r",
"before",
"switching",
"to",
"deliberate",
"on",
"it",
".",
"4",
"Analysis",
"Having",
"described",
"the",
"X",
"##RP",
"L",
"##CP",
"from",
"a",
"protocol",
"perspective",
",",
"we",
"now",
"formally",
"prove",
"results",
"about",
"its",
"safety",
"and",
"live",
"##ness",
".",
"10",
"4",
".",
"1",
"Safety",
"In",
"this",
"section",
"we",
"will",
"prove",
"conditions",
"on",
"the",
"network",
"configuration",
"that",
"g",
"##ua",
"##r",
"-",
"ant",
"##ee",
"different",
"nodes",
"running",
"the",
"X",
"##RP",
"L",
"##CP",
"will",
"remain",
"consistent",
".",
"In",
"the",
"following",
"analysis",
",",
"we",
"find",
"it",
"convenient",
"to",
"assume",
"that",
"fully",
"valid",
"##ating",
"a",
"ledge",
"##r",
"does",
"not",
"fully",
"valid",
"##ate",
"its",
"ancestors",
".",
"As",
"we",
"will",
"find",
",",
"it",
"turns",
"that",
"it",
"may",
"be",
"possible",
"in",
"some",
"configurations",
"for",
"two",
"nodes",
"to",
"fully",
"valid",
"##ate",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
"with",
"different",
"sequence",
"numbers",
"even",
"if",
"fully",
"valid",
"##ating",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
"is",
"impossible",
".",
"The",
"former",
"is",
"just",
"as",
"problematic",
"as",
"the",
"latter",
",",
"but",
"we",
"find",
"it",
"convenient",
"to",
"separate",
"out",
"the",
"two",
"failure",
"types",
"and",
"prove",
"conditions",
"preventing",
"them",
"separately",
".",
"For",
"the",
"initial",
"analysis",
",",
"we",
"make",
"a",
"si",
"##mp",
"##lify",
"##ing",
"assumption",
".",
"Later",
"in",
"the",
"paper",
"we",
"will",
"re",
"##ana",
"##ly",
"##ze",
"the",
"problem",
"without",
"these",
"assumptions",
".",
"The",
"assumption",
"we",
"make",
"is",
"that",
"a",
"Byzantine",
"fault",
"##y",
"node",
"cannot",
"convince",
"two",
"honest",
"nodes",
"that",
"it",
"valid",
"##ated",
"different",
"ledge",
"##rs",
".",
"This",
"assumption",
"was",
"used",
"in",
"the",
"original",
"white",
"##paper",
"[",
"10",
"]",
"and",
"is",
"rational",
"##ized",
"by",
"the",
"idea",
"that",
"all",
"communication",
"is",
"done",
"through",
"generic",
"multi",
"##cast",
"over",
"a",
"peer",
"-",
"to",
"-",
"peer",
"network",
",",
"so",
"that",
"the",
"\"",
"echoes",
"\"",
"of",
"two",
"con",
"##tra",
"##dict",
"##ory",
"messages",
"would",
"be",
"noticed",
"in",
"time",
"for",
"the",
"message",
"to",
"be",
"ignored",
",",
"since",
"the",
"messages",
"are",
"signed",
".",
"Unfortunately",
"this",
"assumption",
"does",
"not",
"hold",
"in",
"a",
"fully",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"network",
",",
"since",
"a",
"network",
"partition",
"could",
"se",
"##g",
"##re",
"##gate",
"the",
"con",
"##tra",
"##dict",
"##ory",
"messages",
"long",
"enough",
"for",
"damage",
"to",
"occur",
".",
"We",
"call",
"this",
"assumption",
"Byzantine",
"account",
"##ability",
",",
"and",
"will",
"always",
"reference",
"when",
"we",
"are",
"using",
"it",
"as",
"an",
"assumption",
".",
"As",
"##suming",
"Byzantine",
"account",
"##ability",
"holds",
",",
"we",
"now",
"analyze",
"when",
"it",
"is",
"possible",
"for",
"two",
"nodes",
"to",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"in",
"a",
"single",
"round",
"of",
"consensus",
".",
"Mo",
"##di",
"##fying",
"the",
"notation",
"slightly",
",",
"the",
"condition",
"suggested",
"in",
"the",
"white",
"##paper",
"[",
"10",
"]",
"was",
"that",
"two",
"nodes",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"conflicting",
"ledge",
"##rs",
"if",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ma",
"##x",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
".",
"With",
"q",
"##uo",
"##rum",
"##s",
"of"
] | Analysis of the XRP Ledger Consensus Protocol | 174 |
sume that trust is symmetric, so for instance there may be a node Pj β UNLi
such that Pi /β UNLj . Figure 1 shows an example trust network.
A node that is not crashed and behaves exactly according to the XRP LCP
specification is said to be honest or correct; we use the two terms inter-
changeably. Any node that does not behave according to protocol is said to
be Byzantine. Byzantine behavior can include not responding to messages,
sending incorrect messages, and even sending different messages to differe | [
2908,
110,
1112,
3228,
117,
1142,
3879,
1110,
1167,
3253,
3626,
1114,
1103,
4315,
3879,
1549,
1107,
1103,
1653,
26311,
117,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
121,
119,
123,
22871,
196,
11437,
117,
183,
3361,
198,
119,
1130,
170,
1224,
2457,
3622,
117,
24446,
1377,
1673,
9817,
3084,
2393,
119,
164,
122,
166,
2799,
1115,
1142,
14255,
3309,
118,
189,
1988,
1110,
18238,
119,
1220,
1939,
5996,
1115,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
1191,
1105,
1178,
1191,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
123,
22871,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
119,
1135,
1110,
2276,
1115,
1191,
1103,
1807,
3879,
3486,
1173,
21902,
1105,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
119,
1438,
117,
1103,
14255,
10840,
1110,
1136,
2276,
1112,
1103,
1378,
21133,
2196,
119,
5096,
14572,
122,
119,
1249,
19951,
8377,
3300,
6328,
117,
1160,
7345,
15029,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
1191,
2087,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
119,
1429,
5322,
1115,
123,
22871,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
117,
1133,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
1110,
10802,
2964,
7747,
11437,
851,
186,
1182,
127,
134,
183,
3361,
851,
186,
3361,
119,
4516,
1103,
3879,
3228,
1118,
24446,
1377,
1673,
9817,
3084,
2393,
119,
1110,
6664,
1133,
1136,
3238,
119,
5096,
10008,
1104,
21133,
122,
119,
1284,
1148,
5424,
28117,
3101,
23864,
119,
15463,
8661,
6787,
21902,
3106,
9221,
5430,
1103,
21340,
1197,
149,
1105,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
119,
2421,
156,
1129,
1103,
1383,
1104,
15029,
1107,
7414,
2162,
1182,
1115,
9221,
2913,
149,
119,
1967,
21902,
3106,
9221,
2913,
149,
117,
197,
156,
197,
135,
186,
1182,
119,
1650,
8377,
3300,
6328,
117,
1451,
14372,
1107,
156,
858,
7414,
2162,
3361,
1180,
1136,
1138,
1850,
170,
9221,
1891,
1106,
153,
3361,
1111,
1251,
21340,
1197,
149,
797,
127,
134,
149,
119,
4516,
1122,
28117,
3101,
18117,
1106,
1437,
1115,
197,
156,
858,
7414,
2162,
3361,
197,
135,
183,
3361,
851,
186,
3361,
117,
1290,
1173,
1175,
2834,
1129,
1251,
21340,
1197,
149,
797,
127,
134,
149,
1114,
186,
3361,
1619,
1107,
7414,
2162,
3361,
119,
1650,
1103,
19235,
11066,
117,
1195,
1138,
197,
156,
858,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
197,
156,
165,
7414,
2162,
3361,
197,
135,
197,
156,
197,
851,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
113,
197,
7414,
2162,
1182,
197,
851,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
114,
135,
197,
156,
197,
851,
113,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"80",
"%",
"as",
"suggested",
",",
"this",
"condition",
"is",
"more",
"easily",
"identified",
"with",
"the",
"actual",
"condition",
"given",
"in",
"the",
"white",
"##paper",
",",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"0",
".",
"2",
"##max",
"{",
"ni",
",",
"n",
"##j",
"}",
".",
"In",
"a",
"later",
"independent",
"analysis",
",",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
"[",
"1",
"]",
"showed",
"that",
"this",
"con",
"##di",
"-",
"t",
"##ion",
"is",
"incorrect",
".",
"They",
"instead",
"suggest",
"that",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"if",
"and",
"only",
"if",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"2",
"##max",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
".",
"It",
"is",
"true",
"that",
"if",
"the",
"above",
"condition",
"holds",
"then",
"Pi",
"and",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
".",
"However",
",",
"the",
"con",
"##verse",
"is",
"not",
"true",
"as",
"the",
"following",
"proposition",
"shows",
".",
"Pro",
"##position",
"1",
".",
"As",
"##suming",
"Byzantine",
"account",
"##ability",
",",
"two",
"honest",
"nodes",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
"if",
"##f",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
".",
"11",
"Note",
"that",
"2",
"##max",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
",",
"but",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
"is",
"strictly",
"smaller",
"whenever",
"ni",
"β",
"q",
"##i",
"6",
"=",
"n",
"##j",
"β",
"q",
"##j",
".",
"Thus",
"the",
"condition",
"suggested",
"by",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
"is",
"sufficient",
"but",
"not",
"necessary",
".",
"Pro",
"##of",
"of",
"proposition",
"1",
".",
"We",
"first",
"prove",
"su",
"##ff",
"##iciency",
".",
"Su",
"##pp",
"##ose",
"Pi",
"fully",
"valid",
"##ates",
"the",
"ledge",
"##r",
"L",
"and",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
".",
"Let",
"S",
"be",
"the",
"set",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"valid",
"##ated",
"L",
".",
"Since",
"Pi",
"fully",
"valid",
"##ated",
"L",
",",
"|",
"S",
"|",
">",
"q",
"##i",
".",
"By",
"Byzantine",
"account",
"##ability",
",",
"every",
"node",
"in",
"S",
"β©",
"UN",
"##L",
"##j",
"could",
"not",
"have",
"sent",
"a",
"valid",
"##ation",
"to",
"P",
"##j",
"for",
"any",
"ledge",
"##r",
"L",
"β²",
"6",
"=",
"L",
".",
"Thus",
"it",
"su",
"##ff",
"##ices",
"to",
"show",
"that",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"β",
"q",
"##j",
",",
"since",
"then",
"there",
"cannot",
"be",
"any",
"ledge",
"##r",
"L",
"β²",
"6",
"=",
"L",
"with",
"q",
"##j",
"support",
"in",
"UN",
"##L",
"##j",
".",
"By",
"the",
"overlap",
"hypothesis",
",",
"we",
"have",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"|",
"S",
"\\",
"UN",
"##L",
"##j",
"|",
">",
"|",
"S",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"(",
"|",
"UN",
"##L",
"##i",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
")",
">",
"|",
"S",
"|",
"β",
"(",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")"
] | Analysis of the XRP Ledger Consensus Protocol | 175 |
sume that trust is symmetric, so for instance there may be a node Pj β UNLi
such that Pi /β UNLj . Figure 1 shows an example trust network.
A node that is not crashed and behaves exactly according to the XRP LCP
specification is said to be honest or correct; we use the two terms inter-
changeably. Any node that does not behave according to protocol is said to
be Byzantine. Byzantine behavior can include not responding to messages,
sending incorrect messages, and even sending different messages to differe | [
2908,
110,
1112,
3228,
117,
1142,
3879,
1110,
1167,
3253,
3626,
1114,
1103,
4315,
3879,
1549,
1107,
1103,
1653,
26311,
117,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
121,
119,
123,
22871,
196,
11437,
117,
183,
3361,
198,
119,
1130,
170,
1224,
2457,
3622,
117,
24446,
1377,
1673,
9817,
3084,
2393,
119,
164,
122,
166,
2799,
1115,
1142,
14255,
3309,
118,
189,
1988,
1110,
18238,
119,
1220,
1939,
5996,
1115,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
1191,
1105,
1178,
1191,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
123,
22871,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
119,
1135,
1110,
2276,
1115,
1191,
1103,
1807,
3879,
3486,
1173,
21902,
1105,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
119,
1438,
117,
1103,
14255,
10840,
1110,
1136,
2276,
1112,
1103,
1378,
21133,
2196,
119,
5096,
14572,
122,
119,
1249,
19951,
8377,
3300,
6328,
117,
1160,
7345,
15029,
21902,
117,
153,
3361,
2834,
3106,
9221,
2193,
1472,
21340,
1733,
1114,
1103,
1269,
4954,
1295,
1191,
2087,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
119,
1429,
5322,
1115,
123,
22871,
196,
11437,
851,
186,
1182,
117,
183,
3361,
851,
186,
3361,
198,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
117,
1133,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
1110,
10802,
2964,
7747,
11437,
851,
186,
1182,
127,
134,
183,
3361,
851,
186,
3361,
119,
4516,
1103,
3879,
3228,
1118,
24446,
1377,
1673,
9817,
3084,
2393,
119,
1110,
6664,
1133,
1136,
3238,
119,
5096,
10008,
1104,
21133,
122,
119,
1284,
1148,
5424,
28117,
3101,
23864,
119,
15463,
8661,
6787,
21902,
3106,
9221,
5430,
1103,
21340,
1197,
149,
1105,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
119,
2421,
156,
1129,
1103,
1383,
1104,
15029,
1107,
7414,
2162,
1182,
1115,
9221,
2913,
149,
119,
1967,
21902,
3106,
9221,
2913,
149,
117,
197,
156,
197,
135,
186,
1182,
119,
1650,
8377,
3300,
6328,
117,
1451,
14372,
1107,
156,
858,
7414,
2162,
3361,
1180,
1136,
1138,
1850,
170,
9221,
1891,
1106,
153,
3361,
1111,
1251,
21340,
1197,
149,
797,
127,
134,
149,
119,
4516,
1122,
28117,
3101,
18117,
1106,
1437,
1115,
197,
156,
858,
7414,
2162,
3361,
197,
135,
183,
3361,
851,
186,
3361,
117,
1290,
1173,
1175,
2834,
1129,
1251,
21340,
1197,
149,
797,
127,
134,
149,
1114,
186,
3361,
1619,
1107,
7414,
2162,
3361,
119,
1650,
1103,
19235,
11066,
117,
1195,
1138,
197,
156,
858,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
197,
156,
165,
7414,
2162,
3361,
197,
135,
197,
156,
197,
851,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
113,
197,
7414,
2162,
1182,
197,
851,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
114,
135,
197,
156,
197,
851,
113,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"80",
"%",
"as",
"suggested",
",",
"this",
"condition",
"is",
"more",
"easily",
"identified",
"with",
"the",
"actual",
"condition",
"given",
"in",
"the",
"white",
"##paper",
",",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"0",
".",
"2",
"##max",
"{",
"ni",
",",
"n",
"##j",
"}",
".",
"In",
"a",
"later",
"independent",
"analysis",
",",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
"[",
"1",
"]",
"showed",
"that",
"this",
"con",
"##di",
"-",
"t",
"##ion",
"is",
"incorrect",
".",
"They",
"instead",
"suggest",
"that",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"if",
"and",
"only",
"if",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"2",
"##max",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
".",
"It",
"is",
"true",
"that",
"if",
"the",
"above",
"condition",
"holds",
"then",
"Pi",
"and",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
".",
"However",
",",
"the",
"con",
"##verse",
"is",
"not",
"true",
"as",
"the",
"following",
"proposition",
"shows",
".",
"Pro",
"##position",
"1",
".",
"As",
"##suming",
"Byzantine",
"account",
"##ability",
",",
"two",
"honest",
"nodes",
"Pi",
",",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"different",
"ledge",
"##rs",
"with",
"the",
"same",
"sequence",
"number",
"if",
"##f",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
".",
"11",
"Note",
"that",
"2",
"##max",
"{",
"ni",
"β",
"q",
"##i",
",",
"n",
"##j",
"β",
"q",
"##j",
"}",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
",",
"but",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
"is",
"strictly",
"smaller",
"whenever",
"ni",
"β",
"q",
"##i",
"6",
"=",
"n",
"##j",
"β",
"q",
"##j",
".",
"Thus",
"the",
"condition",
"suggested",
"by",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
"is",
"sufficient",
"but",
"not",
"necessary",
".",
"Pro",
"##of",
"of",
"proposition",
"1",
".",
"We",
"first",
"prove",
"su",
"##ff",
"##iciency",
".",
"Su",
"##pp",
"##ose",
"Pi",
"fully",
"valid",
"##ates",
"the",
"ledge",
"##r",
"L",
"and",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
".",
"Let",
"S",
"be",
"the",
"set",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"valid",
"##ated",
"L",
".",
"Since",
"Pi",
"fully",
"valid",
"##ated",
"L",
",",
"|",
"S",
"|",
">",
"q",
"##i",
".",
"By",
"Byzantine",
"account",
"##ability",
",",
"every",
"node",
"in",
"S",
"β©",
"UN",
"##L",
"##j",
"could",
"not",
"have",
"sent",
"a",
"valid",
"##ation",
"to",
"P",
"##j",
"for",
"any",
"ledge",
"##r",
"L",
"β²",
"6",
"=",
"L",
".",
"Thus",
"it",
"su",
"##ff",
"##ices",
"to",
"show",
"that",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"β",
"q",
"##j",
",",
"since",
"then",
"there",
"cannot",
"be",
"any",
"ledge",
"##r",
"L",
"β²",
"6",
"=",
"L",
"with",
"q",
"##j",
"support",
"in",
"UN",
"##L",
"##j",
".",
"By",
"the",
"overlap",
"hypothesis",
",",
"we",
"have",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"|",
"S",
"\\",
"UN",
"##L",
"##j",
"|",
">",
"|",
"S",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"(",
"|",
"UN",
"##L",
"##i",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
")",
">",
"|",
"S",
"|",
"β",
"(",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")"
] | Analysis of the XRP Ledger Consensus Protocol | 176 |
nt
parties. In section 4, we initially consider a restriction on the adversary called
Byzantine accountability, which states that all nodes β even Byzantine ones
β cannot send different messages to different nodes. This was part of the original
whitepaper [10], which assumed such behavior in a peer-to-peer network could
be identified and corrected by honest nodes. However, due to asynchrony and
the possibility of honest nodes being temporarily partitioned, this assumption
is in practice tenuous at best. T | [
114,
135,
186,
1182,
851,
113,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114,
114,
134,
183,
3361,
851,
186,
3361,
119,
1370,
14176,
117,
1148,
6699,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
127,
183,
3361,
851,
186,
3361,
119,
1599,
1155,
1103,
15029,
1107,
7414,
2162,
1182,
1169,
9221,
2193,
149,
117,
1229,
1155,
1103,
15029,
1107,
7414,
2162,
3361,
165,
7414,
2162,
1182,
9221,
2193,
149,
797,
117,
1105,
1118,
13457,
197,
7414,
2162,
3361,
165,
7414,
2162,
1182,
197,
135,
186,
3361,
1177,
153,
3361,
3106,
9221,
5430,
149,
797,
1229,
21902,
3106,
9221,
5430,
149,
119,
1986,
6699,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
127,
11437,
25532,
186,
1182,
116,
183,
3361,
25532,
186,
3361,
1105,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
135,
183,
3361,
25532,
186,
3361,
119,
1599,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
7414,
2162,
1182,
197,
851,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114,
134,
186,
1182,
116,
186,
3361,
851,
183,
3361,
119,
4516,
1191,
1155,
15029,
1107,
7414,
2162,
1182,
165,
7414,
2162,
3361,
9221,
2193,
149,
1105,
183,
3361,
25532,
4426,
3361,
15029,
1107,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
1145,
9221,
2193,
149,
113,
1134,
1110,
1936,
1290,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
135,
183,
3361,
25532,
4426,
3361,
1118,
13457,
114,
117,
1173,
21902,
1209,
3531,
113,
186,
1182,
116,
186,
3361,
851,
183,
3361,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
134,
186,
1182,
9221,
6006,
1111,
149,
1105,
3106,
9221,
2193,
149,
119,
5459,
117,
1191,
1155,
1103,
1168,
15029,
1107,
7414,
2162,
3361,
9221,
2193,
149,
797,
117,
1173,
1290,
1178,
183,
3361,
851,
186,
3361,
15029,
1107,
7414,
2162,
3361,
9221,
2913,
149,
117,
183,
3361,
851,
113,
183,
3361,
851,
186,
3361,
114,
134,
186,
3361,
15029,
1209,
9221,
2193,
149,
797,
117,
1177,
153,
3361,
1209,
3106,
9221,
2193,
149,
797,
119,
1249,
19951,
170,
186,
11848,
5697,
1104,
2908,
110,
117,
1292,
19235,
2975,
1336,
1129,
25172,
1112,
3226,
131,
794,
17834,
3084,
2393,
119,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
1406,
110,
1103,
4177,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
794,
24446,
1377,
1673,
9817,
3084,
2393,
119,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
3746,
110,
1103,
12477,
8745,
118,
23993,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
1367,
794,
2173,
4746,
3879,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
3746,
110,
1104,
1103,
1903,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
1370,
1103,
6311,
1104,
1103,
2526,
1195,
1209,
1185,
2039,
7568,
8377,
3300,
118,
2912,
119,
1130,
170,
1686,
2443,
117,
1141,
1156,
9353,
7846,
3429,
1897,
1190,
20790,
1113,
9304,
26775,
1119,
26900,
1116,
1115,
5996,
1122,
1110,
9803,
1115,
170,
8377,
14372,
1180,
3952,
21776,
7416,
1106,
1472,
15029
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0
] | [
")",
">",
"q",
"##i",
"β",
"(",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")",
")",
"=",
"n",
"##j",
"β",
"q",
"##j",
".",
"For",
"necessity",
",",
"first",
"suppose",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
"6",
"n",
"##j",
"β",
"q",
"##j",
".",
"Then",
"all",
"the",
"nodes",
"in",
"UN",
"##L",
"##i",
"can",
"valid",
"##ate",
"L",
",",
"while",
"all",
"the",
"nodes",
"in",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"valid",
"##ate",
"L",
"β²",
",",
"and",
"by",
"assumption",
"|",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"|",
">",
"q",
"##j",
"so",
"P",
"##j",
"fully",
"valid",
"##ates",
"L",
"β²",
"while",
"Pi",
"fully",
"valid",
"##ates",
"L",
".",
"Now",
"suppose",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
"6",
"ni",
"##β",
"q",
"##i",
"+",
"n",
"##j",
"##β",
"q",
"##j",
"and",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"##β",
"q",
"##j",
".",
"Then",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"UN",
"##L",
"##i",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##i",
"+",
"q",
"##j",
"β",
"n",
"##j",
".",
"Thus",
"if",
"all",
"nodes",
"in",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"valid",
"##ate",
"L",
"and",
"n",
"##j",
"##β",
"##q",
"##j",
"nodes",
"in",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"also",
"valid",
"##ate",
"L",
"(",
"which",
"is",
"possible",
"since",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"##β",
"##q",
"##j",
"by",
"assumption",
")",
",",
"then",
"Pi",
"will",
"receive",
"(",
"q",
"##i",
"+",
"q",
"##j",
"β",
"n",
"##j",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##i",
"valid",
"##ations",
"for",
"L",
"and",
"fully",
"valid",
"##ate",
"L",
".",
"Meanwhile",
",",
"if",
"all",
"the",
"other",
"nodes",
"in",
"UN",
"##L",
"##j",
"valid",
"##ate",
"L",
"β²",
",",
"then",
"since",
"only",
"n",
"##j",
"β",
"q",
"##j",
"nodes",
"in",
"UN",
"##L",
"##j",
"valid",
"##ated",
"L",
",",
"n",
"##j",
"β",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##j",
"nodes",
"will",
"valid",
"##ate",
"L",
"β²",
",",
"so",
"P",
"##j",
"will",
"fully",
"valid",
"##ate",
"L",
"β²",
".",
"As",
"##suming",
"a",
"q",
"##uo",
"##rum",
"of",
"80",
"%",
",",
"these",
"overlap",
"conditions",
"may",
"be",
"summarized",
"as",
"follows",
":",
"β’",
"Schwartz",
"et",
"al",
".",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"20",
"%",
"the",
"maximum",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"β’",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"41",
"%",
"the",
"ma",
"##xi",
"-",
"mum",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"12",
"β’",
"Act",
"##ual",
"condition",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"41",
"%",
"of",
"the",
"average",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"For",
"the",
"remainder",
"of",
"the",
"paper",
"we",
"will",
"no",
"longer",
"assume",
"Byzantine",
"account",
"-",
"ability",
".",
"In",
"a",
"live",
"network",
",",
"one",
"would",
"prefer",
"absolute",
"safety",
"rather",
"than",
"relying",
"on",
"br",
"##ittle",
"he",
"##uristic",
"##s",
"that",
"suggest",
"it",
"is",
"unlikely",
"that",
"a",
"Byzantine",
"node",
"could",
"send",
"conflicting",
"messages",
"to",
"different",
"nodes"
] | Analysis of the XRP Ledger Consensus Protocol | 177 |
nt
parties. In section 4, we initially consider a restriction on the adversary called
Byzantine accountability, which states that all nodes β even Byzantine ones
β cannot send different messages to different nodes. This was part of the original
whitepaper [10], which assumed such behavior in a peer-to-peer network could
be identified and corrected by honest nodes. However, due to asynchrony and
the possibility of honest nodes being temporarily partitioned, this assumption
is in practice tenuous at best. T | [
114,
135,
186,
1182,
851,
113,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114,
114,
134,
183,
3361,
851,
186,
3361,
119,
1370,
14176,
117,
1148,
6699,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
127,
183,
3361,
851,
186,
3361,
119,
1599,
1155,
1103,
15029,
1107,
7414,
2162,
1182,
1169,
9221,
2193,
149,
117,
1229,
1155,
1103,
15029,
1107,
7414,
2162,
3361,
165,
7414,
2162,
1182,
9221,
2193,
149,
797,
117,
1105,
1118,
13457,
197,
7414,
2162,
3361,
165,
7414,
2162,
1182,
197,
135,
186,
3361,
1177,
153,
3361,
3106,
9221,
5430,
149,
797,
1229,
21902,
3106,
9221,
5430,
149,
119,
1986,
6699,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
127,
11437,
25532,
186,
1182,
116,
183,
3361,
25532,
186,
3361,
1105,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
135,
183,
3361,
25532,
186,
3361,
119,
1599,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
7414,
2162,
1182,
197,
851,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
135,
11437,
851,
113,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
114,
134,
186,
1182,
116,
186,
3361,
851,
183,
3361,
119,
4516,
1191,
1155,
15029,
1107,
7414,
2162,
1182,
165,
7414,
2162,
3361,
9221,
2193,
149,
1105,
183,
3361,
25532,
4426,
3361,
15029,
1107,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
1145,
9221,
2193,
149,
113,
1134,
1110,
1936,
1290,
197,
7414,
2162,
1182,
28752,
27370,
2162,
3361,
197,
135,
183,
3361,
25532,
4426,
3361,
1118,
13457,
114,
117,
1173,
21902,
1209,
3531,
113,
186,
1182,
116,
186,
3361,
851,
183,
3361,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
134,
186,
1182,
9221,
6006,
1111,
149,
1105,
3106,
9221,
2193,
149,
119,
5459,
117,
1191,
1155,
1103,
1168,
15029,
1107,
7414,
2162,
3361,
9221,
2193,
149,
797,
117,
1173,
1290,
1178,
183,
3361,
851,
186,
3361,
15029,
1107,
7414,
2162,
3361,
9221,
2913,
149,
117,
183,
3361,
851,
113,
183,
3361,
851,
186,
3361,
114,
134,
186,
3361,
15029,
1209,
9221,
2193,
149,
797,
117,
1177,
153,
3361,
1209,
3106,
9221,
2193,
149,
797,
119,
1249,
19951,
170,
186,
11848,
5697,
1104,
2908,
110,
117,
1292,
19235,
2975,
1336,
1129,
25172,
1112,
3226,
131,
794,
17834,
3084,
2393,
119,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
1406,
110,
1103,
4177,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
794,
24446,
1377,
1673,
9817,
3084,
2393,
119,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
3746,
110,
1103,
12477,
8745,
118,
23993,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
1367,
794,
2173,
4746,
3879,
131,
4081,
3111,
1104,
15029,
2993,
1126,
19235,
1104,
3746,
110,
1104,
1103,
1903,
2060,
1104,
1147,
7514,
7414,
2162,
1116,
119,
1370,
1103,
6311,
1104,
1103,
2526,
1195,
1209,
1185,
2039,
7568,
8377,
3300,
118,
2912,
119,
1130,
170,
1686,
2443,
117,
1141,
1156,
9353,
7846,
3429,
1897,
1190,
20790,
1113,
9304,
26775,
1119,
26900,
1116,
1115,
5996,
1122,
1110,
9803,
1115,
170,
8377,
14372,
1180,
3952,
21776,
7416,
1106,
1472,
15029
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
")",
">",
"q",
"##i",
"β",
"(",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")",
")",
"=",
"n",
"##j",
"β",
"q",
"##j",
".",
"For",
"necessity",
",",
"first",
"suppose",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
"6",
"n",
"##j",
"β",
"q",
"##j",
".",
"Then",
"all",
"the",
"nodes",
"in",
"UN",
"##L",
"##i",
"can",
"valid",
"##ate",
"L",
",",
"while",
"all",
"the",
"nodes",
"in",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"valid",
"##ate",
"L",
"β²",
",",
"and",
"by",
"assumption",
"|",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"|",
">",
"q",
"##j",
"so",
"P",
"##j",
"fully",
"valid",
"##ates",
"L",
"β²",
"while",
"Pi",
"fully",
"valid",
"##ates",
"L",
".",
"Now",
"suppose",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
"6",
"ni",
"##β",
"q",
"##i",
"+",
"n",
"##j",
"##β",
"q",
"##j",
"and",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"##β",
"q",
"##j",
".",
"Then",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"UN",
"##L",
"##i",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
">",
"ni",
"β",
"(",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##i",
"+",
"q",
"##j",
"β",
"n",
"##j",
".",
"Thus",
"if",
"all",
"nodes",
"in",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"valid",
"##ate",
"L",
"and",
"n",
"##j",
"##β",
"##q",
"##j",
"nodes",
"in",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"also",
"valid",
"##ate",
"L",
"(",
"which",
"is",
"possible",
"since",
"|",
"UN",
"##L",
"##i",
"##β©",
"##UN",
"##L",
"##j",
"|",
">",
"n",
"##j",
"##β",
"##q",
"##j",
"by",
"assumption",
")",
",",
"then",
"Pi",
"will",
"receive",
"(",
"q",
"##i",
"+",
"q",
"##j",
"β",
"n",
"##j",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##i",
"valid",
"##ations",
"for",
"L",
"and",
"fully",
"valid",
"##ate",
"L",
".",
"Meanwhile",
",",
"if",
"all",
"the",
"other",
"nodes",
"in",
"UN",
"##L",
"##j",
"valid",
"##ate",
"L",
"β²",
",",
"then",
"since",
"only",
"n",
"##j",
"β",
"q",
"##j",
"nodes",
"in",
"UN",
"##L",
"##j",
"valid",
"##ated",
"L",
",",
"n",
"##j",
"β",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"=",
"q",
"##j",
"nodes",
"will",
"valid",
"##ate",
"L",
"β²",
",",
"so",
"P",
"##j",
"will",
"fully",
"valid",
"##ate",
"L",
"β²",
".",
"As",
"##suming",
"a",
"q",
"##uo",
"##rum",
"of",
"80",
"%",
",",
"these",
"overlap",
"conditions",
"may",
"be",
"summarized",
"as",
"follows",
":",
"β’",
"Schwartz",
"et",
"al",
".",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"20",
"%",
"the",
"maximum",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"β’",
"Arm",
"##k",
"##ne",
"##cht",
"et",
"al",
".",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"41",
"%",
"the",
"ma",
"##xi",
"-",
"mum",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"12",
"β’",
"Act",
"##ual",
"condition",
":",
"Every",
"pair",
"of",
"nodes",
"needs",
"an",
"overlap",
"of",
"41",
"%",
"of",
"the",
"average",
"size",
"of",
"their",
"respective",
"UN",
"##L",
"##s",
".",
"For",
"the",
"remainder",
"of",
"the",
"paper",
"we",
"will",
"no",
"longer",
"assume",
"Byzantine",
"account",
"-",
"ability",
".",
"In",
"a",
"live",
"network",
",",
"one",
"would",
"prefer",
"absolute",
"safety",
"rather",
"than",
"relying",
"on",
"br",
"##ittle",
"he",
"##uristic",
"##s",
"that",
"suggest",
"it",
"is",
"unlikely",
"that",
"a",
"Byzantine",
"node",
"could",
"send",
"conflicting",
"messages",
"to",
"different",
"nodes"
] | Analysis of the XRP Ledger Consensus Protocol | 178 |
hus the bulk of our results do not depend on
this assumption and we will clearly state when it is assumed.
For any node Pi, we denote ni = |UNLi| and define the quorum, denoted
qi, a parameter which roughly specifies the minimum number of agreeing nodes
in UNLi that Pi needs to hear from to commit to a decision. Each node sets qi
to be 80% of its UNL size, or, more exactly, qi = β0.8niβ. We assume at most
ti 6 ni β qi nodes in UNLi may be Byzantine faulty.
Let L represent a ledger, which is the shared s | [
1443,
2033,
2347,
119,
4516,
1195,
2812,
1103,
1844,
6765,
1105,
7568,
1115,
8377,
15029,
1169,
3952,
16439,
7416,
1106,
16439,
15029,
119,
1370,
1251,
3111,
1104,
15029,
21902,
1105,
153,
3361,
117,
1519,
152,
1182,
117,
179,
134,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
1105,
1519,
189,
1182,
117,
179,
134,
11241,
196,
189,
1182,
117,
189,
3361,
117,
152,
1182,
117,
179,
198,
119,
189,
1182,
117,
179,
1110,
1103,
4177,
1295,
1104,
2148,
8377,
21688,
1107,
7414,
2162,
1182,
858,
27370,
2162,
3361,
117,
11577,
1115,
1175,
1132,
1120,
1211,
189,
1182,
21688,
1107,
7414,
2162,
1182,
1105,
1120,
1211,
189,
3361,
21688,
1107,
7414,
2162,
3361,
119,
1109,
1378,
5837,
12917,
1209,
1129,
5616,
2032,
1103,
2526,
119,
3180,
12917,
123,
119,
1409,
1126,
7345,
14372,
21902,
5302,
182,
9221,
6006,
1111,
1103,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
117,
1173,
1111,
1251,
1168,
7345,
14372,
153,
3361,
117,
1175,
1132,
1120,
1655,
152,
1182,
117,
179,
116,
182,
25532,
2605,
25532,
3121,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
9221,
2913,
149,
119,
7282,
117,
1175,
1169,
1129,
2839,
152,
1182,
117,
179,
116,
182,
25532,
11437,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
9221,
2913,
149,
119,
3291,
10747,
3113,
124,
119,
1409,
1126,
7345,
14372,
21902,
5302,
182,
9221,
6006,
1111,
1103,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
117,
1173,
153,
3361,
1169,
1267,
1120,
1211,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
134,
188,
119,
7282,
117,
1122,
1110,
1936,
1111,
153,
3361,
1106,
1267,
2839,
11437,
116,
183,
3361,
851,
2346,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1114,
4954,
1295,
188,
119,
5096,
10008,
119,
1409,
1126,
7345,
14372,
9221,
5430,
149,
117,
1173,
153,
3361,
2834,
3531,
170,
9221,
1891,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1121,
1122,
119,
1650,
5837,
12917,
123,
117,
1175,
1132,
1120,
1655,
152,
1182,
117,
179,
116,
182,
25532,
2605,
25532,
3121,
117,
179,
7345,
15029,
1115,
9221,
2193,
149,
119,
1409,
1451,
1168,
14372,
1107,
7414,
2162,
3361,
10130,
170,
9221,
1891,
1106,
153,
3361,
1111,
1199,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
117,
1173,
153,
3361,
1169,
3531,
1146,
1106,
113,
1105,
1259,
117,
1118,
1103,
3718,
13620,
1104,
5837,
12917,
123,
114,
183,
3361,
851,
113,
152,
1182,
117,
179,
116,
182,
25532,
11437,
851,
189,
1182,
117,
179,
114,
134,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
134,
188,
119,
5322,
1115,
1884,
10747,
3113,
124,
1674,
1136,
3073,
1665,
12906,
1103,
5417,
1115,
153,
3361,
1209,
1267,
1167
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"without",
"getting",
"caught",
".",
"Thus",
"we",
"follow",
"the",
"research",
"convention",
"and",
"assume",
"that",
"Byzantine",
"nodes",
"can",
"send",
"arbitrary",
"messages",
"to",
"arbitrary",
"nodes",
".",
"For",
"any",
"pair",
"of",
"nodes",
"Pi",
"and",
"P",
"##j",
",",
"let",
"O",
"##i",
",",
"j",
"=",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
"and",
"let",
"t",
"##i",
",",
"j",
"=",
"min",
"{",
"t",
"##i",
",",
"t",
"##j",
",",
"O",
"##i",
",",
"j",
"}",
".",
"t",
"##i",
",",
"j",
"is",
"the",
"maximum",
"number",
"of",
"allowed",
"Byzantine",
"faults",
"in",
"UN",
"##L",
"##i",
"β©",
"##UN",
"##L",
"##j",
",",
"assuming",
"that",
"there",
"are",
"at",
"most",
"t",
"##i",
"faults",
"in",
"UN",
"##L",
"##i",
"and",
"at",
"most",
"t",
"##j",
"faults",
"in",
"UN",
"##L",
"##j",
".",
"The",
"following",
"le",
"##mma",
"will",
"be",
"useful",
"throughout",
"the",
"paper",
".",
"Le",
"##mma",
"2",
".",
"If",
"an",
"honest",
"node",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
",",
"then",
"for",
"any",
"other",
"honest",
"node",
"P",
"##j",
",",
"there",
"are",
"at",
"least",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"##ni",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"valid",
"##ated",
"L",
".",
"Furthermore",
",",
"there",
"can",
"be",
"exactly",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"ni",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"valid",
"##ated",
"L",
".",
"Co",
"##roll",
"##ary",
"3",
".",
"If",
"an",
"honest",
"node",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
",",
"then",
"P",
"##j",
"can",
"see",
"at",
"most",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
"=",
"s",
".",
"Furthermore",
",",
"it",
"is",
"possible",
"for",
"P",
"##j",
"to",
"see",
"exactly",
"ni",
"+",
"n",
"##j",
"β",
"##O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"with",
"sequence",
"number",
"s",
".",
"Pro",
"##of",
".",
"If",
"an",
"honest",
"node",
"valid",
"##ates",
"L",
",",
"then",
"P",
"##j",
"cannot",
"receive",
"a",
"valid",
"##ation",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"from",
"it",
".",
"By",
"le",
"##mma",
"2",
",",
"there",
"are",
"at",
"least",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"##ni",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"that",
"valid",
"##ate",
"L",
".",
"If",
"every",
"other",
"node",
"in",
"UN",
"##L",
"##j",
"sends",
"a",
"valid",
"##ation",
"to",
"P",
"##j",
"for",
"some",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
",",
"then",
"P",
"##j",
"can",
"receive",
"up",
"to",
"(",
"and",
"including",
",",
"by",
"the",
"secondary",
"clause",
"of",
"le",
"##mma",
"2",
")",
"n",
"##j",
"β",
"(",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"ni",
"β",
"t",
"##i",
",",
"j",
")",
"=",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
"=",
"s",
".",
"Note",
"that",
"co",
"##roll",
"##ary",
"3",
"does",
"not",
"pre",
"##c",
"##lude",
"the",
"possibility",
"that",
"P",
"##j",
"will",
"see",
"more"
] | Analysis of the XRP Ledger Consensus Protocol | 179 |
hus the bulk of our results do not depend on
this assumption and we will clearly state when it is assumed.
For any node Pi, we denote ni = |UNLi| and define the quorum, denoted
qi, a parameter which roughly specifies the minimum number of agreeing nodes
in UNLi that Pi needs to hear from to commit to a decision. Each node sets qi
to be 80% of its UNL size, or, more exactly, qi = β0.8niβ. We assume at most
ti 6 ni β qi nodes in UNLi may be Byzantine faulty.
Let L represent a ledger, which is the shared s | [
1443,
2033,
2347,
119,
4516,
1195,
2812,
1103,
1844,
6765,
1105,
7568,
1115,
8377,
15029,
1169,
3952,
16439,
7416,
1106,
16439,
15029,
119,
1370,
1251,
3111,
1104,
15029,
21902,
1105,
153,
3361,
117,
1519,
152,
1182,
117,
179,
134,
197,
7414,
2162,
1182,
858,
7414,
2162,
3361,
197,
1105,
1519,
189,
1182,
117,
179,
134,
11241,
196,
189,
1182,
117,
189,
3361,
117,
152,
1182,
117,
179,
198,
119,
189,
1182,
117,
179,
1110,
1103,
4177,
1295,
1104,
2148,
8377,
21688,
1107,
7414,
2162,
1182,
858,
27370,
2162,
3361,
117,
11577,
1115,
1175,
1132,
1120,
1211,
189,
1182,
21688,
1107,
7414,
2162,
1182,
1105,
1120,
1211,
189,
3361,
21688,
1107,
7414,
2162,
3361,
119,
1109,
1378,
5837,
12917,
1209,
1129,
5616,
2032,
1103,
2526,
119,
3180,
12917,
123,
119,
1409,
1126,
7345,
14372,
21902,
5302,
182,
9221,
6006,
1111,
1103,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
117,
1173,
1111,
1251,
1168,
7345,
14372,
153,
3361,
117,
1175,
1132,
1120,
1655,
152,
1182,
117,
179,
116,
182,
25532,
2605,
25532,
3121,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
9221,
2913,
149,
119,
7282,
117,
1175,
1169,
1129,
2839,
152,
1182,
117,
179,
116,
182,
25532,
11437,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
9221,
2913,
149,
119,
3291,
10747,
3113,
124,
119,
1409,
1126,
7345,
14372,
21902,
5302,
182,
9221,
6006,
1111,
1103,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
117,
1173,
153,
3361,
1169,
1267,
1120,
1211,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
134,
188,
119,
7282,
117,
1122,
1110,
1936,
1111,
153,
3361,
1106,
1267,
2839,
11437,
116,
183,
3361,
851,
2346,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1114,
4954,
1295,
188,
119,
5096,
10008,
119,
1409,
1126,
7345,
14372,
9221,
5430,
149,
117,
1173,
153,
3361,
2834,
3531,
170,
9221,
1891,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
1121,
1122,
119,
1650,
5837,
12917,
123,
117,
1175,
1132,
1120,
1655,
152,
1182,
117,
179,
116,
182,
25532,
2605,
25532,
3121,
117,
179,
7345,
15029,
1115,
9221,
2193,
149,
119,
1409,
1451,
1168,
14372,
1107,
7414,
2162,
3361,
10130,
170,
9221,
1891,
1106,
153,
3361,
1111,
1199,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
117,
1173,
153,
3361,
1169,
3531,
1146,
1106,
113,
1105,
1259,
117,
1118,
1103,
3718,
13620,
1104,
5837,
12917,
123,
114,
183,
3361,
851,
113,
152,
1182,
117,
179,
116,
182,
25532,
11437,
851,
189,
1182,
117,
179,
114,
134,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
134,
188,
119,
5322,
1115,
1884,
10747,
3113,
124,
1674,
1136,
3073,
1665,
12906,
1103,
5417,
1115,
153,
3361,
1209,
1267,
1167
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"without",
"getting",
"caught",
".",
"Thus",
"we",
"follow",
"the",
"research",
"convention",
"and",
"assume",
"that",
"Byzantine",
"nodes",
"can",
"send",
"arbitrary",
"messages",
"to",
"arbitrary",
"nodes",
".",
"For",
"any",
"pair",
"of",
"nodes",
"Pi",
"and",
"P",
"##j",
",",
"let",
"O",
"##i",
",",
"j",
"=",
"|",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"|",
"and",
"let",
"t",
"##i",
",",
"j",
"=",
"min",
"{",
"t",
"##i",
",",
"t",
"##j",
",",
"O",
"##i",
",",
"j",
"}",
".",
"t",
"##i",
",",
"j",
"is",
"the",
"maximum",
"number",
"of",
"allowed",
"Byzantine",
"faults",
"in",
"UN",
"##L",
"##i",
"β©",
"##UN",
"##L",
"##j",
",",
"assuming",
"that",
"there",
"are",
"at",
"most",
"t",
"##i",
"faults",
"in",
"UN",
"##L",
"##i",
"and",
"at",
"most",
"t",
"##j",
"faults",
"in",
"UN",
"##L",
"##j",
".",
"The",
"following",
"le",
"##mma",
"will",
"be",
"useful",
"throughout",
"the",
"paper",
".",
"Le",
"##mma",
"2",
".",
"If",
"an",
"honest",
"node",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
",",
"then",
"for",
"any",
"other",
"honest",
"node",
"P",
"##j",
",",
"there",
"are",
"at",
"least",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"##ni",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"valid",
"##ated",
"L",
".",
"Furthermore",
",",
"there",
"can",
"be",
"exactly",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"ni",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"valid",
"##ated",
"L",
".",
"Co",
"##roll",
"##ary",
"3",
".",
"If",
"an",
"honest",
"node",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"the",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
",",
"then",
"P",
"##j",
"can",
"see",
"at",
"most",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
"=",
"s",
".",
"Furthermore",
",",
"it",
"is",
"possible",
"for",
"P",
"##j",
"to",
"see",
"exactly",
"ni",
"+",
"n",
"##j",
"β",
"##O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"with",
"sequence",
"number",
"s",
".",
"Pro",
"##of",
".",
"If",
"an",
"honest",
"node",
"valid",
"##ates",
"L",
",",
"then",
"P",
"##j",
"cannot",
"receive",
"a",
"valid",
"##ation",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
"from",
"it",
".",
"By",
"le",
"##mma",
"2",
",",
"there",
"are",
"at",
"least",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"##ni",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"that",
"valid",
"##ate",
"L",
".",
"If",
"every",
"other",
"node",
"in",
"UN",
"##L",
"##j",
"sends",
"a",
"valid",
"##ation",
"to",
"P",
"##j",
"for",
"some",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
",",
"then",
"P",
"##j",
"can",
"receive",
"up",
"to",
"(",
"and",
"including",
",",
"by",
"the",
"secondary",
"clause",
"of",
"le",
"##mma",
"2",
")",
"n",
"##j",
"β",
"(",
"O",
"##i",
",",
"j",
"+",
"m",
"##β",
"ni",
"β",
"t",
"##i",
",",
"j",
")",
"=",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
"=",
"s",
".",
"Note",
"that",
"co",
"##roll",
"##ary",
"3",
"does",
"not",
"pre",
"##c",
"##lude",
"the",
"possibility",
"that",
"P",
"##j",
"will",
"see",
"more"
] | Analysis of the XRP Ledger Consensus Protocol | 180 |
tate of the system and includes
account settings, balances, order books, etc. Two ledgers L,Lβ² are the same if
they represent the same ordered history of transactions starting from the unique
genesis ledger. Each ledger also has sequence number seq(L) that is one greater
than its parent ledger's sequence number. The genesis ledger has seq(L) = 1.
A ledger L is created by applying a sequence of transactions T = [x0, x1, . . .]
to its parent parent(L) according to the protocol rules. Two ledgers may have
th | [
1190,
11437,
116,
183,
3361,
25532,
2346,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
170,
2610,
4954,
1295,
1190,
188,
119,
10364,
117,
1443,
11577,
1703,
1785,
117,
1122,
3587,
1149,
1115,
1216,
1126,
15299,
1110,
1936,
117,
1134,
2088,
1103,
9932,
1106,
1329,
1277,
12567,
3429,
18717,
119,
5096,
10008,
1104,
5837,
12917,
123,
119,
1109,
6777,
1110,
1861,
1106,
1103,
6777,
1104,
21133,
122,
119,
15463,
8661,
6787,
21902,
5302,
182,
9221,
6006,
1111,
149,
119,
5630,
5074,
156,
1129,
1103,
1383,
1104,
15029,
1107,
7414,
2162,
1182,
1115,
1850,
9221,
6006,
1106,
21902,
1111,
149,
117,
1173,
197,
156,
858,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
197,
156,
165,
7414,
2162,
3361,
197,
135,
197,
156,
197,
851,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
113,
11437,
851,
152,
1182,
117,
179,
114,
134,
182,
25532,
11437,
116,
152,
1182,
117,
179,
119,
1492,
1247,
1180,
1129,
189,
1182,
117,
179,
8377,
15029,
1107,
156,
858,
7414,
2162,
3361,
1115,
3952,
153,
3361,
170,
9221,
1891,
1111,
1380,
1168,
1190,
149,
117,
1177,
1120,
1655,
182,
25532,
2605,
116,
152,
1182,
117,
179,
25532,
3121,
117,
179,
7345,
15029,
9221,
2913,
149,
119,
1370,
1103,
1248,
1553,
117,
7568,
1115,
1451,
14372,
1107,
7414,
2162,
1182,
165,
7414,
2162,
3361,
9221,
5430,
149,
117,
189,
1182,
117,
179,
8377,
15029,
1107,
7414,
2162,
1182,
858,
27370,
2162,
3361,
3952,
170,
9221,
1891,
1111,
149,
1106,
21902,
1105,
149,
797,
1106,
153,
3361,
119,
1599,
1175,
1132,
2839,
182,
851,
11437,
116,
152,
1182,
117,
179,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
1182,
858,
7414,
2162,
3361,
1115,
3952,
170,
9221,
1891,
1111,
149,
1106,
153,
3361,
119,
1967,
1451,
14372,
1107,
7414,
2162,
3361,
165,
7414,
2162,
1182,
1169,
9221,
2193,
1199,
21340,
1197,
1168,
1190,
149,
117,
1175,
1169,
1129,
2839,
182,
25532,
2605,
116,
152,
1182,
117,
179,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
3952,
170,
9221,
1891,
1111,
149,
1106,
153,
3361,
119,
5096,
14572,
125,
119,
21902,
3106,
9221,
3798,
1199,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
12942,
1115,
153,
3361,
2834,
3106,
9221,
2193,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
1103,
1269,
4954,
1295,
188,
1191,
2087,
152,
1182,
117,
179,
135,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
119,
5096,
10008,
119,
1650,
5074,
182,
134,
186,
1182,
117,
1884,
10747,
3113,
124,
3301,
1366,
1115,
21902,
3106,
9221,
3798,
149,
12942,
1115,
153,
3361,
1169,
1267,
1120,
1211,
11437,
116,
183,
3361,
25532,
2346,
1182,
117,
179,
25532,
17276,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
4954,
1295,
188,
119,
4516,
1191,
186,
3361,
135,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
186,
1182,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"than",
"ni",
"+",
"n",
"##j",
"##β",
"##O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"a",
"larger",
"sequence",
"number",
"than",
"s",
".",
"Indeed",
",",
"without",
"assuming",
"total",
"##ity",
",",
"it",
"turns",
"out",
"that",
"such",
"an",
"occurrence",
"is",
"possible",
",",
"which",
"forces",
"the",
"algorithm",
"to",
"use",
"much",
"tighter",
"safety",
"margins",
".",
"Pro",
"##of",
"of",
"le",
"##mma",
"2",
".",
"The",
"proof",
"is",
"similar",
"to",
"the",
"proof",
"of",
"proposition",
"1",
".",
"Su",
"##pp",
"##ose",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"L",
".",
"Again",
"letting",
"S",
"be",
"the",
"set",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"sent",
"valid",
"##ations",
"to",
"Pi",
"for",
"L",
",",
"then",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"|",
"S",
"\\",
"UN",
"##L",
"##j",
"|",
">",
"|",
"S",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"(",
"ni",
"β",
"O",
"##i",
",",
"j",
")",
"=",
"m",
"##β",
"ni",
"+",
"O",
"##i",
",",
"j",
".",
"13",
"There",
"could",
"be",
"t",
"##i",
",",
"j",
"Byzantine",
"nodes",
"in",
"S",
"β©",
"UN",
"##L",
"##j",
"that",
"send",
"P",
"##j",
"a",
"valid",
"##ation",
"for",
"something",
"other",
"than",
"L",
",",
"so",
"at",
"least",
"m",
"##β",
"##ni",
"+",
"O",
"##i",
",",
"j",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"valid",
"##ated",
"L",
".",
"For",
"the",
"second",
"point",
",",
"assume",
"that",
"every",
"node",
"in",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"valid",
"##ates",
"L",
",",
"t",
"##i",
",",
"j",
"Byzantine",
"nodes",
"in",
"UN",
"##L",
"##i",
"β©",
"##UN",
"##L",
"##j",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"Pi",
"and",
"L",
"β²",
"to",
"P",
"##j",
".",
"Then",
"there",
"are",
"exactly",
"m",
"β",
"ni",
"+",
"O",
"##i",
",",
"j",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"that",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"P",
"##j",
".",
"Since",
"every",
"node",
"in",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"can",
"valid",
"##ate",
"some",
"ledge",
"##r",
"other",
"than",
"L",
",",
"there",
"can",
"be",
"exactly",
"m",
"##β",
"##ni",
"+",
"O",
"##i",
",",
"j",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"P",
"##j",
".",
"Pro",
"##position",
"4",
".",
"Pi",
"fully",
"valid",
"##ating",
"some",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
"implies",
"that",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"the",
"same",
"sequence",
"number",
"s",
"if",
"##f",
"O",
"##i",
",",
"j",
">",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
".",
"Pro",
"##of",
".",
"By",
"letting",
"m",
"=",
"q",
"##i",
",",
"co",
"##roll",
"##ary",
"3",
"tells",
"us",
"that",
"Pi",
"fully",
"valid",
"##ating",
"L",
"implies",
"that",
"P",
"##j",
"can",
"see",
"at",
"most",
"ni",
"+",
"n",
"##j",
"##β",
"##O",
"##i",
",",
"j",
"##β",
"##qi",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"sequence",
"number",
"s",
".",
"Thus",
"if",
"q",
"##j",
">",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"q",
"##i",
"+"
] | Analysis of the XRP Ledger Consensus Protocol | 181 |
tate of the system and includes
account settings, balances, order books, etc. Two ledgers L,Lβ² are the same if
they represent the same ordered history of transactions starting from the unique
genesis ledger. Each ledger also has sequence number seq(L) that is one greater
than its parent ledger's sequence number. The genesis ledger has seq(L) = 1.
A ledger L is created by applying a sequence of transactions T = [x0, x1, . . .]
to its parent parent(L) according to the protocol rules. Two ledgers may have
th | [
1190,
11437,
116,
183,
3361,
25532,
2346,
1182,
117,
179,
851,
1306,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
170,
2610,
4954,
1295,
1190,
188,
119,
10364,
117,
1443,
11577,
1703,
1785,
117,
1122,
3587,
1149,
1115,
1216,
1126,
15299,
1110,
1936,
117,
1134,
2088,
1103,
9932,
1106,
1329,
1277,
12567,
3429,
18717,
119,
5096,
10008,
1104,
5837,
12917,
123,
119,
1109,
6777,
1110,
1861,
1106,
1103,
6777,
1104,
21133,
122,
119,
15463,
8661,
6787,
21902,
5302,
182,
9221,
6006,
1111,
149,
119,
5630,
5074,
156,
1129,
1103,
1383,
1104,
15029,
1107,
7414,
2162,
1182,
1115,
1850,
9221,
6006,
1106,
21902,
1111,
149,
117,
1173,
197,
156,
858,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
197,
156,
165,
7414,
2162,
3361,
197,
135,
197,
156,
197,
851,
197,
7414,
2162,
1182,
165,
7414,
2162,
3361,
197,
134,
197,
156,
197,
851,
113,
11437,
851,
152,
1182,
117,
179,
114,
134,
182,
25532,
11437,
116,
152,
1182,
117,
179,
119,
1492,
1247,
1180,
1129,
189,
1182,
117,
179,
8377,
15029,
1107,
156,
858,
7414,
2162,
3361,
1115,
3952,
153,
3361,
170,
9221,
1891,
1111,
1380,
1168,
1190,
149,
117,
1177,
1120,
1655,
182,
25532,
2605,
116,
152,
1182,
117,
179,
25532,
3121,
117,
179,
7345,
15029,
9221,
2913,
149,
119,
1370,
1103,
1248,
1553,
117,
7568,
1115,
1451,
14372,
1107,
7414,
2162,
1182,
165,
7414,
2162,
3361,
9221,
5430,
149,
117,
189,
1182,
117,
179,
8377,
15029,
1107,
7414,
2162,
1182,
858,
27370,
2162,
3361,
3952,
170,
9221,
1891,
1111,
149,
1106,
21902,
1105,
149,
797,
1106,
153,
3361,
119,
1599,
1175,
1132,
2839,
182,
851,
11437,
116,
152,
1182,
117,
179,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
1182,
858,
7414,
2162,
3361,
1115,
3952,
170,
9221,
1891,
1111,
149,
1106,
153,
3361,
119,
1967,
1451,
14372,
1107,
7414,
2162,
3361,
165,
7414,
2162,
1182,
1169,
9221,
2193,
1199,
21340,
1197,
1168,
1190,
149,
117,
1175,
1169,
1129,
2839,
182,
25532,
2605,
116,
152,
1182,
117,
179,
851,
189,
1182,
117,
179,
7345,
15029,
1107,
7414,
2162,
3361,
1115,
3952,
170,
9221,
1891,
1111,
149,
1106,
153,
3361,
119,
5096,
14572,
125,
119,
21902,
3106,
9221,
3798,
1199,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
12942,
1115,
153,
3361,
2834,
3106,
9221,
2193,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
1103,
1269,
4954,
1295,
188,
1191,
2087,
152,
1182,
117,
179,
135,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
119,
5096,
10008,
119,
1650,
5074,
182,
134,
186,
1182,
117,
1884,
10747,
3113,
124,
3301,
1366,
1115,
21902,
3106,
9221,
3798,
149,
12942,
1115,
153,
3361,
1169,
1267,
1120,
1211,
11437,
116,
183,
3361,
25532,
2346,
1182,
117,
179,
25532,
17276,
116,
189,
1182,
117,
179,
9221,
6006,
1111,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
4954,
1295,
188,
119,
4516,
1191,
186,
3361,
135,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
186,
1182,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"than",
"ni",
"+",
"n",
"##j",
"##β",
"##O",
"##i",
",",
"j",
"β",
"##m",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"a",
"larger",
"sequence",
"number",
"than",
"s",
".",
"Indeed",
",",
"without",
"assuming",
"total",
"##ity",
",",
"it",
"turns",
"out",
"that",
"such",
"an",
"occurrence",
"is",
"possible",
",",
"which",
"forces",
"the",
"algorithm",
"to",
"use",
"much",
"tighter",
"safety",
"margins",
".",
"Pro",
"##of",
"of",
"le",
"##mma",
"2",
".",
"The",
"proof",
"is",
"similar",
"to",
"the",
"proof",
"of",
"proposition",
"1",
".",
"Su",
"##pp",
"##ose",
"Pi",
"sees",
"m",
"valid",
"##ations",
"for",
"L",
".",
"Again",
"letting",
"S",
"be",
"the",
"set",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"sent",
"valid",
"##ations",
"to",
"Pi",
"for",
"L",
",",
"then",
"|",
"S",
"β©",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"|",
"S",
"\\",
"UN",
"##L",
"##j",
"|",
">",
"|",
"S",
"|",
"β",
"|",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"|",
"=",
"|",
"S",
"|",
"β",
"(",
"ni",
"β",
"O",
"##i",
",",
"j",
")",
"=",
"m",
"##β",
"ni",
"+",
"O",
"##i",
",",
"j",
".",
"13",
"There",
"could",
"be",
"t",
"##i",
",",
"j",
"Byzantine",
"nodes",
"in",
"S",
"β©",
"UN",
"##L",
"##j",
"that",
"send",
"P",
"##j",
"a",
"valid",
"##ation",
"for",
"something",
"other",
"than",
"L",
",",
"so",
"at",
"least",
"m",
"##β",
"##ni",
"+",
"O",
"##i",
",",
"j",
"##β",
"##ti",
",",
"j",
"honest",
"nodes",
"valid",
"##ated",
"L",
".",
"For",
"the",
"second",
"point",
",",
"assume",
"that",
"every",
"node",
"in",
"UN",
"##L",
"##i",
"\\",
"UN",
"##L",
"##j",
"valid",
"##ates",
"L",
",",
"t",
"##i",
",",
"j",
"Byzantine",
"nodes",
"in",
"UN",
"##L",
"##i",
"β©",
"##UN",
"##L",
"##j",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"Pi",
"and",
"L",
"β²",
"to",
"P",
"##j",
".",
"Then",
"there",
"are",
"exactly",
"m",
"β",
"ni",
"+",
"O",
"##i",
",",
"j",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"β©",
"UN",
"##L",
"##j",
"that",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"P",
"##j",
".",
"Since",
"every",
"node",
"in",
"UN",
"##L",
"##j",
"\\",
"UN",
"##L",
"##i",
"can",
"valid",
"##ate",
"some",
"ledge",
"##r",
"other",
"than",
"L",
",",
"there",
"can",
"be",
"exactly",
"m",
"##β",
"##ni",
"+",
"O",
"##i",
",",
"j",
"β",
"t",
"##i",
",",
"j",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"that",
"send",
"a",
"valid",
"##ation",
"for",
"L",
"to",
"P",
"##j",
".",
"Pro",
"##position",
"4",
".",
"Pi",
"fully",
"valid",
"##ating",
"some",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
"implies",
"that",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"the",
"same",
"sequence",
"number",
"s",
"if",
"##f",
"O",
"##i",
",",
"j",
">",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
".",
"Pro",
"##of",
".",
"By",
"letting",
"m",
"=",
"q",
"##i",
",",
"co",
"##roll",
"##ary",
"3",
"tells",
"us",
"that",
"Pi",
"fully",
"valid",
"##ating",
"L",
"implies",
"that",
"P",
"##j",
"can",
"see",
"at",
"most",
"ni",
"+",
"n",
"##j",
"##β",
"##O",
"##i",
",",
"j",
"##β",
"##qi",
"+",
"t",
"##i",
",",
"j",
"valid",
"##ations",
"for",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"sequence",
"number",
"s",
".",
"Thus",
"if",
"q",
"##j",
">",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"q",
"##i",
"+"
] | Analysis of the XRP Ledger Consensus Protocol | 182 |
e same parent ledger and sequence number, but differ because they applied
different transactions. Note though that the protocol specifies that every set of
transactions has a deterministic ordering, so it is not possible for two correct
nodes to apply the same transactions but in a different order.
The nodes communicate over a peer-to-peer network which has no prescribed
relation with the UNL structure. We simply assume that for every node Pi and
every node Pj β UNLi, there is a reliable authenticated ch | [
189,
1182,
117,
179,
152,
1182,
117,
179,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
116,
189,
1182,
117,
179,
1173,
153,
3361,
2834,
3106,
9221,
2193,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
14516,
4426,
14272,
7008,
1295,
188,
119,
1370,
14176,
117,
1191,
152,
1182,
117,
179,
127,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
117,
1173,
1103,
1248,
13620,
1104,
1884,
10747,
3113,
124,
12942,
1115,
153,
3361,
1169,
1267,
2839,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
186,
1182,
116,
189,
1182,
117,
179,
135,
11437,
116,
183,
3361,
851,
113,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
114,
851,
186,
1182,
116,
189,
1182,
117,
179,
134,
186,
3361,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
117,
3525,
153,
3361,
1106,
3106,
9221,
2193,
149,
797,
119,
2857,
1254,
11577,
2908,
110,
186,
11848,
5697,
1116,
1105,
1406,
110,
6088,
15745,
1112,
1107,
1103,
1653,
26311,
117,
1142,
19235,
3879,
1169,
1129,
25172,
1112,
8753,
4986,
5391,
110,
7414,
2162,
19235,
1116,
119,
1706,
1267,
1725,
1103,
19235,
11066,
1107,
21133,
125,
1674,
1136,
11865,
1554,
3429,
117,
3805,
1115,
1122,
1110,
1936,
1111,
170,
14372,
1106,
6300,
1121,
3687,
24851,
1891,
1111,
4954,
188,
1105,
1173,
1129,
3372,
1106,
3106,
9221,
2193,
1251,
21340,
1197,
1114,
4954,
188,
117,
1112,
1103,
1378,
1859,
2196,
119,
16409,
26671,
126,
119,
25515,
170,
2335,
2443,
1114,
1275,
15029,
119,
2421,
161,
21185,
1103,
1148,
126,
15029,
1105,
162,
21185,
1103,
1168,
126,
15029,
119,
1249,
2602,
1107,
2482,
126,
117,
6699,
1155,
1103,
15029,
1107,
3190,
3295,
3687,
24851,
1891,
24637,
1103,
13618,
1383,
157,
134,
196,
193,
1568,
117,
193,
1475,
198,
1105,
1155,
1103,
15029,
1107,
162,
3295,
3687,
24851,
1891,
24637,
1103,
1383,
157,
797,
134,
196,
193,
1568,
198,
119,
4516,
1111,
170,
13618,
11810,
1104,
437,
117,
4172,
437,
10698,
1111,
157,
1209,
2612,
1126,
7345,
14372,
1106,
17794,
1489,
161,
162,
163,
163,
797,
122,
123,
124,
125,
126,
127,
128,
129,
130,
1275,
157,
157,
157,
157,
157,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1969,
110,
4200,
117,
11810,
187,
851,
122,
117,
1851,
110,
157,
157,
157,
157,
157,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
187,
117,
1851,
110,
157,
157,
157,
157,
157,
157,
157,
157,
157,
157,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
2539,
110,
187,
116,
122,
117,
2625,
110,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"t",
"##i",
",",
"j",
"O",
"##i",
",",
"j",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
"+",
"t",
"##i",
",",
"j",
"then",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"se",
"##q",
"##eu",
"##ence",
"number",
"s",
".",
"For",
"necessity",
",",
"if",
"O",
"##i",
",",
"j",
"6",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
",",
"then",
"the",
"second",
"clause",
"of",
"co",
"##roll",
"##ary",
"3",
"implies",
"that",
"P",
"##j",
"can",
"see",
"exactly",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
">",
"ni",
"+",
"n",
"##j",
"β",
"(",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
")",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
"=",
"q",
"##j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
",",
"allowing",
"P",
"##j",
"to",
"fully",
"valid",
"##ate",
"L",
"β²",
".",
"Once",
"again",
"assuming",
"80",
"%",
"q",
"##uo",
"##rum",
"##s",
"and",
"20",
"%",
"fault",
"tolerance",
"as",
"in",
"the",
"white",
"##paper",
",",
"this",
"overlap",
"condition",
"can",
"be",
"summarized",
"as",
"requiring",
"roughly",
"61",
"%",
"UN",
"##L",
"overlap",
"##s",
".",
"To",
"see",
"why",
"the",
"overlap",
"hypothesis",
"in",
"proposition",
"4",
"does",
"not",
"guarantee",
"full",
"safety",
",",
"note",
"that",
"it",
"is",
"possible",
"for",
"a",
"node",
"to",
"exit",
"from",
"del",
"##iber",
"##ation",
"for",
"sequence",
"s",
"and",
"then",
"be",
"unable",
"to",
"fully",
"valid",
"##ate",
"any",
"ledge",
"##r",
"with",
"sequence",
"s",
",",
"as",
"the",
"following",
"example",
"shows",
".",
"Ex",
"##ample",
"5",
".",
"Consider",
"a",
"complete",
"network",
"with",
"10",
"nodes",
".",
"Let",
"X",
"denote",
"the",
"first",
"5",
"nodes",
"and",
"Y",
"denote",
"the",
"other",
"5",
"nodes",
".",
"As",
"shown",
"in",
"figure",
"5",
",",
"suppose",
"all",
"the",
"nodes",
"in",
"##X",
"begin",
"del",
"##iber",
"##ation",
"proposing",
"the",
"transaction",
"set",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
"}",
"and",
"all",
"the",
"nodes",
"in",
"Y",
"begin",
"del",
"##iber",
"##ation",
"proposing",
"the",
"set",
"T",
"β²",
"=",
"{",
"x",
"##0",
"}",
".",
"Thus",
"for",
"a",
"transaction",
"threshold",
"of",
"Ο",
",",
"receiving",
"Ο",
"proposals",
"for",
"T",
"will",
"cause",
"an",
"honest",
"node",
"to",
"propose",
"14",
"X",
"Y",
"Z",
"Z",
"β²",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"T",
"T",
"T",
"T",
"T",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"40",
"%",
"Round",
",",
"threshold",
"r",
"β",
"1",
",",
"50",
"%",
"T",
"T",
"T",
"T",
"T",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"r",
",",
"50",
"%",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"60",
"%",
"r",
"+",
"1",
",",
"65",
"%",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²"
] | Analysis of the XRP Ledger Consensus Protocol | 183 |
e same parent ledger and sequence number, but differ because they applied
different transactions. Note though that the protocol specifies that every set of
transactions has a deterministic ordering, so it is not possible for two correct
nodes to apply the same transactions but in a different order.
The nodes communicate over a peer-to-peer network which has no prescribed
relation with the UNL structure. We simply assume that for every node Pi and
every node Pj β UNLi, there is a reliable authenticated ch | [
189,
1182,
117,
179,
152,
1182,
117,
179,
135,
11437,
851,
186,
1182,
116,
183,
3361,
851,
186,
3361,
116,
189,
1182,
117,
179,
1173,
153,
3361,
2834,
3106,
9221,
2193,
1251,
14255,
4487,
28113,
4649,
21340,
1197,
1114,
14516,
4426,
14272,
7008,
1295,
188,
119,
1370,
14176,
117,
1191,
152,
1182,
117,
179,
127,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
117,
1173,
1103,
1248,
13620,
1104,
1884,
10747,
3113,
124,
12942,
1115,
153,
3361,
1169,
1267,
2839,
11437,
116,
183,
3361,
851,
152,
1182,
117,
179,
851,
186,
1182,
116,
189,
1182,
117,
179,
135,
11437,
116,
183,
3361,
851,
113,
113,
11437,
851,
186,
1182,
114,
116,
113,
183,
3361,
851,
186,
3361,
114,
116,
189,
1182,
117,
179,
114,
851,
186,
1182,
116,
189,
1182,
117,
179,
134,
186,
3361,
9221,
6006,
1111,
170,
14255,
4487,
28113,
4649,
21340,
1197,
149,
797,
117,
3525,
153,
3361,
1106,
3106,
9221,
2193,
149,
797,
119,
2857,
1254,
11577,
2908,
110,
186,
11848,
5697,
1116,
1105,
1406,
110,
6088,
15745,
1112,
1107,
1103,
1653,
26311,
117,
1142,
19235,
3879,
1169,
1129,
25172,
1112,
8753,
4986,
5391,
110,
7414,
2162,
19235,
1116,
119,
1706,
1267,
1725,
1103,
19235,
11066,
1107,
21133,
125,
1674,
1136,
11865,
1554,
3429,
117,
3805,
1115,
1122,
1110,
1936,
1111,
170,
14372,
1106,
6300,
1121,
3687,
24851,
1891,
1111,
4954,
188,
1105,
1173,
1129,
3372,
1106,
3106,
9221,
2193,
1251,
21340,
1197,
1114,
4954,
188,
117,
1112,
1103,
1378,
1859,
2196,
119,
16409,
26671,
126,
119,
25515,
170,
2335,
2443,
1114,
1275,
15029,
119,
2421,
161,
21185,
1103,
1148,
126,
15029,
1105,
162,
21185,
1103,
1168,
126,
15029,
119,
1249,
2602,
1107,
2482,
126,
117,
6699,
1155,
1103,
15029,
1107,
3190,
3295,
3687,
24851,
1891,
24637,
1103,
13618,
1383,
157,
134,
196,
193,
1568,
117,
193,
1475,
198,
1105,
1155,
1103,
15029,
1107,
162,
3295,
3687,
24851,
1891,
24637,
1103,
1383,
157,
797,
134,
196,
193,
1568,
198,
119,
4516,
1111,
170,
13618,
11810,
1104,
437,
117,
4172,
437,
10698,
1111,
157,
1209,
2612,
1126,
7345,
14372,
1106,
17794,
1489,
161,
162,
163,
163,
797,
122,
123,
124,
125,
126,
127,
128,
129,
130,
1275,
157,
157,
157,
157,
157,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1969,
110,
4200,
117,
11810,
187,
851,
122,
117,
1851,
110,
157,
157,
157,
157,
157,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
187,
117,
1851,
110,
157,
157,
157,
157,
157,
157,
157,
157,
157,
157,
193,
1568,
131,
1620,
110,
193,
1475,
131,
1851,
110,
193,
1568,
131,
1620,
110,
193,
1475,
131,
2539,
110,
187,
116,
122,
117,
2625,
110,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797,
157,
797
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"t",
"##i",
",",
"j",
"O",
"##i",
",",
"j",
">",
"ni",
"β",
"q",
"##i",
"+",
"n",
"##j",
"β",
"q",
"##j",
"+",
"t",
"##i",
",",
"j",
"then",
"P",
"##j",
"cannot",
"fully",
"valid",
"##ate",
"any",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"with",
"se",
"##q",
"##eu",
"##ence",
"number",
"s",
".",
"For",
"necessity",
",",
"if",
"O",
"##i",
",",
"j",
"6",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
",",
"then",
"the",
"second",
"clause",
"of",
"co",
"##roll",
"##ary",
"3",
"implies",
"that",
"P",
"##j",
"can",
"see",
"exactly",
"ni",
"+",
"n",
"##j",
"β",
"O",
"##i",
",",
"j",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
">",
"ni",
"+",
"n",
"##j",
"β",
"(",
"(",
"ni",
"β",
"q",
"##i",
")",
"+",
"(",
"n",
"##j",
"β",
"q",
"##j",
")",
"+",
"t",
"##i",
",",
"j",
")",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
"=",
"q",
"##j",
"valid",
"##ations",
"for",
"a",
"con",
"##tra",
"##dict",
"##ory",
"ledge",
"##r",
"L",
"β²",
",",
"allowing",
"P",
"##j",
"to",
"fully",
"valid",
"##ate",
"L",
"β²",
".",
"Once",
"again",
"assuming",
"80",
"%",
"q",
"##uo",
"##rum",
"##s",
"and",
"20",
"%",
"fault",
"tolerance",
"as",
"in",
"the",
"white",
"##paper",
",",
"this",
"overlap",
"condition",
"can",
"be",
"summarized",
"as",
"requiring",
"roughly",
"61",
"%",
"UN",
"##L",
"overlap",
"##s",
".",
"To",
"see",
"why",
"the",
"overlap",
"hypothesis",
"in",
"proposition",
"4",
"does",
"not",
"guarantee",
"full",
"safety",
",",
"note",
"that",
"it",
"is",
"possible",
"for",
"a",
"node",
"to",
"exit",
"from",
"del",
"##iber",
"##ation",
"for",
"sequence",
"s",
"and",
"then",
"be",
"unable",
"to",
"fully",
"valid",
"##ate",
"any",
"ledge",
"##r",
"with",
"sequence",
"s",
",",
"as",
"the",
"following",
"example",
"shows",
".",
"Ex",
"##ample",
"5",
".",
"Consider",
"a",
"complete",
"network",
"with",
"10",
"nodes",
".",
"Let",
"X",
"denote",
"the",
"first",
"5",
"nodes",
"and",
"Y",
"denote",
"the",
"other",
"5",
"nodes",
".",
"As",
"shown",
"in",
"figure",
"5",
",",
"suppose",
"all",
"the",
"nodes",
"in",
"##X",
"begin",
"del",
"##iber",
"##ation",
"proposing",
"the",
"transaction",
"set",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
"}",
"and",
"all",
"the",
"nodes",
"in",
"Y",
"begin",
"del",
"##iber",
"##ation",
"proposing",
"the",
"set",
"T",
"β²",
"=",
"{",
"x",
"##0",
"}",
".",
"Thus",
"for",
"a",
"transaction",
"threshold",
"of",
"Ο",
",",
"receiving",
"Ο",
"proposals",
"for",
"T",
"will",
"cause",
"an",
"honest",
"node",
"to",
"propose",
"14",
"X",
"Y",
"Z",
"Z",
"β²",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"T",
"T",
"T",
"T",
"T",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"40",
"%",
"Round",
",",
"threshold",
"r",
"β",
"1",
",",
"50",
"%",
"T",
"T",
"T",
"T",
"T",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"r",
",",
"50",
"%",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"T",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"50",
"%",
"x",
"##0",
":",
"100",
"%",
"x",
"##1",
":",
"60",
"%",
"r",
"+",
"1",
",",
"65",
"%",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²",
"T",
"β²"
] | Analysis of the XRP Ledger Consensus Protocol | 184 |
annel for Pi to receive
3
a
c
b
e
d
g
f
i
h
j
Figure 1: Example trust graph. The highlighted edges represent the UNL of
node Pi.
messages from Pj . To implement such an authenticated channel, all messages
are cryptographically signed and verified by receivers. Each node uses a single
communication primitive broadcast, which when called from node Pj sends
the same message to all nodes Pi for which Pj β UNLi. In the algorithms
presented in appendix A, we use a corresponding receive primitive | [
187,
116,
123,
117,
2625,
110,
15982,
126,
131,
20452,
15391,
7698,
1104,
1859,
126,
119,
1109,
1160,
14372,
2114,
161,
1105,
162,
3295,
1118,
24637,
157,
134,
196,
193,
1568,
117,
193,
1475,
198,
1105,
157,
797,
134,
196,
193,
1568,
198,
3569,
119,
1109,
1286,
113,
1268,
114,
8171,
7977,
10698,
1562,
1118,
14372,
122,
113,
1275,
114,
1105,
1132,
4248,
2109,
1104,
1155,
15029,
1107,
1372,
161,
113,
162,
114,
119,
4823,
15130,
5057,
10698,
1115,
1127,
1460,
1107,
1159,
1106,
20446,
1103,
11810,
1116,
1111,
170,
1549,
1668,
119,
5322,
1115,
1107,
1668,
187,
851,
122,
117,
1103,
5835,
1121,
14372,
126,
1108,
1136,
1460,
1118,
15029,
1107,
162,
119,
1109,
1160,
16416,
1116,
163,
1105,
163,
797,
1132,
2533,
1118,
1103,
19647,
8171,
119,
5322,
1115,
1155,
15029,
2934,
1103,
1269,
1423,
7414,
2162,
119,
1405,
157,
117,
1229,
4172,
1750,
1115,
437,
10698,
1111,
157,
1133,
437,
10698,
1111,
1719,
157,
1137,
157,
797,
1209,
2612,
1126,
7345,
14372,
1106,
17794,
157,
797,
117,
1290,
157,
858,
157,
797,
134,
157,
797,
119,
2421,
187,
1129,
1216,
1115,
1103,
13618,
11810,
1110,
1851,
110,
1107,
3687,
24851,
1891,
1668,
187,
1105,
2625,
110,
1107,
1668,
187,
116,
122,
119,
1650,
1103,
11631,
17374,
1158,
11810,
11309,
1758,
1107,
4841,
25461,
124,
119,
122,
117,
1216,
1126,
187,
5903,
119,
1507,
1103,
1148,
187,
851,
122,
5720,
117,
1103,
15029,
1107,
161,
3531,
1155,
1103,
10698,
117,
1229,
1103,
15029,
1107,
162,
3531,
1155,
1103,
10698,
2589,
1111,
1141,
5835,
1121,
170,
14372,
1107,
161,
119,
1967,
1103,
15029,
1107,
161,
17794,
157,
1229,
1103,
15029,
1107,
162,
17794,
157,
797,
117,
1103,
15029,
1107,
161,
2760,
24637,
157,
117,
1229,
1103,
15029,
1107,
162,
1178,
3531,
125,
10698,
1111,
157,
1105,
2760,
24637,
157,
797,
1118,
1103,
19129,
1113,
157,
1105,
157,
797,
119,
1986,
1107,
1668,
187,
1155,
15029,
3531,
1155,
10698,
119,
1188,
4680,
1155,
15029,
1106,
17794,
157,
1107,
1668,
187,
116,
122,
119,
1252,
1107,
1668,
187,
116,
122,
117,
170,
2443,
4290,
4680,
3839,
1104,
1103,
15029,
1106,
3531,
2256,
1950,
112,
188,
10698,
119,
7457,
1113,
1103,
1211,
3055,
1460,
3687,
24851,
1891,
10698,
117,
2490,
16956,
1115,
1155,
1103,
1168,
15029,
1132,
1253,
24637,
1184,
1152,
3000,
1107,
1103,
2166,
1668,
119,
4516,
1103,
15029,
1107,
161,
1267,
1178,
126,
10698,
1111,
157,
1229,
1103,
15029,
1107,
162,
1267,
1178,
127,
10698,
1111,
157,
113,
1290,
1152,
1104,
1736,
3531,
1147,
1319,
8054,
10698,
114,
119,
1302,
1141,
5302,
2625,
110,
1619,
1111,
193,
1475,
117,
1133,
2490,
5302,
1620,
110,
1619,
1111,
193,
1568,
117,
1177,
2490,
18381,
157,
797,
1107,
1668,
187,
116,
123,
119,
1986,
3368,
1126,
16439,
16416,
1104,
1103,
2443,
1154,
1160,
3741,
117,
163,
1105,
163,
797,
119,
1109,
15029,
1107,
163,
3531,
1155,
1103,
10698,
1121,
1668,
187,
116,
122,
1133,
3839,
1104,
1103,
10698,
1121,
1668,
187,
116,
123,
119,
4516,
1152,
1267,
1620,
110,
1619,
1111,
157,
1105,
9221,
2193,
157,
119,
5459,
1103,
15029,
1107,
163,
797
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"r",
"+",
"2",
",",
"65",
"%",
"Figure",
"5",
":",
"Sc",
"##hem",
"##atic",
"of",
"example",
"5",
".",
"The",
"two",
"node",
"groups",
"X",
"and",
"Y",
"begin",
"by",
"proposing",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
"}",
"and",
"T",
"β²",
"=",
"{",
"x",
"##0",
"}",
"respectively",
".",
"The",
"left",
"(",
"right",
")",
"boxes",
"reflect",
"proposals",
"seen",
"by",
"node",
"1",
"(",
"10",
")",
"and",
"are",
"represent",
"##ive",
"of",
"all",
"nodes",
"in",
"group",
"X",
"(",
"Y",
")",
".",
"Gray",
"arrows",
"indicate",
"proposals",
"that",
"were",
"received",
"in",
"time",
"to",
"calculate",
"the",
"threshold",
"##s",
"for",
"a",
"given",
"round",
".",
"Note",
"that",
"in",
"round",
"r",
"β",
"1",
",",
"the",
"proposal",
"from",
"node",
"5",
"was",
"not",
"received",
"by",
"nodes",
"in",
"Y",
".",
"The",
"two",
"partition",
"##s",
"Z",
"and",
"Z",
"β²",
"are",
"represented",
"by",
"the",
"dashed",
"boxes",
".",
"Note",
"that",
"all",
"nodes",
"share",
"the",
"same",
"single",
"UN",
"##L",
".",
"15",
"T",
",",
"while",
"receiving",
"less",
"that",
"Ο",
"proposals",
"for",
"T",
"but",
"Ο",
"proposals",
"for",
"either",
"T",
"or",
"T",
"β²",
"will",
"cause",
"an",
"honest",
"node",
"to",
"propose",
"T",
"β²",
",",
"since",
"T",
"β©",
"T",
"β²",
"=",
"T",
"β²",
".",
"Let",
"r",
"be",
"such",
"that",
"the",
"transaction",
"threshold",
"is",
"50",
"%",
"in",
"del",
"##iber",
"##ation",
"round",
"r",
"and",
"65",
"%",
"in",
"round",
"r",
"+",
"1",
".",
"By",
"the",
"rat",
"##chet",
"##ing",
"threshold",
"protocol",
"described",
"in",
"sub",
"##section",
"3",
".",
"1",
",",
"such",
"an",
"r",
"exists",
".",
"During",
"the",
"first",
"r",
"β",
"1",
"rounds",
",",
"the",
"nodes",
"in",
"X",
"receive",
"all",
"the",
"proposals",
",",
"while",
"the",
"nodes",
"in",
"Y",
"receive",
"all",
"the",
"proposals",
"except",
"for",
"one",
"proposal",
"from",
"a",
"node",
"in",
"X",
".",
"Since",
"the",
"nodes",
"in",
"X",
"propose",
"T",
"while",
"the",
"nodes",
"in",
"Y",
"propose",
"T",
"β²",
",",
"the",
"nodes",
"in",
"X",
"continue",
"proposing",
"T",
",",
"while",
"the",
"nodes",
"in",
"Y",
"only",
"receive",
"4",
"proposals",
"for",
"T",
"and",
"continue",
"proposing",
"T",
"β²",
"by",
"the",
"assumptions",
"on",
"T",
"and",
"T",
"β²",
".",
"Now",
"in",
"round",
"r",
"all",
"nodes",
"receive",
"all",
"proposals",
".",
"This",
"causes",
"all",
"nodes",
"to",
"propose",
"T",
"in",
"round",
"r",
"+",
"1",
".",
"But",
"in",
"round",
"r",
"+",
"1",
",",
"a",
"network",
"failure",
"causes",
"none",
"of",
"the",
"nodes",
"to",
"receive",
"anyone",
"else",
"'",
"s",
"proposals",
".",
"Based",
"on",
"the",
"most",
"recently",
"received",
"del",
"##iber",
"##ation",
"proposals",
",",
"everyone",
"assumes",
"that",
"all",
"the",
"other",
"nodes",
"are",
"still",
"proposing",
"what",
"they",
"proposed",
"in",
"the",
"previous",
"round",
".",
"Thus",
"the",
"nodes",
"in",
"X",
"see",
"only",
"5",
"proposals",
"for",
"T",
"while",
"the",
"nodes",
"in",
"Y",
"see",
"only",
"6",
"proposals",
"for",
"T",
"(",
"since",
"they",
"of",
"course",
"receive",
"their",
"own",
"updated",
"proposals",
")",
".",
"No",
"one",
"sees",
"65",
"%",
"support",
"for",
"x",
"##1",
",",
"but",
"everyone",
"sees",
"100",
"%",
"support",
"for",
"x",
"##0",
",",
"so",
"everyone",
"proposes",
"T",
"β²",
"in",
"round",
"r",
"+",
"2",
".",
"Now",
"pick",
"an",
"arbitrary",
"partition",
"of",
"the",
"network",
"into",
"two",
"sets",
",",
"Z",
"and",
"Z",
"β²",
".",
"The",
"nodes",
"in",
"Z",
"receive",
"all",
"the",
"proposals",
"from",
"round",
"r",
"+",
"1",
"but",
"none",
"of",
"the",
"proposals",
"from",
"round",
"r",
"+",
"2",
".",
"Thus",
"they",
"see",
"100",
"%",
"support",
"for",
"T",
"and",
"valid",
"##ate",
"T",
".",
"Meanwhile",
"the",
"nodes",
"in",
"Z",
"β²"
] | Analysis of the XRP Ledger Consensus Protocol | 185 |
annel for Pi to receive
3
a
c
b
e
d
g
f
i
h
j
Figure 1: Example trust graph. The highlighted edges represent the UNL of
node Pi.
messages from Pj . To implement such an authenticated channel, all messages
are cryptographically signed and verified by receivers. Each node uses a single
communication primitive broadcast, which when called from node Pj sends
the same message to all nodes Pi for which Pj β UNLi. In the algorithms
presented in appendix A, we use a corresponding receive primitive | [
187,
116,
123,
117,
2625,
110,
15982,
126,
131,
20452,
15391,
7698,
1104,
1859,
126,
119,
1109,
1160,
14372,
2114,
161,
1105,
162,
3295,
1118,
24637,
157,
134,
196,
193,
1568,
117,
193,
1475,
198,
1105,
157,
797,
134,
196,
193,
1568,
198,
3569,
119,
1109,
1286,
113,
1268,
114,
8171,
7977,
10698,
1562,
1118,
14372,
122,
113,
1275,
114,
1105,
1132,
4248,
2109,
1104,
1155,
15029,
1107,
1372,
161,
113,
162,
114,
119,
4823,
15130,
5057,
10698,
1115,
1127,
1460,
1107,
1159,
1106,
20446,
1103,
11810,
1116,
1111,
170,
1549,
1668,
119,
5322,
1115,
1107,
1668,
187,
851,
122,
117,
1103,
5835,
1121,
14372,
126,
1108,
1136,
1460,
1118,
15029,
1107,
162,
119,
1109,
1160,
16416,
1116,
163,
1105,
163,
797,
1132,
2533,
1118,
1103,
19647,
8171,
119,
5322,
1115,
1155,
15029,
2934,
1103,
1269,
1423,
7414,
2162,
119,
1405,
157,
117,
1229,
4172,
1750,
1115,
437,
10698,
1111,
157,
1133,
437,
10698,
1111,
1719,
157,
1137,
157,
797,
1209,
2612,
1126,
7345,
14372,
1106,
17794,
157,
797,
117,
1290,
157,
858,
157,
797,
134,
157,
797,
119,
2421,
187,
1129,
1216,
1115,
1103,
13618,
11810,
1110,
1851,
110,
1107,
3687,
24851,
1891,
1668,
187,
1105,
2625,
110,
1107,
1668,
187,
116,
122,
119,
1650,
1103,
11631,
17374,
1158,
11810,
11309,
1758,
1107,
4841,
25461,
124,
119,
122,
117,
1216,
1126,
187,
5903,
119,
1507,
1103,
1148,
187,
851,
122,
5720,
117,
1103,
15029,
1107,
161,
3531,
1155,
1103,
10698,
117,
1229,
1103,
15029,
1107,
162,
3531,
1155,
1103,
10698,
2589,
1111,
1141,
5835,
1121,
170,
14372,
1107,
161,
119,
1967,
1103,
15029,
1107,
161,
17794,
157,
1229,
1103,
15029,
1107,
162,
17794,
157,
797,
117,
1103,
15029,
1107,
161,
2760,
24637,
157,
117,
1229,
1103,
15029,
1107,
162,
1178,
3531,
125,
10698,
1111,
157,
1105,
2760,
24637,
157,
797,
1118,
1103,
19129,
1113,
157,
1105,
157,
797,
119,
1986,
1107,
1668,
187,
1155,
15029,
3531,
1155,
10698,
119,
1188,
4680,
1155,
15029,
1106,
17794,
157,
1107,
1668,
187,
116,
122,
119,
1252,
1107,
1668,
187,
116,
122,
117,
170,
2443,
4290,
4680,
3839,
1104,
1103,
15029,
1106,
3531,
2256,
1950,
112,
188,
10698,
119,
7457,
1113,
1103,
1211,
3055,
1460,
3687,
24851,
1891,
10698,
117,
2490,
16956,
1115,
1155,
1103,
1168,
15029,
1132,
1253,
24637,
1184,
1152,
3000,
1107,
1103,
2166,
1668,
119,
4516,
1103,
15029,
1107,
161,
1267,
1178,
126,
10698,
1111,
157,
1229,
1103,
15029,
1107,
162,
1267,
1178,
127,
10698,
1111,
157,
113,
1290,
1152,
1104,
1736,
3531,
1147,
1319,
8054,
10698,
114,
119,
1302,
1141,
5302,
2625,
110,
1619,
1111,
193,
1475,
117,
1133,
2490,
5302,
1620,
110,
1619,
1111,
193,
1568,
117,
1177,
2490,
18381,
157,
797,
1107,
1668,
187,
116,
123,
119,
1986,
3368,
1126,
16439,
16416,
1104,
1103,
2443,
1154,
1160,
3741,
117,
163,
1105,
163,
797,
119,
1109,
15029,
1107,
163,
3531,
1155,
1103,
10698,
1121,
1668,
187,
116,
122,
1133,
3839,
1104,
1103,
10698,
1121,
1668,
187,
116,
123,
119,
4516,
1152,
1267,
1620,
110,
1619,
1111,
157,
1105,
9221,
2193,
157,
119,
5459,
1103,
15029,
1107,
163,
797
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"r",
"+",
"2",
",",
"65",
"%",
"Figure",
"5",
":",
"Sc",
"##hem",
"##atic",
"of",
"example",
"5",
".",
"The",
"two",
"node",
"groups",
"X",
"and",
"Y",
"begin",
"by",
"proposing",
"T",
"=",
"{",
"x",
"##0",
",",
"x",
"##1",
"}",
"and",
"T",
"β²",
"=",
"{",
"x",
"##0",
"}",
"respectively",
".",
"The",
"left",
"(",
"right",
")",
"boxes",
"reflect",
"proposals",
"seen",
"by",
"node",
"1",
"(",
"10",
")",
"and",
"are",
"represent",
"##ive",
"of",
"all",
"nodes",
"in",
"group",
"X",
"(",
"Y",
")",
".",
"Gray",
"arrows",
"indicate",
"proposals",
"that",
"were",
"received",
"in",
"time",
"to",
"calculate",
"the",
"threshold",
"##s",
"for",
"a",
"given",
"round",
".",
"Note",
"that",
"in",
"round",
"r",
"β",
"1",
",",
"the",
"proposal",
"from",
"node",
"5",
"was",
"not",
"received",
"by",
"nodes",
"in",
"Y",
".",
"The",
"two",
"partition",
"##s",
"Z",
"and",
"Z",
"β²",
"are",
"represented",
"by",
"the",
"dashed",
"boxes",
".",
"Note",
"that",
"all",
"nodes",
"share",
"the",
"same",
"single",
"UN",
"##L",
".",
"15",
"T",
",",
"while",
"receiving",
"less",
"that",
"Ο",
"proposals",
"for",
"T",
"but",
"Ο",
"proposals",
"for",
"either",
"T",
"or",
"T",
"β²",
"will",
"cause",
"an",
"honest",
"node",
"to",
"propose",
"T",
"β²",
",",
"since",
"T",
"β©",
"T",
"β²",
"=",
"T",
"β²",
".",
"Let",
"r",
"be",
"such",
"that",
"the",
"transaction",
"threshold",
"is",
"50",
"%",
"in",
"del",
"##iber",
"##ation",
"round",
"r",
"and",
"65",
"%",
"in",
"round",
"r",
"+",
"1",
".",
"By",
"the",
"rat",
"##chet",
"##ing",
"threshold",
"protocol",
"described",
"in",
"sub",
"##section",
"3",
".",
"1",
",",
"such",
"an",
"r",
"exists",
".",
"During",
"the",
"first",
"r",
"β",
"1",
"rounds",
",",
"the",
"nodes",
"in",
"X",
"receive",
"all",
"the",
"proposals",
",",
"while",
"the",
"nodes",
"in",
"Y",
"receive",
"all",
"the",
"proposals",
"except",
"for",
"one",
"proposal",
"from",
"a",
"node",
"in",
"X",
".",
"Since",
"the",
"nodes",
"in",
"X",
"propose",
"T",
"while",
"the",
"nodes",
"in",
"Y",
"propose",
"T",
"β²",
",",
"the",
"nodes",
"in",
"X",
"continue",
"proposing",
"T",
",",
"while",
"the",
"nodes",
"in",
"Y",
"only",
"receive",
"4",
"proposals",
"for",
"T",
"and",
"continue",
"proposing",
"T",
"β²",
"by",
"the",
"assumptions",
"on",
"T",
"and",
"T",
"β²",
".",
"Now",
"in",
"round",
"r",
"all",
"nodes",
"receive",
"all",
"proposals",
".",
"This",
"causes",
"all",
"nodes",
"to",
"propose",
"T",
"in",
"round",
"r",
"+",
"1",
".",
"But",
"in",
"round",
"r",
"+",
"1",
",",
"a",
"network",
"failure",
"causes",
"none",
"of",
"the",
"nodes",
"to",
"receive",
"anyone",
"else",
"'",
"s",
"proposals",
".",
"Based",
"on",
"the",
"most",
"recently",
"received",
"del",
"##iber",
"##ation",
"proposals",
",",
"everyone",
"assumes",
"that",
"all",
"the",
"other",
"nodes",
"are",
"still",
"proposing",
"what",
"they",
"proposed",
"in",
"the",
"previous",
"round",
".",
"Thus",
"the",
"nodes",
"in",
"X",
"see",
"only",
"5",
"proposals",
"for",
"T",
"while",
"the",
"nodes",
"in",
"Y",
"see",
"only",
"6",
"proposals",
"for",
"T",
"(",
"since",
"they",
"of",
"course",
"receive",
"their",
"own",
"updated",
"proposals",
")",
".",
"No",
"one",
"sees",
"65",
"%",
"support",
"for",
"x",
"##1",
",",
"but",
"everyone",
"sees",
"100",
"%",
"support",
"for",
"x",
"##0",
",",
"so",
"everyone",
"proposes",
"T",
"β²",
"in",
"round",
"r",
"+",
"2",
".",
"Now",
"pick",
"an",
"arbitrary",
"partition",
"of",
"the",
"network",
"into",
"two",
"sets",
",",
"Z",
"and",
"Z",
"β²",
".",
"The",
"nodes",
"in",
"Z",
"receive",
"all",
"the",
"proposals",
"from",
"round",
"r",
"+",
"1",
"but",
"none",
"of",
"the",
"proposals",
"from",
"round",
"r",
"+",
"2",
".",
"Thus",
"they",
"see",
"100",
"%",
"support",
"for",
"T",
"and",
"valid",
"##ate",
"T",
".",
"Meanwhile",
"the",
"nodes",
"in",
"Z",
"β²"
] | Analysis of the XRP Ledger Consensus Protocol | 186 |
which is
called asynchronously upon the receipt of a broadcast message.
The outcome of XRP LCP is for a node to fully validate ledgers. A fully
validated ledger is irrevocable and authoritative, and reflects transactions sub-
mitted by network clients and accepted by the consensus algorithm. Fully vali-
dating a ledger also fully validates all of its ancestors. In this context, a fork is
a situation in which two honest nodes fully validate contradictory ledgers, i.e.,
different ledgers with the same sequ | [
3531,
1155,
1103,
10698,
1121,
1668,
180,
116,
123,
117,
1267,
1620,
110,
1619,
1111,
157,
797,
117,
1105,
9221,
2193,
157,
797,
119,
4516,
1195,
1169,
6300,
1121,
3687,
24851,
1891,
1114,
1160,
16439,
18005,
1116,
9221,
3798,
1472,
21340,
1733,
119,
1130,
1142,
1692,
1191,
197,
163,
197,
135,
123,
1105,
197,
163,
797,
197,
135,
123,
117,
1173,
3839,
1104,
1103,
15029,
1209,
3106,
9221,
2193,
170,
21340,
1197,
1219,
1142,
10923,
1668,
119,
2279,
1104,
5136,
1176,
1859,
126,
117,
1195,
3335,
1294,
1103,
4728,
13457,
1115,
3687,
24851,
1891,
1169,
22516,
1114,
1126,
16439,
1871,
119,
1130,
2415,
117,
1142,
1336,
4752,
170,
5409,
1260,
18590,
2443,
117,
1133,
1110,
14642,
170,
1842,
3187,
119,
1622,
170,
10093,
7281,
117,
3687,
24851,
1891,
1110,
3335,
2423,
25707,
132,
1122,
1110,
12098,
1126,
25161,
1115,
2228,
1122,
1177,
1115,
1219,
2987,
26107,
1211,
15029,
1209,
1301,
1154,
9221,
1891,
1114,
1103,
1269,
21340,
1197,
117,
3525,
1451,
14372,
1106,
3106,
9221,
2193,
1932,
117,
1105,
1122,
1180,
1129,
2856,
1443,
8148,
1193,
4787,
1103,
11309,
119,
4516,
1195,
5212,
1412,
2817,
2019,
9221,
1891,
1443,
1543,
1251,
19129,
1164,
1103,
1871,
1104,
3687,
24851,
1891,
119,
1284,
1444,
1106,
5424,
1115,
1191,
1251,
14372,
3106,
9221,
5430,
170,
21340,
1197,
149,
117,
1173,
1122,
1110,
1309,
1936,
1111,
170,
14372,
1106,
3106,
9221,
2193,
170,
21340,
1197,
149,
797,
1216,
1115,
14516,
4426,
113,
149,
797,
114,
135,
14516,
4426,
113,
149,
114,
1105,
149,
797,
1110,
1136,
170,
12920,
1104,
149,
119,
1109,
1378,
5837,
12917,
2790,
1103,
2438,
1111,
11865,
1158,
1142,
119,
3180,
12917,
127,
119,
1409,
1111,
1451,
14372,
21902,
117,
1175,
1132,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1115,
12295,
170,
9221,
1891,
1111,
1199,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
117,
1173,
1111,
1451,
14372,
21902,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1209,
1579,
12295,
9221,
6006,
1111,
21340,
1733,
9026,
1121,
149,
119,
5096,
10008,
119,
1284,
5424,
1142,
1118,
14255,
4487,
15906,
119,
1409,
1103,
5837,
12917,
1110,
1136,
2276,
117,
1173,
1223,
1103,
5837,
12917,
112,
188,
177,
1183,
11439,
18769,
1175,
1538,
1129,
1199,
7345,
14372,
1134,
12295,
1116,
170,
9221,
1891,
1479,
1111,
149,
1105,
1145,
2028,
12295,
1116,
170,
9221,
1891,
1111,
1199,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
14516,
4426,
113,
149,
114,
1105,
149,
797,
1136,
9026,
1121,
149,
119,
1967,
5663,
15029,
1169,
1178,
12295,
1207,
9221,
6006,
1111,
21340,
1733,
1114,
4954,
10802,
3407,
1190,
1251,
21340,
1197,
1152,
1138,
2331,
7402,
170,
9221,
1891,
1111,
117,
1216,
170,
14372,
1538,
12295,
1157,
9221,
1891,
1111,
149,
797,
1170,
1515,
7402,
1157,
9221,
1891,
1111,
149,
119,
4516,
1519,
21902,
1129,
1103,
7345,
14372,
1115,
7402,
170,
9221,
1891,
1111,
149,
1105,
1224,
1110,
1103,
1148,
1106,
12295,
170,
9221,
1891,
1111,
170,
21340,
1197,
149,
797,
1136,
9026,
1121,
149,
119,
1109,
1178,
1236,
1111,
21902,
1106,
1224,
12295,
170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"receive",
"all",
"the",
"proposals",
"from",
"round",
"k",
"+",
"2",
",",
"see",
"100",
"%",
"support",
"for",
"T",
"β²",
",",
"and",
"valid",
"##ate",
"T",
"β²",
".",
"Thus",
"we",
"can",
"exit",
"from",
"del",
"##iber",
"##ation",
"with",
"two",
"arbitrary",
"subset",
"##s",
"valid",
"##ating",
"different",
"ledge",
"##rs",
".",
"In",
"this",
"case",
"if",
"|",
"Z",
"|",
">",
"2",
"and",
"|",
"Z",
"β²",
"|",
">",
"2",
",",
"then",
"none",
"of",
"the",
"nodes",
"will",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"during",
"this",
"consensus",
"round",
".",
"Because",
"of",
"examples",
"like",
"example",
"5",
",",
"we",
"therefore",
"make",
"the",
"broad",
"assumption",
"that",
"del",
"##iber",
"##ation",
"can",
"terminate",
"with",
"an",
"arbitrary",
"result",
".",
"In",
"practice",
",",
"this",
"may",
"require",
"a",
"significantly",
"de",
"##graded",
"network",
",",
"but",
"is",
"nonetheless",
"a",
"real",
"risk",
".",
"From",
"a",
"theoretical",
"perspective",
",",
"del",
"##iber",
"##ation",
"is",
"therefore",
"completely",
"irrelevant",
";",
"it",
"is",
"purely",
"an",
"optimization",
"that",
"makes",
"it",
"so",
"that",
"during",
"civil",
"executions",
"most",
"nodes",
"will",
"go",
"into",
"valid",
"##ation",
"with",
"the",
"same",
"ledge",
"##r",
",",
"allowing",
"every",
"node",
"to",
"fully",
"valid",
"##ate",
"usually",
",",
"and",
"it",
"could",
"be",
"removed",
"without",
"fundamental",
"##ly",
"changing",
"the",
"protocol",
".",
"Thus",
"we",
"shift",
"our",
"focus",
"towards",
"valid",
"##ation",
"without",
"making",
"any",
"assumptions",
"about",
"the",
"result",
"of",
"del",
"##iber",
"##ation",
".",
"We",
"need",
"to",
"prove",
"that",
"if",
"any",
"node",
"fully",
"valid",
"##ates",
"a",
"ledge",
"##r",
"L",
",",
"then",
"it",
"is",
"never",
"possible",
"for",
"a",
"node",
"to",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"L",
"β²",
"such",
"that",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"se",
"##q",
"(",
"L",
")",
"and",
"L",
"β²",
"is",
"not",
"a",
"descendant",
"of",
"L",
".",
"The",
"following",
"le",
"##mma",
"provides",
"the",
"route",
"for",
"guarantee",
"##ing",
"this",
".",
"Le",
"##mma",
"6",
".",
"If",
"for",
"every",
"node",
"Pi",
",",
"there",
"are",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"submit",
"a",
"valid",
"##ation",
"for",
"some",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
",",
"then",
"for",
"every",
"node",
"Pi",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"will",
"always",
"submit",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"descended",
"from",
"L",
".",
"Pro",
"##of",
".",
"We",
"prove",
"this",
"by",
"con",
"##tra",
"##diction",
".",
"If",
"the",
"le",
"##mma",
"is",
"not",
"true",
",",
"then",
"under",
"the",
"le",
"##mma",
"'",
"s",
"h",
"##y",
"##pot",
"##heses",
"there",
"must",
"be",
"some",
"honest",
"node",
"which",
"submit",
"##s",
"a",
"valid",
"##ation",
"16",
"for",
"L",
"and",
"also",
"eventually",
"submit",
"##s",
"a",
"valid",
"##ation",
"for",
"some",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"se",
"##q",
"(",
"L",
")",
"and",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"Since",
"correct",
"nodes",
"can",
"only",
"submit",
"new",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"with",
"sequence",
"strictly",
"greater",
"than",
"any",
"ledge",
"##r",
"they",
"have",
"previously",
"submitted",
"a",
"valid",
"##ation",
"for",
",",
"such",
"a",
"node",
"must",
"submit",
"its",
"valid",
"##ation",
"for",
"L",
"β²",
"after",
"having",
"submitted",
"its",
"valid",
"##ation",
"for",
"L",
".",
"Thus",
"let",
"Pi",
"be",
"the",
"honest",
"node",
"that",
"submitted",
"a",
"valid",
"##ation",
"for",
"L",
"and",
"later",
"is",
"the",
"first",
"to",
"submit",
"a",
"valid",
"##ation",
"for",
"a",
"ledge",
"##r",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"The",
"only",
"way",
"for",
"Pi",
"to",
"later",
"submit",
"a"
] | Analysis of the XRP Ledger Consensus Protocol | 187 |
which is
called asynchronously upon the receipt of a broadcast message.
The outcome of XRP LCP is for a node to fully validate ledgers. A fully
validated ledger is irrevocable and authoritative, and reflects transactions sub-
mitted by network clients and accepted by the consensus algorithm. Fully vali-
dating a ledger also fully validates all of its ancestors. In this context, a fork is
a situation in which two honest nodes fully validate contradictory ledgers, i.e.,
different ledgers with the same sequ | [
3531,
1155,
1103,
10698,
1121,
1668,
180,
116,
123,
117,
1267,
1620,
110,
1619,
1111,
157,
797,
117,
1105,
9221,
2193,
157,
797,
119,
4516,
1195,
1169,
6300,
1121,
3687,
24851,
1891,
1114,
1160,
16439,
18005,
1116,
9221,
3798,
1472,
21340,
1733,
119,
1130,
1142,
1692,
1191,
197,
163,
197,
135,
123,
1105,
197,
163,
797,
197,
135,
123,
117,
1173,
3839,
1104,
1103,
15029,
1209,
3106,
9221,
2193,
170,
21340,
1197,
1219,
1142,
10923,
1668,
119,
2279,
1104,
5136,
1176,
1859,
126,
117,
1195,
3335,
1294,
1103,
4728,
13457,
1115,
3687,
24851,
1891,
1169,
22516,
1114,
1126,
16439,
1871,
119,
1130,
2415,
117,
1142,
1336,
4752,
170,
5409,
1260,
18590,
2443,
117,
1133,
1110,
14642,
170,
1842,
3187,
119,
1622,
170,
10093,
7281,
117,
3687,
24851,
1891,
1110,
3335,
2423,
25707,
132,
1122,
1110,
12098,
1126,
25161,
1115,
2228,
1122,
1177,
1115,
1219,
2987,
26107,
1211,
15029,
1209,
1301,
1154,
9221,
1891,
1114,
1103,
1269,
21340,
1197,
117,
3525,
1451,
14372,
1106,
3106,
9221,
2193,
1932,
117,
1105,
1122,
1180,
1129,
2856,
1443,
8148,
1193,
4787,
1103,
11309,
119,
4516,
1195,
5212,
1412,
2817,
2019,
9221,
1891,
1443,
1543,
1251,
19129,
1164,
1103,
1871,
1104,
3687,
24851,
1891,
119,
1284,
1444,
1106,
5424,
1115,
1191,
1251,
14372,
3106,
9221,
5430,
170,
21340,
1197,
149,
117,
1173,
1122,
1110,
1309,
1936,
1111,
170,
14372,
1106,
3106,
9221,
2193,
170,
21340,
1197,
149,
797,
1216,
1115,
14516,
4426,
113,
149,
797,
114,
135,
14516,
4426,
113,
149,
114,
1105,
149,
797,
1110,
1136,
170,
12920,
1104,
149,
119,
1109,
1378,
5837,
12917,
2790,
1103,
2438,
1111,
11865,
1158,
1142,
119,
3180,
12917,
127,
119,
1409,
1111,
1451,
14372,
21902,
117,
1175,
1132,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1115,
12295,
170,
9221,
1891,
1111,
1199,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
117,
1173,
1111,
1451,
14372,
21902,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1209,
1579,
12295,
9221,
6006,
1111,
21340,
1733,
9026,
1121,
149,
119,
5096,
10008,
119,
1284,
5424,
1142,
1118,
14255,
4487,
15906,
119,
1409,
1103,
5837,
12917,
1110,
1136,
2276,
117,
1173,
1223,
1103,
5837,
12917,
112,
188,
177,
1183,
11439,
18769,
1175,
1538,
1129,
1199,
7345,
14372,
1134,
12295,
1116,
170,
9221,
1891,
1479,
1111,
149,
1105,
1145,
2028,
12295,
1116,
170,
9221,
1891,
1111,
1199,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
14516,
4426,
113,
149,
114,
1105,
149,
797,
1136,
9026,
1121,
149,
119,
1967,
5663,
15029,
1169,
1178,
12295,
1207,
9221,
6006,
1111,
21340,
1733,
1114,
4954,
10802,
3407,
1190,
1251,
21340,
1197,
1152,
1138,
2331,
7402,
170,
9221,
1891,
1111,
117,
1216,
170,
14372,
1538,
12295,
1157,
9221,
1891,
1111,
149,
797,
1170,
1515,
7402,
1157,
9221,
1891,
1111,
149,
119,
4516,
1519,
21902,
1129,
1103,
7345,
14372,
1115,
7402,
170,
9221,
1891,
1111,
149,
1105,
1224,
1110,
1103,
1148,
1106,
12295,
170,
9221,
1891,
1111,
170,
21340,
1197,
149,
797,
1136,
9026,
1121,
149,
119,
1109,
1178,
1236,
1111,
21902,
1106,
1224,
12295,
170
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"receive",
"all",
"the",
"proposals",
"from",
"round",
"k",
"+",
"2",
",",
"see",
"100",
"%",
"support",
"for",
"T",
"β²",
",",
"and",
"valid",
"##ate",
"T",
"β²",
".",
"Thus",
"we",
"can",
"exit",
"from",
"del",
"##iber",
"##ation",
"with",
"two",
"arbitrary",
"subset",
"##s",
"valid",
"##ating",
"different",
"ledge",
"##rs",
".",
"In",
"this",
"case",
"if",
"|",
"Z",
"|",
">",
"2",
"and",
"|",
"Z",
"β²",
"|",
">",
"2",
",",
"then",
"none",
"of",
"the",
"nodes",
"will",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"during",
"this",
"consensus",
"round",
".",
"Because",
"of",
"examples",
"like",
"example",
"5",
",",
"we",
"therefore",
"make",
"the",
"broad",
"assumption",
"that",
"del",
"##iber",
"##ation",
"can",
"terminate",
"with",
"an",
"arbitrary",
"result",
".",
"In",
"practice",
",",
"this",
"may",
"require",
"a",
"significantly",
"de",
"##graded",
"network",
",",
"but",
"is",
"nonetheless",
"a",
"real",
"risk",
".",
"From",
"a",
"theoretical",
"perspective",
",",
"del",
"##iber",
"##ation",
"is",
"therefore",
"completely",
"irrelevant",
";",
"it",
"is",
"purely",
"an",
"optimization",
"that",
"makes",
"it",
"so",
"that",
"during",
"civil",
"executions",
"most",
"nodes",
"will",
"go",
"into",
"valid",
"##ation",
"with",
"the",
"same",
"ledge",
"##r",
",",
"allowing",
"every",
"node",
"to",
"fully",
"valid",
"##ate",
"usually",
",",
"and",
"it",
"could",
"be",
"removed",
"without",
"fundamental",
"##ly",
"changing",
"the",
"protocol",
".",
"Thus",
"we",
"shift",
"our",
"focus",
"towards",
"valid",
"##ation",
"without",
"making",
"any",
"assumptions",
"about",
"the",
"result",
"of",
"del",
"##iber",
"##ation",
".",
"We",
"need",
"to",
"prove",
"that",
"if",
"any",
"node",
"fully",
"valid",
"##ates",
"a",
"ledge",
"##r",
"L",
",",
"then",
"it",
"is",
"never",
"possible",
"for",
"a",
"node",
"to",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"L",
"β²",
"such",
"that",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"se",
"##q",
"(",
"L",
")",
"and",
"L",
"β²",
"is",
"not",
"a",
"descendant",
"of",
"L",
".",
"The",
"following",
"le",
"##mma",
"provides",
"the",
"route",
"for",
"guarantee",
"##ing",
"this",
".",
"Le",
"##mma",
"6",
".",
"If",
"for",
"every",
"node",
"Pi",
",",
"there",
"are",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"that",
"submit",
"a",
"valid",
"##ation",
"for",
"some",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
",",
"then",
"for",
"every",
"node",
"Pi",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"will",
"always",
"submit",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"descended",
"from",
"L",
".",
"Pro",
"##of",
".",
"We",
"prove",
"this",
"by",
"con",
"##tra",
"##diction",
".",
"If",
"the",
"le",
"##mma",
"is",
"not",
"true",
",",
"then",
"under",
"the",
"le",
"##mma",
"'",
"s",
"h",
"##y",
"##pot",
"##heses",
"there",
"must",
"be",
"some",
"honest",
"node",
"which",
"submit",
"##s",
"a",
"valid",
"##ation",
"16",
"for",
"L",
"and",
"also",
"eventually",
"submit",
"##s",
"a",
"valid",
"##ation",
"for",
"some",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"se",
"##q",
"(",
"L",
")",
"and",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"Since",
"correct",
"nodes",
"can",
"only",
"submit",
"new",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"with",
"sequence",
"strictly",
"greater",
"than",
"any",
"ledge",
"##r",
"they",
"have",
"previously",
"submitted",
"a",
"valid",
"##ation",
"for",
",",
"such",
"a",
"node",
"must",
"submit",
"its",
"valid",
"##ation",
"for",
"L",
"β²",
"after",
"having",
"submitted",
"its",
"valid",
"##ation",
"for",
"L",
".",
"Thus",
"let",
"Pi",
"be",
"the",
"honest",
"node",
"that",
"submitted",
"a",
"valid",
"##ation",
"for",
"L",
"and",
"later",
"is",
"the",
"first",
"to",
"submit",
"a",
"valid",
"##ation",
"for",
"a",
"ledge",
"##r",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"The",
"only",
"way",
"for",
"Pi",
"to",
"later",
"submit",
"a"
] | Analysis of the XRP Ledger Consensus Protocol | 188 |
ence number. The network is said to be
fork-safe if it can never fork with a tolerated configuration of Byzantine nodes.
Although XRP LCP is typically defined in terms of the fully validated chain
of ledgers, since each ledger in the chain represents a deterministically-ordered
sequence of transactions it also can be considered as an atomic broadcast pro-
tocol with batching of transactions for efficiency. Formally, an atomic broadcast
protocol is an algorithm in which a set of clients, arbitrarily many | [
9221,
1891,
1111,
170,
21340,
1197,
1228,
1104,
1103,
149,
3392,
1110,
1191,
1122,
2326,
1103,
6349,
3392,
9932,
1105,
5302,
170,
21340,
1197,
1228,
1103,
149,
3392,
1112,
6349,
119,
1370,
170,
1549,
188,
127,
14516,
4426,
113,
149,
114,
117,
1519,
6486,
113,
188,
117,
149,
114,
21185,
1103,
13596,
1104,
149,
1114,
4954,
188,
119,
1967,
21902,
7402,
170,
9221,
1891,
1111,
149,
1118,
13457,
117,
1122,
10500,
1155,
9221,
6006,
1111,
21340,
1733,
1114,
4954,
2071,
14516,
4426,
113,
149,
114,
1112,
8362,
8178,
9084,
1906,
1107,
1103,
6349,
3392,
11309,
119,
1252,
1290,
21902,
1110,
4260,
1106,
1129,
1103,
1148,
1106,
6878,
1283,
1121,
1103,
149,
3392,
117,
1167,
1190,
11437,
120,
123,
15029,
1107,
7414,
2162,
1182,
2834,
1138,
1850,
1149,
170,
9221,
1891,
1111,
1251,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
188,
1105,
149,
797,
1136,
9026,
1121,
149,
119,
4516,
1111,
1451,
188,
127,
14516,
4426,
113,
149,
114,
117,
21902,
5302,
170,
2656,
1104,
15029,
1107,
7414,
2162,
1182,
1112,
1217,
1719,
8362,
8178,
9084,
1906,
1619,
1120,
188,
1137,
3392,
1619,
1111,
6486,
113,
188,
117,
149,
114,
119,
1130,
1168,
1734,
117,
1111,
1155,
188,
127,
14516,
4426,
113,
149,
114,
117,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
117,
149,
114,
114,
135,
11437,
120,
123,
25532,
8362,
8178,
9084,
1906,
113,
188,
114,
119,
1370,
170,
1549,
188,
133,
14516,
4426,
113,
149,
114,
117,
6699,
6486,
113,
188,
117,
149,
114,
1110,
1103,
1954,
2259,
21340,
1197,
1107,
1103,
7812,
1113,
1413,
1275,
1104,
2586,
18791,
7088,
1306,
124,
119,
1599,
1719,
140,
164,
121,
166,
134,
6486,
113,
188,
116,
122,
117,
149,
114,
1137,
1175,
1110,
1199,
149,
797,
127,
134,
6486,
113,
188,
116,
122,
117,
149,
114,
1114,
6486,
113,
149,
797,
114,
134,
6486,
113,
188,
117,
149,
114,
1105,
140,
164,
121,
166,
134,
149,
797,
119,
1130,
1103,
2985,
1692,
117,
1103,
3392,
1619,
1111,
140,
164,
122,
166,
1538,
1129,
1120,
1655,
4463,
1106,
1103,
3392,
1619,
1111,
6486,
113,
188,
116,
122,
117,
149,
114,
113,
4440,
7057,
1114,
439,
114,
1118,
5754,
1104,
1103,
13649,
1104,
140,
119,
6940,
117,
1103,
3392,
1619,
1111,
140,
164,
121,
166,
1538,
1129,
1750,
1190,
11437,
120,
123,
119,
4516,
1107,
1413,
1479,
117,
100,
134,
28117,
8661,
6766,
11273,
113,
140,
164,
121,
166,
114,
851,
28117,
8661,
6766,
11273,
113,
140,
164,
122,
166,
114,
116,
439,
113,
140,
164,
121,
166,
117,
140,
164,
122,
166,
114,
127,
28117,
8661,
6766,
11273,
113,
140,
164,
121,
166,
114,
851,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
116,
122,
117,
149,
114,
114,
116,
122,
133,
11437,
120,
123,
25532,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
116,
122,
117,
149,
114,
114,
116,
122,
133,
11437,
120,
123,
25532,
113,
11437,
120,
123,
25532,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
114,
116,
122,
127,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"valid",
"##ation",
"for",
"a",
"ledge",
"##r",
"off",
"of",
"the",
"L",
"branch",
"is",
"if",
"it",
"runs",
"the",
"preferred",
"branch",
"algorithm",
"and",
"sees",
"a",
"ledge",
"##r",
"off",
"the",
"L",
"branch",
"as",
"preferred",
".",
"For",
"a",
"given",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"let",
"parent",
"(",
"s",
",",
"L",
")",
"denote",
"the",
"ancestor",
"of",
"L",
"with",
"sequence",
"s",
".",
"Since",
"Pi",
"submitted",
"a",
"valid",
"##ation",
"for",
"L",
"by",
"assumption",
",",
"it",
"considers",
"all",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"with",
"sequence",
"below",
"se",
"##q",
"(",
"L",
")",
"as",
"un",
"##com",
"##mit",
"##ted",
"in",
"the",
"preferred",
"branch",
"protocol",
".",
"But",
"since",
"Pi",
"is",
"assumed",
"to",
"be",
"the",
"first",
"to",
"switch",
"away",
"from",
"the",
"L",
"branch",
",",
"more",
"than",
"ni",
"/",
"2",
"nodes",
"in",
"UN",
"##L",
"##i",
"cannot",
"have",
"sent",
"out",
"a",
"valid",
"##ation",
"for",
"any",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"s",
"and",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"Thus",
"for",
"every",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"Pi",
"sees",
"a",
"majority",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"as",
"being",
"either",
"un",
"##com",
"##mit",
"##ted",
"support",
"at",
"s",
"or",
"branch",
"support",
"for",
"parent",
"(",
"s",
",",
"L",
")",
".",
"In",
"other",
"words",
",",
"for",
"all",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
",",
"L",
")",
")",
">",
"ni",
"/",
"2",
"##β",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
".",
"For",
"a",
"given",
"s",
"<",
"se",
"##q",
"(",
"L",
")",
",",
"suppose",
"parent",
"(",
"s",
",",
"L",
")",
"is",
"the",
"current",
"base",
"ledge",
"##r",
"in",
"the",
"loop",
"on",
"line",
"10",
"of",
"Al",
"##gor",
"##ith",
"##m",
"3",
".",
"Then",
"either",
"C",
"[",
"0",
"]",
"=",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"or",
"there",
"is",
"some",
"L",
"β²",
"6",
"=",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"with",
"parent",
"(",
"L",
"β²",
")",
"=",
"parent",
"(",
"s",
",",
"L",
")",
"and",
"C",
"[",
"0",
"]",
"=",
"L",
"β²",
".",
"In",
"the",
"latter",
"case",
",",
"the",
"branch",
"support",
"for",
"C",
"[",
"1",
"]",
"must",
"be",
"at",
"least",
"equal",
"to",
"the",
"branch",
"support",
"for",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"(",
"breaking",
"ties",
"with",
"Ο",
")",
"by",
"definition",
"of",
"the",
"ordering",
"of",
"C",
".",
"Further",
",",
"the",
"branch",
"support",
"for",
"C",
"[",
"0",
"]",
"must",
"be",
"less",
"than",
"ni",
"/",
"2",
".",
"Thus",
"in",
"line",
"16",
",",
"[UNK]",
"=",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"0",
"]",
")",
"β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"1",
"]",
")",
"+",
"Ο",
"(",
"C",
"[",
"0",
"]",
",",
"C",
"[",
"1",
"]",
")",
"6",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"0",
"]",
")",
"β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
")",
"+",
"1",
"<",
"ni",
"/",
"2",
"##β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
")",
"+",
"1",
"<",
"ni",
"/",
"2",
"##β",
"(",
"ni",
"/",
"2",
"##β",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
")",
"+",
"1",
"6",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
"+"
] | Analysis of the XRP Ledger Consensus Protocol | 189 |
ence number. The network is said to be
fork-safe if it can never fork with a tolerated configuration of Byzantine nodes.
Although XRP LCP is typically defined in terms of the fully validated chain
of ledgers, since each ledger in the chain represents a deterministically-ordered
sequence of transactions it also can be considered as an atomic broadcast pro-
tocol with batching of transactions for efficiency. Formally, an atomic broadcast
protocol is an algorithm in which a set of clients, arbitrarily many | [
9221,
1891,
1111,
170,
21340,
1197,
1228,
1104,
1103,
149,
3392,
1110,
1191,
1122,
2326,
1103,
6349,
3392,
9932,
1105,
5302,
170,
21340,
1197,
1228,
1103,
149,
3392,
1112,
6349,
119,
1370,
170,
1549,
188,
127,
14516,
4426,
113,
149,
114,
117,
1519,
6486,
113,
188,
117,
149,
114,
21185,
1103,
13596,
1104,
149,
1114,
4954,
188,
119,
1967,
21902,
7402,
170,
9221,
1891,
1111,
149,
1118,
13457,
117,
1122,
10500,
1155,
9221,
6006,
1111,
21340,
1733,
1114,
4954,
2071,
14516,
4426,
113,
149,
114,
1112,
8362,
8178,
9084,
1906,
1107,
1103,
6349,
3392,
11309,
119,
1252,
1290,
21902,
1110,
4260,
1106,
1129,
1103,
1148,
1106,
6878,
1283,
1121,
1103,
149,
3392,
117,
1167,
1190,
11437,
120,
123,
15029,
1107,
7414,
2162,
1182,
2834,
1138,
1850,
1149,
170,
9221,
1891,
1111,
1251,
21340,
1197,
149,
797,
1114,
14516,
4426,
113,
149,
797,
114,
135,
188,
1105,
149,
797,
1136,
9026,
1121,
149,
119,
4516,
1111,
1451,
188,
127,
14516,
4426,
113,
149,
114,
117,
21902,
5302,
170,
2656,
1104,
15029,
1107,
7414,
2162,
1182,
1112,
1217,
1719,
8362,
8178,
9084,
1906,
1619,
1120,
188,
1137,
3392,
1619,
1111,
6486,
113,
188,
117,
149,
114,
119,
1130,
1168,
1734,
117,
1111,
1155,
188,
127,
14516,
4426,
113,
149,
114,
117,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
117,
149,
114,
114,
135,
11437,
120,
123,
25532,
8362,
8178,
9084,
1906,
113,
188,
114,
119,
1370,
170,
1549,
188,
133,
14516,
4426,
113,
149,
114,
117,
6699,
6486,
113,
188,
117,
149,
114,
1110,
1103,
1954,
2259,
21340,
1197,
1107,
1103,
7812,
1113,
1413,
1275,
1104,
2586,
18791,
7088,
1306,
124,
119,
1599,
1719,
140,
164,
121,
166,
134,
6486,
113,
188,
116,
122,
117,
149,
114,
1137,
1175,
1110,
1199,
149,
797,
127,
134,
6486,
113,
188,
116,
122,
117,
149,
114,
1114,
6486,
113,
149,
797,
114,
134,
6486,
113,
188,
117,
149,
114,
1105,
140,
164,
121,
166,
134,
149,
797,
119,
1130,
1103,
2985,
1692,
117,
1103,
3392,
1619,
1111,
140,
164,
122,
166,
1538,
1129,
1120,
1655,
4463,
1106,
1103,
3392,
1619,
1111,
6486,
113,
188,
116,
122,
117,
149,
114,
113,
4440,
7057,
1114,
439,
114,
1118,
5754,
1104,
1103,
13649,
1104,
140,
119,
6940,
117,
1103,
3392,
1619,
1111,
140,
164,
121,
166,
1538,
1129,
1750,
1190,
11437,
120,
123,
119,
4516,
1107,
1413,
1479,
117,
100,
134,
28117,
8661,
6766,
11273,
113,
140,
164,
121,
166,
114,
851,
28117,
8661,
6766,
11273,
113,
140,
164,
122,
166,
114,
116,
439,
113,
140,
164,
121,
166,
117,
140,
164,
122,
166,
114,
127,
28117,
8661,
6766,
11273,
113,
140,
164,
121,
166,
114,
851,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
116,
122,
117,
149,
114,
114,
116,
122,
133,
11437,
120,
123,
25532,
28117,
8661,
6766,
11273,
113,
6486,
113,
188,
116,
122,
117,
149,
114,
114,
116,
122,
133,
11437,
120,
123,
25532,
113,
11437,
120,
123,
25532,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
114,
116,
122,
127,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
116
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"valid",
"##ation",
"for",
"a",
"ledge",
"##r",
"off",
"of",
"the",
"L",
"branch",
"is",
"if",
"it",
"runs",
"the",
"preferred",
"branch",
"algorithm",
"and",
"sees",
"a",
"ledge",
"##r",
"off",
"the",
"L",
"branch",
"as",
"preferred",
".",
"For",
"a",
"given",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"let",
"parent",
"(",
"s",
",",
"L",
")",
"denote",
"the",
"ancestor",
"of",
"L",
"with",
"sequence",
"s",
".",
"Since",
"Pi",
"submitted",
"a",
"valid",
"##ation",
"for",
"L",
"by",
"assumption",
",",
"it",
"considers",
"all",
"valid",
"##ations",
"for",
"ledge",
"##rs",
"with",
"sequence",
"below",
"se",
"##q",
"(",
"L",
")",
"as",
"un",
"##com",
"##mit",
"##ted",
"in",
"the",
"preferred",
"branch",
"protocol",
".",
"But",
"since",
"Pi",
"is",
"assumed",
"to",
"be",
"the",
"first",
"to",
"switch",
"away",
"from",
"the",
"L",
"branch",
",",
"more",
"than",
"ni",
"/",
"2",
"nodes",
"in",
"UN",
"##L",
"##i",
"cannot",
"have",
"sent",
"out",
"a",
"valid",
"##ation",
"for",
"any",
"ledge",
"##r",
"L",
"β²",
"with",
"se",
"##q",
"(",
"L",
"β²",
")",
">",
"s",
"and",
"L",
"β²",
"not",
"descended",
"from",
"L",
".",
"Thus",
"for",
"every",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"Pi",
"sees",
"a",
"majority",
"of",
"nodes",
"in",
"UN",
"##L",
"##i",
"as",
"being",
"either",
"un",
"##com",
"##mit",
"##ted",
"support",
"at",
"s",
"or",
"branch",
"support",
"for",
"parent",
"(",
"s",
",",
"L",
")",
".",
"In",
"other",
"words",
",",
"for",
"all",
"s",
"6",
"se",
"##q",
"(",
"L",
")",
",",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
",",
"L",
")",
")",
">",
"ni",
"/",
"2",
"##β",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
")",
".",
"For",
"a",
"given",
"s",
"<",
"se",
"##q",
"(",
"L",
")",
",",
"suppose",
"parent",
"(",
"s",
",",
"L",
")",
"is",
"the",
"current",
"base",
"ledge",
"##r",
"in",
"the",
"loop",
"on",
"line",
"10",
"of",
"Al",
"##gor",
"##ith",
"##m",
"3",
".",
"Then",
"either",
"C",
"[",
"0",
"]",
"=",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"or",
"there",
"is",
"some",
"L",
"β²",
"6",
"=",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"with",
"parent",
"(",
"L",
"β²",
")",
"=",
"parent",
"(",
"s",
",",
"L",
")",
"and",
"C",
"[",
"0",
"]",
"=",
"L",
"β²",
".",
"In",
"the",
"latter",
"case",
",",
"the",
"branch",
"support",
"for",
"C",
"[",
"1",
"]",
"must",
"be",
"at",
"least",
"equal",
"to",
"the",
"branch",
"support",
"for",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"(",
"breaking",
"ties",
"with",
"Ο",
")",
"by",
"definition",
"of",
"the",
"ordering",
"of",
"C",
".",
"Further",
",",
"the",
"branch",
"support",
"for",
"C",
"[",
"0",
"]",
"must",
"be",
"less",
"than",
"ni",
"/",
"2",
".",
"Thus",
"in",
"line",
"16",
",",
"[UNK]",
"=",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"0",
"]",
")",
"β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"1",
"]",
")",
"+",
"Ο",
"(",
"C",
"[",
"0",
"]",
",",
"C",
"[",
"1",
"]",
")",
"6",
"su",
"##pp",
"##bra",
"##nch",
"(",
"C",
"[",
"0",
"]",
")",
"β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
")",
"+",
"1",
"<",
"ni",
"/",
"2",
"##β",
"su",
"##pp",
"##bra",
"##nch",
"(",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
")",
"+",
"1",
"<",
"ni",
"/",
"2",
"##β",
"(",
"ni",
"/",
"2",
"##β",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
")",
"+",
"1",
"6",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
"+"
] | Analysis of the XRP Ledger Consensus Protocol | 190 |
of which may
be Byzantine faulty, can broadcast transactions, and each node can accept
some of those transactions according to the following properties:
1. ABC-Agreement: If a correct node accepts a transaction into a ledger,
then eventually all correct nodes accept the transaction into a ledger.
4
2. ABC-Linearizability: If a correct node accepts transaction x before trans-
action xβ², then all correct nodes accept transaction x before xβ².
3. ABC-Censorship-Resilience: If a correct client broadcast | [
122,
117,
1177,
1103,
3879,
100,
135,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
1110,
1579,
6014,
119,
4516,
1107,
1103,
2985,
1692,
21902,
5302,
6486,
113,
188,
117,
149,
114,
1112,
1103,
6349,
21340,
1197,
119,
1130,
1103,
1393,
1692,
117,
21902,
1719,
5302,
6486,
113,
188,
116,
122,
117,
149,
114,
1112,
1103,
6349,
21340,
1197,
1137,
3430,
1103,
7812,
1114,
6486,
113,
188,
116,
122,
117,
149,
114,
1112,
1103,
2259,
21340,
1197,
119,
1650,
18293,
117,
21902,
1110,
13008,
1106,
1267,
1199,
21340,
1197,
1113,
1103,
149,
3392,
1112,
6349,
117,
1177,
21902,
2834,
1817,
1103,
149,
3392,
117,
14255,
4487,
28113,
1158,
1412,
13457,
1164,
21902,
119,
1409,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1178,
1518,
9221,
2193,
8395,
1104,
149,
117,
1173,
4664,
21902,
2834,
3106,
9221,
2193,
170,
21340,
1197,
1115,
2144,
112,
189,
20649,
1121,
149,
117,
1290,
4303,
1175,
1156,
1129,
186,
1182,
135,
11437,
120,
123,
15029,
1115,
1850,
9221,
6006,
1111,
1199,
21340,
1197,
149,
797,
1114,
4954,
1295,
188,
797,
1115,
2144,
112,
189,
20649,
1121,
149,
119,
4516,
1195,
1169,
1542,
1437,
1115,
10923,
1110,
2914,
1191,
1195,
1169,
11865,
1115,
1191,
1251,
7345,
14372,
3106,
9221,
5430,
170,
21340,
1197,
149,
1114,
4954,
1295,
188,
117,
1173,
1111,
1451,
14372,
21902,
117,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1538,
1138,
9221,
2913,
149,
119,
1109,
1378,
21133,
3114,
1103,
19235,
3879,
11865,
1158,
1142,
2400,
119,
5096,
14572,
128,
119,
10470,
1160,
7345,
15029,
21902,
117,
153,
3361,
117,
21902,
3106,
9221,
3798,
170,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
12942,
1115,
1175,
1132,
1167,
1190,
183,
3361,
120,
123,
7345,
15029,
1107,
7414,
2162,
3361,
1134,
9221,
2913,
149,
1191,
2087,
152,
1182,
117,
179,
135,
183,
3361,
120,
123,
116,
11437,
851,
186,
1182,
116,
189,
1182,
117,
179,
119,
5096,
10008,
119,
1109,
6777,
1110,
2626,
21960,
1106,
1103,
6777,
1104,
21133,
125,
117,
2589,
1897,
1190,
4930,
1158,
1103,
7893,
1118,
186,
3361,
1195,
4930,
1122,
1118,
183,
3361,
120,
123,
119,
15840,
16996,
129,
119,
161,
20336,
149,
13113,
24512,
13097,
3429,
1191,
152,
1182,
117,
179,
135,
183,
3361,
120,
123,
116,
11437,
25532,
186,
1182,
116,
189,
1182,
117,
179,
1111,
1451,
3111,
1104,
15029,
21902,
117,
153,
3361,
119,
5322,
1115,
1780,
21133,
128,
1110,
1126,
1191,
2087,
4195,
117,
1103,
19235,
3879,
1107,
10384,
129,
1110,
1178,
6664,
1133,
1136,
3238,
1111,
161,
20336,
149,
13113,
3429,
119,
1188,
1110,
1272,
5837,
12917,
127,
1110,
1136,
1126,
1191,
2087,
4195,
119,
6940,
117,
1175,
1336,
1129,
1199,
191,
10584,
118,
5358,
2116,
25209,
1115,
2834,
1435,
1149,
1104,
3687,
24851,
1891,
117,
4440,
1412,
4728,
13457,
1115,
1625,
1169,
1435,
1149,
1104,
3687,
24851,
1891,
119,
1438,
117,
1122,
1110,
1103,
4780,
118,
12890,
3879,
1115,
1169,
1129,
4448,
12098,
1112,
170,
4930,
1113,
1103,
2060,
1104,
19235,
1116,
119,
2857,
1254,
11577,
2908,
110,
186,
11848,
5697,
1116,
1105
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
21,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
21,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
23,
24,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
21,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
21,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0
] | [
"1",
",",
"so",
"the",
"condition",
"[UNK]",
">",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
"is",
"always",
"false",
".",
"Thus",
"in",
"the",
"latter",
"case",
"Pi",
"sees",
"parent",
"(",
"s",
",",
"L",
")",
"as",
"the",
"preferred",
"ledge",
"##r",
".",
"In",
"the",
"former",
"case",
",",
"Pi",
"either",
"sees",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"as",
"the",
"preferred",
"ledge",
"##r",
"or",
"continues",
"the",
"loop",
"with",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"as",
"the",
"base",
"ledge",
"##r",
".",
"By",
"induction",
",",
"Pi",
"is",
"guaranteed",
"to",
"see",
"some",
"ledge",
"##r",
"on",
"the",
"L",
"branch",
"as",
"preferred",
",",
"so",
"Pi",
"cannot",
"leave",
"the",
"L",
"branch",
",",
"con",
"##tra",
"##dict",
"##ing",
"our",
"assumption",
"about",
"Pi",
".",
"If",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"only",
"ever",
"valid",
"##ate",
"descendants",
"of",
"L",
",",
"then",
"certainly",
"Pi",
"cannot",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"that",
"doesn",
"'",
"t",
"descend",
"from",
"L",
",",
"since",
"otherwise",
"there",
"would",
"be",
"q",
"##i",
">",
"ni",
"/",
"2",
"nodes",
"that",
"sent",
"valid",
"##ations",
"for",
"some",
"ledge",
"##r",
"L",
"β²",
"with",
"sequence",
"number",
"s",
"β²",
"that",
"doesn",
"'",
"t",
"descend",
"from",
"L",
".",
"Thus",
"we",
"can",
"17",
"show",
"that",
"consensus",
"is",
"safe",
"if",
"we",
"can",
"guarantee",
"that",
"if",
"any",
"honest",
"node",
"fully",
"valid",
"##ates",
"a",
"ledge",
"##r",
"L",
"with",
"sequence",
"number",
"s",
",",
"then",
"for",
"every",
"node",
"Pi",
",",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"must",
"have",
"valid",
"##ated",
"L",
".",
"The",
"following",
"proposition",
"gives",
"the",
"overlap",
"condition",
"guarantee",
"##ing",
"this",
"property",
".",
"Pro",
"##position",
"7",
".",
"Given",
"two",
"honest",
"nodes",
"Pi",
",",
"P",
"##j",
",",
"Pi",
"fully",
"valid",
"##ating",
"a",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
"implies",
"that",
"there",
"are",
"more",
"than",
"n",
"##j",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"which",
"valid",
"##ated",
"L",
"if",
"##f",
"O",
"##i",
",",
"j",
">",
"n",
"##j",
"/",
"2",
"+",
"ni",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
".",
"Pro",
"##of",
".",
"The",
"proof",
"is",
"directly",
"analogous",
"to",
"the",
"proof",
"of",
"proposition",
"4",
",",
"except",
"rather",
"than",
"bound",
"##ing",
"the",
"formula",
"by",
"q",
"##j",
"we",
"bound",
"it",
"by",
"n",
"##j",
"/",
"2",
".",
"Theo",
"##rem",
"8",
".",
"X",
"##RP",
"L",
"##CP",
"guarantees",
"fork",
"safety",
"if",
"O",
"##i",
",",
"j",
">",
"n",
"##j",
"/",
"2",
"+",
"ni",
"##β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
"for",
"every",
"pair",
"of",
"nodes",
"Pi",
",",
"P",
"##j",
".",
"Note",
"that",
"although",
"proposition",
"7",
"is",
"an",
"if",
"##f",
"statement",
",",
"the",
"overlap",
"condition",
"in",
"theorem",
"8",
"is",
"only",
"sufficient",
"but",
"not",
"necessary",
"for",
"X",
"##RP",
"L",
"##CP",
"safety",
".",
"This",
"is",
"because",
"le",
"##mma",
"6",
"is",
"not",
"an",
"if",
"##f",
"statement",
".",
"Further",
",",
"there",
"may",
"be",
"some",
"v",
"##ali",
"-",
"da",
"##tion",
"configurations",
"that",
"cannot",
"come",
"out",
"of",
"del",
"##iber",
"##ation",
",",
"breaking",
"our",
"broad",
"assumption",
"that",
"anything",
"can",
"come",
"out",
"of",
"del",
"##iber",
"##ation",
".",
"However",
",",
"it",
"is",
"the",
"weak",
"-",
"est",
"condition",
"that",
"can",
"be",
"expressed",
"purely",
"as",
"a",
"bound",
"on",
"the",
"size",
"of",
"overlap",
"##s",
".",
"Once",
"again",
"assuming",
"80",
"%",
"q",
"##uo",
"##rum",
"##s",
"and"
] | Analysis of the XRP Ledger Consensus Protocol | 191 |
of which may
be Byzantine faulty, can broadcast transactions, and each node can accept
some of those transactions according to the following properties:
1. ABC-Agreement: If a correct node accepts a transaction into a ledger,
then eventually all correct nodes accept the transaction into a ledger.
4
2. ABC-Linearizability: If a correct node accepts transaction x before trans-
action xβ², then all correct nodes accept transaction x before xβ².
3. ABC-Censorship-Resilience: If a correct client broadcast | [
122,
117,
1177,
1103,
3879,
100,
135,
8362,
8178,
9084,
1906,
113,
188,
116,
122,
114,
1110,
1579,
6014,
119,
4516,
1107,
1103,
2985,
1692,
21902,
5302,
6486,
113,
188,
117,
149,
114,
1112,
1103,
6349,
21340,
1197,
119,
1130,
1103,
1393,
1692,
117,
21902,
1719,
5302,
6486,
113,
188,
116,
122,
117,
149,
114,
1112,
1103,
6349,
21340,
1197,
1137,
3430,
1103,
7812,
1114,
6486,
113,
188,
116,
122,
117,
149,
114,
1112,
1103,
2259,
21340,
1197,
119,
1650,
18293,
117,
21902,
1110,
13008,
1106,
1267,
1199,
21340,
1197,
1113,
1103,
149,
3392,
1112,
6349,
117,
1177,
21902,
2834,
1817,
1103,
149,
3392,
117,
14255,
4487,
28113,
1158,
1412,
13457,
1164,
21902,
119,
1409,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1178,
1518,
9221,
2193,
8395,
1104,
149,
117,
1173,
4664,
21902,
2834,
3106,
9221,
2193,
170,
21340,
1197,
1115,
2144,
112,
189,
20649,
1121,
149,
117,
1290,
4303,
1175,
1156,
1129,
186,
1182,
135,
11437,
120,
123,
15029,
1115,
1850,
9221,
6006,
1111,
1199,
21340,
1197,
149,
797,
1114,
4954,
1295,
188,
797,
1115,
2144,
112,
189,
20649,
1121,
149,
119,
4516,
1195,
1169,
1542,
1437,
1115,
10923,
1110,
2914,
1191,
1195,
1169,
11865,
1115,
1191,
1251,
7345,
14372,
3106,
9221,
5430,
170,
21340,
1197,
149,
1114,
4954,
1295,
188,
117,
1173,
1111,
1451,
14372,
21902,
117,
1167,
1190,
11437,
120,
123,
7345,
15029,
1107,
7414,
2162,
1182,
1538,
1138,
9221,
2913,
149,
119,
1109,
1378,
21133,
3114,
1103,
19235,
3879,
11865,
1158,
1142,
2400,
119,
5096,
14572,
128,
119,
10470,
1160,
7345,
15029,
21902,
117,
153,
3361,
117,
21902,
3106,
9221,
3798,
170,
21340,
1197,
149,
1114,
14516,
4426,
113,
149,
114,
134,
188,
12942,
1115,
1175,
1132,
1167,
1190,
183,
3361,
120,
123,
7345,
15029,
1107,
7414,
2162,
3361,
1134,
9221,
2913,
149,
1191,
2087,
152,
1182,
117,
179,
135,
183,
3361,
120,
123,
116,
11437,
851,
186,
1182,
116,
189,
1182,
117,
179,
119,
5096,
10008,
119,
1109,
6777,
1110,
2626,
21960,
1106,
1103,
6777,
1104,
21133,
125,
117,
2589,
1897,
1190,
4930,
1158,
1103,
7893,
1118,
186,
3361,
1195,
4930,
1122,
1118,
183,
3361,
120,
123,
119,
15840,
16996,
129,
119,
161,
20336,
149,
13113,
24512,
13097,
3429,
1191,
152,
1182,
117,
179,
135,
183,
3361,
120,
123,
116,
11437,
25532,
186,
1182,
116,
189,
1182,
117,
179,
1111,
1451,
3111,
1104,
15029,
21902,
117,
153,
3361,
119,
5322,
1115,
1780,
21133,
128,
1110,
1126,
1191,
2087,
4195,
117,
1103,
19235,
3879,
1107,
10384,
129,
1110,
1178,
6664,
1133,
1136,
3238,
1111,
161,
20336,
149,
13113,
3429,
119,
1188,
1110,
1272,
5837,
12917,
127,
1110,
1136,
1126,
1191,
2087,
4195,
119,
6940,
117,
1175,
1336,
1129,
1199,
191,
10584,
118,
5358,
2116,
25209,
1115,
2834,
1435,
1149,
1104,
3687,
24851,
1891,
117,
4440,
1412,
4728,
13457,
1115,
1625,
1169,
1435,
1149,
1104,
3687,
24851,
1891,
119,
1438,
117,
1122,
1110,
1103,
4780,
118,
12890,
3879,
1115,
1169,
1129,
4448,
12098,
1112,
170,
4930,
1113,
1103,
2060,
1104,
19235,
1116,
119,
2857,
1254,
11577,
2908,
110,
186,
11848,
5697,
1116,
1105
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0
] | [
"1",
",",
"so",
"the",
"condition",
"[UNK]",
">",
"un",
"##com",
"##mit",
"##ted",
"(",
"s",
"+",
"1",
")",
"is",
"always",
"false",
".",
"Thus",
"in",
"the",
"latter",
"case",
"Pi",
"sees",
"parent",
"(",
"s",
",",
"L",
")",
"as",
"the",
"preferred",
"ledge",
"##r",
".",
"In",
"the",
"former",
"case",
",",
"Pi",
"either",
"sees",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"as",
"the",
"preferred",
"ledge",
"##r",
"or",
"continues",
"the",
"loop",
"with",
"parent",
"(",
"s",
"+",
"1",
",",
"L",
")",
"as",
"the",
"base",
"ledge",
"##r",
".",
"By",
"induction",
",",
"Pi",
"is",
"guaranteed",
"to",
"see",
"some",
"ledge",
"##r",
"on",
"the",
"L",
"branch",
"as",
"preferred",
",",
"so",
"Pi",
"cannot",
"leave",
"the",
"L",
"branch",
",",
"con",
"##tra",
"##dict",
"##ing",
"our",
"assumption",
"about",
"Pi",
".",
"If",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"only",
"ever",
"valid",
"##ate",
"descendants",
"of",
"L",
",",
"then",
"certainly",
"Pi",
"cannot",
"fully",
"valid",
"##ate",
"a",
"ledge",
"##r",
"that",
"doesn",
"'",
"t",
"descend",
"from",
"L",
",",
"since",
"otherwise",
"there",
"would",
"be",
"q",
"##i",
">",
"ni",
"/",
"2",
"nodes",
"that",
"sent",
"valid",
"##ations",
"for",
"some",
"ledge",
"##r",
"L",
"β²",
"with",
"sequence",
"number",
"s",
"β²",
"that",
"doesn",
"'",
"t",
"descend",
"from",
"L",
".",
"Thus",
"we",
"can",
"17",
"show",
"that",
"consensus",
"is",
"safe",
"if",
"we",
"can",
"guarantee",
"that",
"if",
"any",
"honest",
"node",
"fully",
"valid",
"##ates",
"a",
"ledge",
"##r",
"L",
"with",
"sequence",
"number",
"s",
",",
"then",
"for",
"every",
"node",
"Pi",
",",
"more",
"than",
"ni",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##i",
"must",
"have",
"valid",
"##ated",
"L",
".",
"The",
"following",
"proposition",
"gives",
"the",
"overlap",
"condition",
"guarantee",
"##ing",
"this",
"property",
".",
"Pro",
"##position",
"7",
".",
"Given",
"two",
"honest",
"nodes",
"Pi",
",",
"P",
"##j",
",",
"Pi",
"fully",
"valid",
"##ating",
"a",
"ledge",
"##r",
"L",
"with",
"se",
"##q",
"(",
"L",
")",
"=",
"s",
"implies",
"that",
"there",
"are",
"more",
"than",
"n",
"##j",
"/",
"2",
"honest",
"nodes",
"in",
"UN",
"##L",
"##j",
"which",
"valid",
"##ated",
"L",
"if",
"##f",
"O",
"##i",
",",
"j",
">",
"n",
"##j",
"/",
"2",
"+",
"ni",
"β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
".",
"Pro",
"##of",
".",
"The",
"proof",
"is",
"directly",
"analogous",
"to",
"the",
"proof",
"of",
"proposition",
"4",
",",
"except",
"rather",
"than",
"bound",
"##ing",
"the",
"formula",
"by",
"q",
"##j",
"we",
"bound",
"it",
"by",
"n",
"##j",
"/",
"2",
".",
"Theo",
"##rem",
"8",
".",
"X",
"##RP",
"L",
"##CP",
"guarantees",
"fork",
"safety",
"if",
"O",
"##i",
",",
"j",
">",
"n",
"##j",
"/",
"2",
"+",
"ni",
"##β",
"q",
"##i",
"+",
"t",
"##i",
",",
"j",
"for",
"every",
"pair",
"of",
"nodes",
"Pi",
",",
"P",
"##j",
".",
"Note",
"that",
"although",
"proposition",
"7",
"is",
"an",
"if",
"##f",
"statement",
",",
"the",
"overlap",
"condition",
"in",
"theorem",
"8",
"is",
"only",
"sufficient",
"but",
"not",
"necessary",
"for",
"X",
"##RP",
"L",
"##CP",
"safety",
".",
"This",
"is",
"because",
"le",
"##mma",
"6",
"is",
"not",
"an",
"if",
"##f",
"statement",
".",
"Further",
",",
"there",
"may",
"be",
"some",
"v",
"##ali",
"-",
"da",
"##tion",
"configurations",
"that",
"cannot",
"come",
"out",
"of",
"del",
"##iber",
"##ation",
",",
"breaking",
"our",
"broad",
"assumption",
"that",
"anything",
"can",
"come",
"out",
"of",
"del",
"##iber",
"##ation",
".",
"However",
",",
"it",
"is",
"the",
"weak",
"-",
"est",
"condition",
"that",
"can",
"be",
"expressed",
"purely",
"as",
"a",
"bound",
"on",
"the",
"size",
"of",
"overlap",
"##s",
".",
"Once",
"again",
"assuming",
"80",
"%",
"q",
"##uo",
"##rum",
"##s",
"and"
] | Analysis of the XRP Ledger Consensus Protocol | 192 |
s a valid transac-
tion x to all correct nodes, x will eventually be accepted by all nodes.
An atomic broadcast algorithm is in particular a variant of consensus [4].
Note that Censorship Resilience is the formalized definition of forward progress.
In practice, the peer-to-peer network weakens the requirement that clients sub-
mit their transaction to all correct nodes, since correct nodes will echo a sub-
mitted transaction to each other, flooding the network until every node receives
it.
In order to e | [
1406,
110,
21688,
117,
1103,
19235,
3879,
1107,
10384,
129,
1169,
1129,
25172,
1112,
8753,
4986,
135,
3078,
110,
7414,
2162,
19235,
1116,
119,
1966,
2385,
170,
4142,
7464,
113,
1105,
4664,
1677,
1167,
4142,
1190,
2034,
2637,
114,
117,
1142,
1674,
1253,
2621,
170,
1353,
2971,
1104,
8516,
117,
1134,
1110,
1304,
24034,
1766,
118,
15925,
1204,
1111,
1103,
161,
20336,
18657,
2895,
2443,
112,
188,
6468,
1106,
170,
6315,
7414,
2162,
11561,
1104,
2457,
11659,
119,
5823,
1199,
18605,
1107,
1103,
7414,
2162,
1116,
1110,
1696,
1241,
1111,
1170,
1103,
22767,
5783,
1104,
9373,
9298,
113,
1112,
1141,
1169,
1309,
11865,
1703,
3311,
1113,
6635,
1165,
1103,
6635,
1132,
2457,
11659,
114,
1105,
1145,
1219,
1103,
22767,
5783,
1965,
113,
1191,
4296,
26805,
1219,
2607,
1106,
1103,
7414,
2162,
2190,
1180,
2612,
170,
13097,
117,
1173,
22767,
5783,
1156,
1579,
1129,
1315,
22185,
1106,
16621,
114,
119,
125,
119,
123,
3374,
1757,
1986,
1115,
1195,
1138,
170,
5019,
12676,
1104,
1165,
1122,
1110,
4763,
1111,
1103,
2443,
1106,
13097,
117,
1195,
1156,
1176,
1106,
1221,
1165,
1122,
2228,
1977,
5070,
119,
1409,
170,
1686,
2443,
6260,
1543,
1977,
5070,
117,
1115,
1110,
1593,
1112,
15812,
1112,
13097,
1158,
117,
1290,
5028,
1547,
1129,
20790,
1113,
1217,
1682,
1106,
1294,
16845,
1113,
1159,
119,
12118,
11088,
1358,
118,
9468,
7854,
1183,
117,
1118,
1103,
23485,
2101,
1871,
164,
126,
166,
1122,
1110,
4763,
1106,
11865,
1977,
5070,
1107,
170,
3106,
1112,
27250,
8167,
23038,
1361,
2443,
119,
1130,
1103,
5884,
1104,
1217,
1682,
1106,
5424,
1115,
1103,
2443,
1579,
2228,
1977,
5070,
117,
1195,
1156,
1176,
1106,
1120,
1655,
1129,
1682,
1106,
5424,
1115,
1103,
2443,
2834,
1243,
107,
5342,
107,
119,
1130,
1168,
1734,
117,
1115,
1103,
2443,
2834,
1243,
1154,
170,
1352,
1107,
1134,
1199,
7345,
15029,
1169,
1309,
3106,
9221,
2193,
170,
1207,
21340,
1197,
119,
7595,
117,
1122,
1110,
1304,
2846,
1107,
1704,
1106,
11865,
1977,
5070,
1114,
161,
20336,
149,
13113,
119,
1109,
1378,
1859,
2196,
1115,
1122,
1110,
1936,
1106,
1243,
5342,
1256,
1114,
4850,
110,
7414,
2162,
19235,
1116,
1105,
1185,
8377,
21688,
119,
1407,
161,
162,
122,
123,
124,
119,
119,
119,
4062,
3882,
119,
119,
119,
1620,
7393,
9081,
149,
149,
149,
119,
119,
119,
149,
149,
797,
119,
119,
119,
149,
797,
149,
797,
149,
797,
15982,
127,
131,
16409,
26671,
1104,
5342,
2443,
1114,
4850,
110,
7414,
2162,
19235,
1105,
1185,
8377,
21688,
119,
16409,
26671,
130,
119,
25515,
170,
2443,
1104,
9081,
14097,
3282,
1394,
1107,
2482,
127,
119,
1247,
1132,
1160,
7414,
2162,
1116,
117,
1103,
1894,
161,
134,
196,
153,
1475,
117,
153,
1477,
117,
119,
119,
119,
117,
153,
10424,
1475,
198,
1105,
2221,
162,
134,
196,
153,
1477,
117,
153,
1495,
117,
119,
119,
119,
117,
153,
10424,
1477,
198,
119,
153,
14350,
122,
851,
4062,
1329,
161,
1105,
14097,
3882,
851,
9081,
1329,
162,
119,
1247,
1132,
1160,
21340,
1733,
117,
149,
1105,
149,
797,
119,
1109,
15029,
5578,
1106,
161,
1155,
9221,
2193,
170,
12920,
1104,
149,
117,
1229,
1103,
15029
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
23,
24,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"20",
"%",
"faults",
",",
"the",
"overlap",
"condition",
"in",
"theorem",
"8",
"can",
"be",
"summarized",
"as",
"requiring",
"roughly",
">",
"90",
"%",
"UN",
"##L",
"overlap",
"##s",
".",
"Although",
"quite",
"a",
"narrow",
"margin",
"(",
"and",
"certainly",
"far",
"more",
"narrow",
"than",
"originally",
"expected",
")",
",",
"this",
"does",
"still",
"allow",
"a",
"small",
"amount",
"of",
"variation",
",",
"which",
"is",
"very",
"imp",
"##or",
"-",
"tan",
"##t",
"for",
"the",
"X",
"##RP",
"Led",
"##ger",
"network",
"'",
"s",
"transition",
"to",
"a",
"recommended",
"UN",
"##L",
"comprised",
"of",
"independent",
"entities",
".",
"Having",
"some",
"flexibility",
"in",
"the",
"UN",
"##L",
"##s",
"is",
"important",
"both",
"for",
"after",
"the",
"divers",
"##ification",
"of",
"trusted",
"operators",
"(",
"as",
"one",
"can",
"never",
"guarantee",
"total",
"agreement",
"on",
"participants",
"when",
"the",
"participants",
"are",
"independent",
"entities",
")",
"and",
"also",
"during",
"the",
"divers",
"##ification",
"process",
"(",
"if",
"tiny",
"disagreements",
"during",
"changes",
"to",
"the",
"UN",
"##L",
"list",
"could",
"cause",
"a",
"fork",
",",
"then",
"divers",
"##ification",
"would",
"always",
"be",
"too",
"risky",
"to",
"execute",
")",
".",
"4",
".",
"2",
"Live",
"##ness",
"Now",
"that",
"we",
"have",
"a",
"concrete",
"metric",
"of",
"when",
"it",
"is",
"impossible",
"for",
"the",
"network",
"to",
"fork",
",",
"we",
"would",
"like",
"to",
"know",
"when",
"it",
"makes",
"forward",
"progress",
".",
"If",
"a",
"live",
"network",
"stops",
"making",
"forward",
"progress",
",",
"that",
"is",
"almost",
"as",
"damaging",
"as",
"fork",
"##ing",
",",
"since",
"businesses",
"might",
"be",
"relying",
"on",
"being",
"able",
"to",
"make",
"transfers",
"on",
"time",
".",
"Un",
"##fort",
"##u",
"-",
"na",
"##tel",
"##y",
",",
"by",
"the",
"FL",
"##P",
"result",
"[",
"5",
"]",
"it",
"is",
"impossible",
"to",
"guarantee",
"forward",
"progress",
"in",
"a",
"fully",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"network",
".",
"In",
"the",
"absence",
"of",
"being",
"able",
"to",
"prove",
"that",
"the",
"network",
"always",
"makes",
"forward",
"progress",
",",
"we",
"would",
"like",
"to",
"at",
"least",
"be",
"able",
"to",
"prove",
"that",
"the",
"network",
"cannot",
"get",
"\"",
"stuck",
"\"",
".",
"In",
"other",
"words",
",",
"that",
"the",
"network",
"cannot",
"get",
"into",
"a",
"state",
"in",
"which",
"some",
"honest",
"nodes",
"can",
"never",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
".",
"Unfortunately",
",",
"it",
"is",
"very",
"difficult",
"in",
"general",
"to",
"guarantee",
"forward",
"progress",
"with",
"X",
"##RP",
"L",
"##CP",
".",
"The",
"following",
"example",
"shows",
"that",
"it",
"is",
"possible",
"to",
"get",
"stuck",
"even",
"with",
"99",
"%",
"UN",
"##L",
"overlap",
"##s",
"and",
"no",
"Byzantine",
"faults",
".",
"18",
"X",
"Y",
"1",
"2",
"3",
".",
".",
".",
"51",
"52",
".",
".",
".",
"100",
"101",
"102",
"L",
"L",
"L",
".",
".",
".",
"L",
"L",
"β²",
".",
".",
".",
"L",
"β²",
"L",
"β²",
"L",
"β²",
"Figure",
"6",
":",
"Ex",
"##ample",
"of",
"stuck",
"network",
"with",
"99",
"%",
"UN",
"##L",
"overlap",
"and",
"no",
"Byzantine",
"faults",
".",
"Ex",
"##ample",
"9",
".",
"Consider",
"a",
"network",
"of",
"102",
"peers",
"draw",
"##in",
"in",
"figure",
"6",
".",
"There",
"are",
"two",
"UN",
"##L",
"##s",
",",
"the",
"red",
"X",
"=",
"{",
"P",
"##1",
",",
"P",
"##2",
",",
".",
".",
".",
",",
"P",
"##10",
"##1",
"}",
"and",
"blue",
"Y",
"=",
"{",
"P",
"##2",
",",
"P",
"##3",
",",
".",
".",
".",
",",
"P",
"##10",
"##2",
"}",
".",
"P",
"##eers",
"1",
"β",
"51",
"use",
"X",
"and",
"peers",
"52",
"β",
"102",
"use",
"Y",
".",
"There",
"are",
"two",
"ledge",
"##rs",
",",
"L",
"and",
"L",
"β²",
".",
"The",
"nodes",
"listening",
"to",
"X",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
",",
"while",
"the",
"nodes"
] | Analysis of the XRP Ledger Consensus Protocol | 193 |
s a valid transac-
tion x to all correct nodes, x will eventually be accepted by all nodes.
An atomic broadcast algorithm is in particular a variant of consensus [4].
Note that Censorship Resilience is the formalized definition of forward progress.
In practice, the peer-to-peer network weakens the requirement that clients sub-
mit their transaction to all correct nodes, since correct nodes will echo a sub-
mitted transaction to each other, flooding the network until every node receives
it.
In order to e | [
1406,
110,
21688,
117,
1103,
19235,
3879,
1107,
10384,
129,
1169,
1129,
25172,
1112,
8753,
4986,
135,
3078,
110,
7414,
2162,
19235,
1116,
119,
1966,
2385,
170,
4142,
7464,
113,
1105,
4664,
1677,
1167,
4142,
1190,
2034,
2637,
114,
117,
1142,
1674,
1253,
2621,
170,
1353,
2971,
1104,
8516,
117,
1134,
1110,
1304,
24034,
1766,
118,
15925,
1204,
1111,
1103,
161,
20336,
18657,
2895,
2443,
112,
188,
6468,
1106,
170,
6315,
7414,
2162,
11561,
1104,
2457,
11659,
119,
5823,
1199,
18605,
1107,
1103,
7414,
2162,
1116,
1110,
1696,
1241,
1111,
1170,
1103,
22767,
5783,
1104,
9373,
9298,
113,
1112,
1141,
1169,
1309,
11865,
1703,
3311,
1113,
6635,
1165,
1103,
6635,
1132,
2457,
11659,
114,
1105,
1145,
1219,
1103,
22767,
5783,
1965,
113,
1191,
4296,
26805,
1219,
2607,
1106,
1103,
7414,
2162,
2190,
1180,
2612,
170,
13097,
117,
1173,
22767,
5783,
1156,
1579,
1129,
1315,
22185,
1106,
16621,
114,
119,
125,
119,
123,
3374,
1757,
1986,
1115,
1195,
1138,
170,
5019,
12676,
1104,
1165,
1122,
1110,
4763,
1111,
1103,
2443,
1106,
13097,
117,
1195,
1156,
1176,
1106,
1221,
1165,
1122,
2228,
1977,
5070,
119,
1409,
170,
1686,
2443,
6260,
1543,
1977,
5070,
117,
1115,
1110,
1593,
1112,
15812,
1112,
13097,
1158,
117,
1290,
5028,
1547,
1129,
20790,
1113,
1217,
1682,
1106,
1294,
16845,
1113,
1159,
119,
12118,
11088,
1358,
118,
9468,
7854,
1183,
117,
1118,
1103,
23485,
2101,
1871,
164,
126,
166,
1122,
1110,
4763,
1106,
11865,
1977,
5070,
1107,
170,
3106,
1112,
27250,
8167,
23038,
1361,
2443,
119,
1130,
1103,
5884,
1104,
1217,
1682,
1106,
5424,
1115,
1103,
2443,
1579,
2228,
1977,
5070,
117,
1195,
1156,
1176,
1106,
1120,
1655,
1129,
1682,
1106,
5424,
1115,
1103,
2443,
2834,
1243,
107,
5342,
107,
119,
1130,
1168,
1734,
117,
1115,
1103,
2443,
2834,
1243,
1154,
170,
1352,
1107,
1134,
1199,
7345,
15029,
1169,
1309,
3106,
9221,
2193,
170,
1207,
21340,
1197,
119,
7595,
117,
1122,
1110,
1304,
2846,
1107,
1704,
1106,
11865,
1977,
5070,
1114,
161,
20336,
149,
13113,
119,
1109,
1378,
1859,
2196,
1115,
1122,
1110,
1936,
1106,
1243,
5342,
1256,
1114,
4850,
110,
7414,
2162,
19235,
1116,
1105,
1185,
8377,
21688,
119,
1407,
161,
162,
122,
123,
124,
119,
119,
119,
4062,
3882,
119,
119,
119,
1620,
7393,
9081,
149,
149,
149,
119,
119,
119,
149,
149,
797,
119,
119,
119,
149,
797,
149,
797,
149,
797,
15982,
127,
131,
16409,
26671,
1104,
5342,
2443,
1114,
4850,
110,
7414,
2162,
19235,
1105,
1185,
8377,
21688,
119,
16409,
26671,
130,
119,
25515,
170,
2443,
1104,
9081,
14097,
3282,
1394,
1107,
2482,
127,
119,
1247,
1132,
1160,
7414,
2162,
1116,
117,
1103,
1894,
161,
134,
196,
153,
1475,
117,
153,
1477,
117,
119,
119,
119,
117,
153,
10424,
1475,
198,
1105,
2221,
162,
134,
196,
153,
1477,
117,
153,
1495,
117,
119,
119,
119,
117,
153,
10424,
1477,
198,
119,
153,
14350,
122,
851,
4062,
1329,
161,
1105,
14097,
3882,
851,
9081,
1329,
162,
119,
1247,
1132,
1160,
21340,
1733,
117,
149,
1105,
149,
797,
119,
1109,
15029,
5578,
1106,
161,
1155,
9221,
2193,
170,
12920,
1104,
149,
117,
1229,
1103,
15029
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"20",
"%",
"faults",
",",
"the",
"overlap",
"condition",
"in",
"theorem",
"8",
"can",
"be",
"summarized",
"as",
"requiring",
"roughly",
">",
"90",
"%",
"UN",
"##L",
"overlap",
"##s",
".",
"Although",
"quite",
"a",
"narrow",
"margin",
"(",
"and",
"certainly",
"far",
"more",
"narrow",
"than",
"originally",
"expected",
")",
",",
"this",
"does",
"still",
"allow",
"a",
"small",
"amount",
"of",
"variation",
",",
"which",
"is",
"very",
"imp",
"##or",
"-",
"tan",
"##t",
"for",
"the",
"X",
"##RP",
"Led",
"##ger",
"network",
"'",
"s",
"transition",
"to",
"a",
"recommended",
"UN",
"##L",
"comprised",
"of",
"independent",
"entities",
".",
"Having",
"some",
"flexibility",
"in",
"the",
"UN",
"##L",
"##s",
"is",
"important",
"both",
"for",
"after",
"the",
"divers",
"##ification",
"of",
"trusted",
"operators",
"(",
"as",
"one",
"can",
"never",
"guarantee",
"total",
"agreement",
"on",
"participants",
"when",
"the",
"participants",
"are",
"independent",
"entities",
")",
"and",
"also",
"during",
"the",
"divers",
"##ification",
"process",
"(",
"if",
"tiny",
"disagreements",
"during",
"changes",
"to",
"the",
"UN",
"##L",
"list",
"could",
"cause",
"a",
"fork",
",",
"then",
"divers",
"##ification",
"would",
"always",
"be",
"too",
"risky",
"to",
"execute",
")",
".",
"4",
".",
"2",
"Live",
"##ness",
"Now",
"that",
"we",
"have",
"a",
"concrete",
"metric",
"of",
"when",
"it",
"is",
"impossible",
"for",
"the",
"network",
"to",
"fork",
",",
"we",
"would",
"like",
"to",
"know",
"when",
"it",
"makes",
"forward",
"progress",
".",
"If",
"a",
"live",
"network",
"stops",
"making",
"forward",
"progress",
",",
"that",
"is",
"almost",
"as",
"damaging",
"as",
"fork",
"##ing",
",",
"since",
"businesses",
"might",
"be",
"relying",
"on",
"being",
"able",
"to",
"make",
"transfers",
"on",
"time",
".",
"Un",
"##fort",
"##u",
"-",
"na",
"##tel",
"##y",
",",
"by",
"the",
"FL",
"##P",
"result",
"[",
"5",
"]",
"it",
"is",
"impossible",
"to",
"guarantee",
"forward",
"progress",
"in",
"a",
"fully",
"as",
"##ync",
"##hr",
"##ono",
"##us",
"network",
".",
"In",
"the",
"absence",
"of",
"being",
"able",
"to",
"prove",
"that",
"the",
"network",
"always",
"makes",
"forward",
"progress",
",",
"we",
"would",
"like",
"to",
"at",
"least",
"be",
"able",
"to",
"prove",
"that",
"the",
"network",
"cannot",
"get",
"\"",
"stuck",
"\"",
".",
"In",
"other",
"words",
",",
"that",
"the",
"network",
"cannot",
"get",
"into",
"a",
"state",
"in",
"which",
"some",
"honest",
"nodes",
"can",
"never",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
".",
"Unfortunately",
",",
"it",
"is",
"very",
"difficult",
"in",
"general",
"to",
"guarantee",
"forward",
"progress",
"with",
"X",
"##RP",
"L",
"##CP",
".",
"The",
"following",
"example",
"shows",
"that",
"it",
"is",
"possible",
"to",
"get",
"stuck",
"even",
"with",
"99",
"%",
"UN",
"##L",
"overlap",
"##s",
"and",
"no",
"Byzantine",
"faults",
".",
"18",
"X",
"Y",
"1",
"2",
"3",
".",
".",
".",
"51",
"52",
".",
".",
".",
"100",
"101",
"102",
"L",
"L",
"L",
".",
".",
".",
"L",
"L",
"β²",
".",
".",
".",
"L",
"β²",
"L",
"β²",
"L",
"β²",
"Figure",
"6",
":",
"Ex",
"##ample",
"of",
"stuck",
"network",
"with",
"99",
"%",
"UN",
"##L",
"overlap",
"and",
"no",
"Byzantine",
"faults",
".",
"Ex",
"##ample",
"9",
".",
"Consider",
"a",
"network",
"of",
"102",
"peers",
"draw",
"##in",
"in",
"figure",
"6",
".",
"There",
"are",
"two",
"UN",
"##L",
"##s",
",",
"the",
"red",
"X",
"=",
"{",
"P",
"##1",
",",
"P",
"##2",
",",
".",
".",
".",
",",
"P",
"##10",
"##1",
"}",
"and",
"blue",
"Y",
"=",
"{",
"P",
"##2",
",",
"P",
"##3",
",",
".",
".",
".",
",",
"P",
"##10",
"##2",
"}",
".",
"P",
"##eers",
"1",
"β",
"51",
"use",
"X",
"and",
"peers",
"52",
"β",
"102",
"use",
"Y",
".",
"There",
"are",
"two",
"ledge",
"##rs",
",",
"L",
"and",
"L",
"β²",
".",
"The",
"nodes",
"listening",
"to",
"X",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
",",
"while",
"the",
"nodes"
] | Analysis of the XRP Ledger Consensus Protocol | 194 |
valuate the correctness of XRP LCP, we model the peer-to-
peer network as if it were controlled by a network adversary that can behave
arbitrarily. The adversary is controls the delivery order of all messages, as well
as at most ti nodes in UNLi for any correct node Pi. We assume though that
the adversary is computationally bounded; in particular, it is unable to break
generally accepted cryptographic protocols. The identities of Byzantine nodes
are unknown in advance by honest nodes in the network.
Sinc | [
5578,
1106,
162,
1155,
9221,
2193,
170,
12920,
1104,
149,
797,
119,
1967,
4062,
135,
121,
119,
126,
197,
161,
197,
15029,
1107,
161,
9221,
2193,
170,
12920,
1104,
149,
119,
4516,
2452,
1106,
1103,
6349,
3392,
11309,
1155,
117,
1103,
15029,
5578,
1106,
161,
2834,
6878,
3392,
1106,
149,
797,
119,
10321,
117,
1290,
4062,
135,
121,
119,
126,
197,
162,
197,
15029,
1107,
162,
1155,
9221,
2193,
170,
12920,
1104,
149,
117,
1103,
15029,
5578,
1106,
162,
2834,
6878,
3392,
1106,
149,
797,
119,
1109,
2443,
2834,
1518,
1231,
25665,
1443,
9506,
9108,
119,
1249,
1104,
1103,
1159,
1142,
2526,
1108,
1637,
117,
1103,
6315,
161,
20336,
3496,
2235,
1144,
1155,
15029,
5578,
1106,
1719,
170,
1423,
7414,
2162,
4721,
1104,
126,
15029,
117,
1137,
170,
7414,
2162,
4721,
1104,
1343,
126,
15029,
4882,
1141,
3908,
14372,
113,
3417,
1103,
3908,
14372,
1110,
1141,
118,
2191,
132,
15029,
1115,
5113,
1106,
1292,
2925,
7414,
2162,
1116,
1132,
2456,
1270,
107,
2972,
107,
117,
1290,
1152,
3392,
1228,
2776,
1121,
1103,
4160,
2443,
114,
119,
1109,
1603,
118,
1858,
2197,
1111,
1260,
118,
2129,
2734,
6808,
9147,
1106,
170,
2610,
117,
1133,
1253,
2675,
118,
1852,
117,
1423,
7414,
2162,
1105,
22767,
8985,
1103,
14372,
9298,
119,
2238,
1158,
1977,
5070,
1229,
21763,
1106,
170,
1207,
14372,
2190,
1110,
1136,
170,
3321,
2463,
113,
1290,
1112,
1770,
1112,
2490,
10052,
1113,
1103,
14372,
2190,
1254,
1977,
5070,
1209,
14926,
117,
1105,
1103,
2166,
2237,
176,
6718,
1197,
118,
22904,
8870,
1111,
107,
1353,
107,
2607,
1122,
1209,
1136,
13097,
1219,
1103,
10572,
114,
132,
2456,
1195,
1180,
1120,
1655,
1243,
170,
3112,
1871,
1118,
15975,
1115,
1103,
2443,
2834,
1243,
5342,
1107,
170,
2335,
10873,
1114,
2972,
119,
1109,
1378,
5837,
12917,
27466,
8223,
2646,
16847,
1103,
2463,
1106,
1178,
12038,
1106,
23073,
1115,
2335,
6379,
2834,
1243,
5342,
119,
3180,
12917,
1275,
119,
15463,
8661,
6787,
151,
1110,
170,
1804,
18005,
1104,
1103,
2443,
113,
178,
119,
174,
119,
117,
1103,
7414,
2162,
1104,
1451,
14372,
1107,
151,
1110,
4049,
1107,
151,
117,
1177,
1115,
1121,
1103,
7281,
1104,
1103,
15029,
1656,
1104,
151,
117,
151,
1110,
1103,
2072,
2443,
114,
1134,
2834,
1243,
5342,
1105,
2834,
13097,
119,
15463,
8661,
6787,
21902,
1110,
170,
14372,
1136,
1107,
151,
1216,
1115,
7414,
2162,
1182,
134,
196,
21902,
198,
859,
2249,
797,
117,
1187,
151,
797,
866,
151,
1105,
197,
151,
797,
197,
135,
186,
1182,
119,
1599,
151,
859,
196,
21902,
198,
2834,
1243,
5342,
1719,
119,
5096,
10008,
119,
1967,
151,
2834,
1243,
5342,
117,
1122,
1110,
1579,
2276,
1115,
1155,
1103,
15029,
1107,
151,
1209,
2028,
3106,
9221,
2193,
170,
1207,
21340,
1197,
119,
1967,
151,
2834,
13097,
117,
1155,
1103,
15029,
1107,
151,
1627,
1169,
1178,
3106,
9221,
2193,
1103,
1269,
21340,
1197,
117,
1177,
2028,
1175,
1110,
1199,
21340,
1197,
149,
1115,
3370,
3106,
9221,
2913,
1118,
1451,
14372,
1107,
151,
119,
4516,
1451,
14372,
1107,
151,
1209,
9221,
2193,
149,
117,
1105,
1290,
197,
7414,
2162,
1182,
858,
151,
197,
134,
197,
151
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
23,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
24,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"listening",
"to",
"Y",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
"β²",
".",
"Since",
"51",
">",
"0",
".",
"5",
"|",
"X",
"|",
"nodes",
"in",
"X",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
".",
"Thus",
"according",
"to",
"the",
"preferred",
"branch",
"protocol",
"all",
",",
"the",
"nodes",
"listening",
"to",
"X",
"cannot",
"switch",
"branch",
"to",
"L",
"β²",
".",
"Similarly",
",",
"since",
"51",
">",
"0",
".",
"5",
"|",
"Y",
"|",
"nodes",
"in",
"Y",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
",",
"the",
"nodes",
"listening",
"to",
"Y",
"cannot",
"switch",
"branch",
"to",
"L",
"β²",
".",
"The",
"network",
"cannot",
"ever",
"re",
"##join",
"without",
"manual",
"intervention",
".",
"As",
"of",
"the",
"time",
"this",
"paper",
"was",
"written",
",",
"the",
"recommended",
"X",
"##RP",
"trust",
"model",
"has",
"all",
"nodes",
"listening",
"to",
"either",
"a",
"single",
"UN",
"##L",
"consisting",
"of",
"5",
"nodes",
",",
"or",
"a",
"UN",
"##L",
"consisting",
"of",
"those",
"5",
"nodes",
"plus",
"one",
"extra",
"node",
"(",
"typically",
"the",
"extra",
"node",
"is",
"one",
"-",
"self",
";",
"nodes",
"that",
"listen",
"to",
"these",
"extended",
"UN",
"##L",
"##s",
"are",
"thus",
"called",
"\"",
"leaves",
"\"",
",",
"since",
"they",
"branch",
"off",
"slightly",
"from",
"the",
"core",
"network",
")",
".",
"The",
"short",
"-",
"term",
"plan",
"for",
"de",
"-",
"central",
"##ization",
"involves",
"expanding",
"to",
"a",
"larger",
",",
"but",
"still",
"agreed",
"-",
"upon",
",",
"single",
"UN",
"##L",
"and",
"divers",
"##ifying",
"the",
"node",
"operators",
".",
"Los",
"##ing",
"forward",
"progress",
"while",
"adjusting",
"to",
"a",
"new",
"node",
"list",
"is",
"not",
"a",
"huge",
"problem",
"(",
"since",
"as",
"soon",
"as",
"everyone",
"agrees",
"on",
"the",
"node",
"list",
"again",
"forward",
"progress",
"will",
"resume",
",",
"and",
"the",
"previous",
"section",
"g",
"##ua",
"##r",
"-",
"ant",
"##ees",
"for",
"\"",
"small",
"\"",
"changes",
"it",
"will",
"not",
"fork",
"during",
"the",
"interim",
")",
";",
"thus",
"we",
"could",
"at",
"least",
"get",
"a",
"positive",
"result",
"by",
"proving",
"that",
"the",
"network",
"cannot",
"get",
"stuck",
"in",
"a",
"complete",
"graph",
"with",
"leaves",
".",
"The",
"following",
"le",
"##mma",
"si",
"##mp",
"##li",
"##fies",
"the",
"problem",
"to",
"only",
"needing",
"to",
"verify",
"that",
"complete",
"networks",
"cannot",
"get",
"stuck",
".",
"Le",
"##mma",
"10",
".",
"Su",
"##pp",
"##ose",
"N",
"is",
"a",
"closed",
"subset",
"of",
"the",
"network",
"(",
"i",
".",
"e",
".",
",",
"the",
"UN",
"##L",
"of",
"every",
"node",
"in",
"N",
"is",
"contained",
"in",
"N",
",",
"so",
"that",
"from",
"the",
"perspective",
"of",
"the",
"nodes",
"inside",
"of",
"N",
",",
"N",
"is",
"the",
"entire",
"network",
")",
"which",
"cannot",
"get",
"stuck",
"and",
"cannot",
"fork",
".",
"Su",
"##pp",
"##ose",
"Pi",
"is",
"a",
"node",
"not",
"in",
"N",
"such",
"that",
"UN",
"##L",
"##i",
"=",
"{",
"Pi",
"}",
"βͺ",
"##N",
"β²",
",",
"where",
"N",
"β²",
"β",
"N",
"and",
"|",
"N",
"β²",
"|",
">",
"q",
"##i",
".",
"Then",
"N",
"βͺ",
"{",
"Pi",
"}",
"cannot",
"get",
"stuck",
"either",
".",
"Pro",
"##of",
".",
"Since",
"N",
"cannot",
"get",
"stuck",
",",
"it",
"is",
"always",
"true",
"that",
"all",
"the",
"nodes",
"in",
"N",
"will",
"eventually",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
".",
"Since",
"N",
"cannot",
"fork",
",",
"all",
"the",
"nodes",
"in",
"N",
"19",
"can",
"only",
"fully",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
",",
"so",
"eventually",
"there",
"is",
"some",
"ledge",
"##r",
"L",
"that",
"gets",
"fully",
"valid",
"##ated",
"by",
"every",
"node",
"in",
"N",
".",
"Thus",
"every",
"node",
"in",
"N",
"will",
"valid",
"##ate",
"L",
",",
"and",
"since",
"|",
"UN",
"##L",
"##i",
"β©",
"N",
"|",
"=",
"|",
"N"
] | Analysis of the XRP Ledger Consensus Protocol | 195 |
valuate the correctness of XRP LCP, we model the peer-to-
peer network as if it were controlled by a network adversary that can behave
arbitrarily. The adversary is controls the delivery order of all messages, as well
as at most ti nodes in UNLi for any correct node Pi. We assume though that
the adversary is computationally bounded; in particular, it is unable to break
generally accepted cryptographic protocols. The identities of Byzantine nodes
are unknown in advance by honest nodes in the network.
Sinc | [
5578,
1106,
162,
1155,
9221,
2193,
170,
12920,
1104,
149,
797,
119,
1967,
4062,
135,
121,
119,
126,
197,
161,
197,
15029,
1107,
161,
9221,
2193,
170,
12920,
1104,
149,
119,
4516,
2452,
1106,
1103,
6349,
3392,
11309,
1155,
117,
1103,
15029,
5578,
1106,
161,
2834,
6878,
3392,
1106,
149,
797,
119,
10321,
117,
1290,
4062,
135,
121,
119,
126,
197,
162,
197,
15029,
1107,
162,
1155,
9221,
2193,
170,
12920,
1104,
149,
117,
1103,
15029,
5578,
1106,
162,
2834,
6878,
3392,
1106,
149,
797,
119,
1109,
2443,
2834,
1518,
1231,
25665,
1443,
9506,
9108,
119,
1249,
1104,
1103,
1159,
1142,
2526,
1108,
1637,
117,
1103,
6315,
161,
20336,
3496,
2235,
1144,
1155,
15029,
5578,
1106,
1719,
170,
1423,
7414,
2162,
4721,
1104,
126,
15029,
117,
1137,
170,
7414,
2162,
4721,
1104,
1343,
126,
15029,
4882,
1141,
3908,
14372,
113,
3417,
1103,
3908,
14372,
1110,
1141,
118,
2191,
132,
15029,
1115,
5113,
1106,
1292,
2925,
7414,
2162,
1116,
1132,
2456,
1270,
107,
2972,
107,
117,
1290,
1152,
3392,
1228,
2776,
1121,
1103,
4160,
2443,
114,
119,
1109,
1603,
118,
1858,
2197,
1111,
1260,
118,
2129,
2734,
6808,
9147,
1106,
170,
2610,
117,
1133,
1253,
2675,
118,
1852,
117,
1423,
7414,
2162,
1105,
22767,
8985,
1103,
14372,
9298,
119,
2238,
1158,
1977,
5070,
1229,
21763,
1106,
170,
1207,
14372,
2190,
1110,
1136,
170,
3321,
2463,
113,
1290,
1112,
1770,
1112,
2490,
10052,
1113,
1103,
14372,
2190,
1254,
1977,
5070,
1209,
14926,
117,
1105,
1103,
2166,
2237,
176,
6718,
1197,
118,
22904,
8870,
1111,
107,
1353,
107,
2607,
1122,
1209,
1136,
13097,
1219,
1103,
10572,
114,
132,
2456,
1195,
1180,
1120,
1655,
1243,
170,
3112,
1871,
1118,
15975,
1115,
1103,
2443,
2834,
1243,
5342,
1107,
170,
2335,
10873,
1114,
2972,
119,
1109,
1378,
5837,
12917,
27466,
8223,
2646,
16847,
1103,
2463,
1106,
1178,
12038,
1106,
23073,
1115,
2335,
6379,
2834,
1243,
5342,
119,
3180,
12917,
1275,
119,
15463,
8661,
6787,
151,
1110,
170,
1804,
18005,
1104,
1103,
2443,
113,
178,
119,
174,
119,
117,
1103,
7414,
2162,
1104,
1451,
14372,
1107,
151,
1110,
4049,
1107,
151,
117,
1177,
1115,
1121,
1103,
7281,
1104,
1103,
15029,
1656,
1104,
151,
117,
151,
1110,
1103,
2072,
2443,
114,
1134,
2834,
1243,
5342,
1105,
2834,
13097,
119,
15463,
8661,
6787,
21902,
1110,
170,
14372,
1136,
1107,
151,
1216,
1115,
7414,
2162,
1182,
134,
196,
21902,
198,
859,
2249,
797,
117,
1187,
151,
797,
866,
151,
1105,
197,
151,
797,
197,
135,
186,
1182,
119,
1599,
151,
859,
196,
21902,
198,
2834,
1243,
5342,
1719,
119,
5096,
10008,
119,
1967,
151,
2834,
1243,
5342,
117,
1122,
1110,
1579,
2276,
1115,
1155,
1103,
15029,
1107,
151,
1209,
2028,
3106,
9221,
2193,
170,
1207,
21340,
1197,
119,
1967,
151,
2834,
13097,
117,
1155,
1103,
15029,
1107,
151,
1627,
1169,
1178,
3106,
9221,
2193,
1103,
1269,
21340,
1197,
117,
1177,
2028,
1175,
1110,
1199,
21340,
1197,
149,
1115,
3370,
3106,
9221,
2913,
1118,
1451,
14372,
1107,
151,
119,
4516,
1451,
14372,
1107,
151,
1209,
9221,
2193,
149,
117,
1105,
1290,
197,
7414,
2162,
1182,
858,
151,
197,
134,
197,
151
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"listening",
"to",
"Y",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
"β²",
".",
"Since",
"51",
">",
"0",
".",
"5",
"|",
"X",
"|",
"nodes",
"in",
"X",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
".",
"Thus",
"according",
"to",
"the",
"preferred",
"branch",
"protocol",
"all",
",",
"the",
"nodes",
"listening",
"to",
"X",
"cannot",
"switch",
"branch",
"to",
"L",
"β²",
".",
"Similarly",
",",
"since",
"51",
">",
"0",
".",
"5",
"|",
"Y",
"|",
"nodes",
"in",
"Y",
"all",
"valid",
"##ate",
"a",
"descendant",
"of",
"L",
",",
"the",
"nodes",
"listening",
"to",
"Y",
"cannot",
"switch",
"branch",
"to",
"L",
"β²",
".",
"The",
"network",
"cannot",
"ever",
"re",
"##join",
"without",
"manual",
"intervention",
".",
"As",
"of",
"the",
"time",
"this",
"paper",
"was",
"written",
",",
"the",
"recommended",
"X",
"##RP",
"trust",
"model",
"has",
"all",
"nodes",
"listening",
"to",
"either",
"a",
"single",
"UN",
"##L",
"consisting",
"of",
"5",
"nodes",
",",
"or",
"a",
"UN",
"##L",
"consisting",
"of",
"those",
"5",
"nodes",
"plus",
"one",
"extra",
"node",
"(",
"typically",
"the",
"extra",
"node",
"is",
"one",
"-",
"self",
";",
"nodes",
"that",
"listen",
"to",
"these",
"extended",
"UN",
"##L",
"##s",
"are",
"thus",
"called",
"\"",
"leaves",
"\"",
",",
"since",
"they",
"branch",
"off",
"slightly",
"from",
"the",
"core",
"network",
")",
".",
"The",
"short",
"-",
"term",
"plan",
"for",
"de",
"-",
"central",
"##ization",
"involves",
"expanding",
"to",
"a",
"larger",
",",
"but",
"still",
"agreed",
"-",
"upon",
",",
"single",
"UN",
"##L",
"and",
"divers",
"##ifying",
"the",
"node",
"operators",
".",
"Los",
"##ing",
"forward",
"progress",
"while",
"adjusting",
"to",
"a",
"new",
"node",
"list",
"is",
"not",
"a",
"huge",
"problem",
"(",
"since",
"as",
"soon",
"as",
"everyone",
"agrees",
"on",
"the",
"node",
"list",
"again",
"forward",
"progress",
"will",
"resume",
",",
"and",
"the",
"previous",
"section",
"g",
"##ua",
"##r",
"-",
"ant",
"##ees",
"for",
"\"",
"small",
"\"",
"changes",
"it",
"will",
"not",
"fork",
"during",
"the",
"interim",
")",
";",
"thus",
"we",
"could",
"at",
"least",
"get",
"a",
"positive",
"result",
"by",
"proving",
"that",
"the",
"network",
"cannot",
"get",
"stuck",
"in",
"a",
"complete",
"graph",
"with",
"leaves",
".",
"The",
"following",
"le",
"##mma",
"si",
"##mp",
"##li",
"##fies",
"the",
"problem",
"to",
"only",
"needing",
"to",
"verify",
"that",
"complete",
"networks",
"cannot",
"get",
"stuck",
".",
"Le",
"##mma",
"10",
".",
"Su",
"##pp",
"##ose",
"N",
"is",
"a",
"closed",
"subset",
"of",
"the",
"network",
"(",
"i",
".",
"e",
".",
",",
"the",
"UN",
"##L",
"of",
"every",
"node",
"in",
"N",
"is",
"contained",
"in",
"N",
",",
"so",
"that",
"from",
"the",
"perspective",
"of",
"the",
"nodes",
"inside",
"of",
"N",
",",
"N",
"is",
"the",
"entire",
"network",
")",
"which",
"cannot",
"get",
"stuck",
"and",
"cannot",
"fork",
".",
"Su",
"##pp",
"##ose",
"Pi",
"is",
"a",
"node",
"not",
"in",
"N",
"such",
"that",
"UN",
"##L",
"##i",
"=",
"{",
"Pi",
"}",
"βͺ",
"##N",
"β²",
",",
"where",
"N",
"β²",
"β",
"N",
"and",
"|",
"N",
"β²",
"|",
">",
"q",
"##i",
".",
"Then",
"N",
"βͺ",
"{",
"Pi",
"}",
"cannot",
"get",
"stuck",
"either",
".",
"Pro",
"##of",
".",
"Since",
"N",
"cannot",
"get",
"stuck",
",",
"it",
"is",
"always",
"true",
"that",
"all",
"the",
"nodes",
"in",
"N",
"will",
"eventually",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
".",
"Since",
"N",
"cannot",
"fork",
",",
"all",
"the",
"nodes",
"in",
"N",
"19",
"can",
"only",
"fully",
"valid",
"##ate",
"the",
"same",
"ledge",
"##r",
",",
"so",
"eventually",
"there",
"is",
"some",
"ledge",
"##r",
"L",
"that",
"gets",
"fully",
"valid",
"##ated",
"by",
"every",
"node",
"in",
"N",
".",
"Thus",
"every",
"node",
"in",
"N",
"will",
"valid",
"##ate",
"L",
",",
"and",
"since",
"|",
"UN",
"##L",
"##i",
"β©",
"N",
"|",
"=",
"|",
"N"
] | Analysis of the XRP Ledger Consensus Protocol | 196 |
e atomic broadcast is a variant of consensus, by the FLP result [5] we
cannot guarantee forward progress in the presence of arbitrary asynchrony and
faulty nodes. Instead, we assume a form of "weak asynchrony": safety should
hold under arbitrary asynchrony, but censorship resilience is only guaranteed to
hold under the assumption that the network is eventually civil, meaning that
messages are delivered within some protocol-specified maximum delay bound
and no nodes are faulty.
In order to help enforce th | [
797,
197,
135,
186,
1182,
117,
21902,
1169,
3106,
9221,
2193,
149,
1112,
1218,
119,
4516,
1122,
1110,
1579,
2276,
1115,
21902,
1209,
2028,
3106,
9221,
2193,
170,
1207,
21340,
1197,
117,
1177,
21902,
2834,
1243,
5342,
119,
15840,
16996,
1429,
119,
15463,
8661,
6787,
1111,
1155,
15029,
1103,
7414,
2162,
186,
11848,
5697,
1110,
1383,
1106,
183,
25532,
100,
113,
183,
25532,
122,
114,
120,
180,
100,
1111,
1199,
18157,
180,
119,
161,
20336,
149,
13113,
2834,
1243,
5342,
1107,
170,
2443,
4721,
1104,
170,
1423,
2675,
118,
1852,
7414,
2162,
161,
1104,
2060,
1120,
1655,
180,
1373,
1114,
1126,
16439,
1295,
1104,
7404,
9221,
11664,
119,
5096,
10008,
119,
1370,
1251,
7404,
9221,
6579,
21902,
117,
11437,
134,
197,
161,
197,
116,
122,
132,
1290,
186,
1182,
134,
197,
161,
197,
116,
122,
25532,
100,
113,
197,
161,
197,
116,
122,
25532,
122,
114,
120,
180,
100,
134,
197,
161,
197,
116,
122,
25532,
100,
197,
161,
197,
120,
180,
100,
127,
197,
161,
197,
117,
1118,
5837,
12917,
1275,
1122,
28117,
3101,
18117,
1106,
1437,
1115,
2335,
6379,
2834,
1243,
5342,
119,
4516,
6699,
1175,
1110,
170,
1423,
2675,
118,
1852,
7414,
2162,
3190,
119,
15463,
8661,
6787,
1107,
1199,
1668,
187,
1155,
9221,
1891,
7416,
1132,
4653,
1976,
1536,
1177,
1115,
8377,
3300,
118,
2912,
3486,
1105,
1451,
14372,
5302,
1451,
1168,
14372,
112,
188,
9221,
6006,
1121,
1668,
187,
119,
1599,
1103,
6349,
3392,
9932,
1209,
1260,
2083,
25685,
5668,
2716,
4684,
1155,
15029,
2135,
1103,
1211,
1927,
21340,
1197,
149,
119,
4516,
1107,
1103,
1397,
1668,
1155,
15029,
1209,
9221,
2193,
170,
2027,
1104,
149,
119,
1409,
7416,
1850,
1219,
3687,
24851,
1891,
1132,
4653,
188,
27250,
8167,
23038,
1361,
1193,
117,
1173,
1155,
15029,
1267,
1103,
1269,
10698,
1121,
1668,
122,
1105,
1719,
1155,
6300,
3687,
24851,
1891,
1114,
1103,
1269,
21340,
1197,
113,
1191,
1199,
13618,
1383,
1110,
3416,
1114,
2908,
110,
1104,
1103,
15029,
1107,
161,
114,
1137,
1950,
3076,
1147,
5835,
1111,
1668,
123,
1260,
2083,
25685,
5668,
2716,
1121,
1103,
1269,
21146,
2155,
118,
2393,
1116,
1121,
1668,
122,
117,
1177,
1155,
15029,
17794,
1103,
1269,
1383,
1104,
14409,
1107,
1668,
123,
117,
1105,
1155,
15029,
1817,
3687,
24851,
1891,
1114,
1103,
1269,
1383,
1104,
14409,
119,
4516,
1451,
14372,
12295,
1116,
170,
9221,
1891,
1111,
1103,
1269,
21340,
1197,
117,
1105,
1155,
15029,
3106,
9221,
2193,
1115,
21340,
1197,
119,
126,
16752,
1665,
17855,
1284,
1138,
1549,
170,
6448,
6136,
1105,
17213,
3622,
1104,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
117,
1134,
1110,
170,
11309,
1111,
3634,
10923,
1443,
8462,
3311,
1104,
2443,
6635,
119,
3458,
1250,
5663,
1116,
2988,
3622,
1107,
164,
1275,
117,
122,
166,
119,
1284,
1437,
1107,
10384,
129,
1115,
4986,
135,
3078,
110,
3311,
1113,
6635,
1110,
1834,
1106,
4989,
2443,
3429,
119,
1130,
1103,
7458,
1692,
1104,
170,
1423,
9147,
7414,
2162,
1114,
2972,
117,
10384,
1429,
2196,
1195,
1169,
1579,
1294,
1977,
5070,
1219,
6461,
1165,
1185,
15029,
1132,
6088,
1183,
1105,
2443,
7416,
1132,
4653,
1114,
10350
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
0,
5,
6,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
15,
16,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
6,
6,
6,
6,
0,
0,
0,
0,
5,
0,
5,
6,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
21,
22,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0
] | [
"β²",
"|",
">",
"q",
"##i",
",",
"Pi",
"can",
"fully",
"valid",
"##ate",
"L",
"as",
"well",
".",
"Thus",
"it",
"is",
"always",
"true",
"that",
"Pi",
"will",
"eventually",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
",",
"so",
"Pi",
"cannot",
"get",
"stuck",
".",
"Theo",
"##rem",
"11",
".",
"Su",
"##pp",
"##ose",
"for",
"all",
"nodes",
"the",
"UN",
"##L",
"q",
"##uo",
"##rum",
"is",
"set",
"to",
"n",
"##β",
"[UNK]",
"(",
"n",
"##β",
"1",
")",
"/",
"k",
"[UNK]",
"for",
"some",
"integer",
"k",
".",
"X",
"##RP",
"L",
"##CP",
"cannot",
"get",
"stuck",
"in",
"a",
"network",
"consisting",
"of",
"a",
"single",
"agreed",
"-",
"upon",
"UN",
"##L",
"X",
"of",
"size",
"at",
"least",
"k",
"along",
"with",
"an",
"arbitrary",
"number",
"of",
"leaf",
"valid",
"##ators",
".",
"Pro",
"##of",
".",
"For",
"any",
"leaf",
"valid",
"##ator",
"Pi",
",",
"ni",
"=",
"|",
"X",
"|",
"+",
"1",
";",
"since",
"q",
"##i",
"=",
"|",
"X",
"|",
"+",
"1",
"##β",
"[UNK]",
"(",
"|",
"X",
"|",
"+",
"1",
"##β",
"1",
")",
"/",
"k",
"[UNK]",
"=",
"|",
"X",
"|",
"+",
"1",
"##β",
"[UNK]",
"|",
"X",
"|",
"/",
"k",
"[UNK]",
"6",
"|",
"X",
"|",
",",
"by",
"le",
"##mma",
"10",
"it",
"su",
"##ff",
"##ices",
"to",
"show",
"that",
"complete",
"networks",
"cannot",
"get",
"stuck",
".",
"Thus",
"suppose",
"there",
"is",
"a",
"single",
"agreed",
"-",
"upon",
"UN",
"##L",
"##X",
".",
"Su",
"##pp",
"##ose",
"in",
"some",
"round",
"r",
"all",
"valid",
"##ation",
"messages",
"are",
"delivered",
"quickly",
"enough",
"so",
"that",
"Byzantine",
"account",
"-",
"ability",
"holds",
"and",
"every",
"node",
"sees",
"every",
"other",
"node",
"'",
"s",
"valid",
"##ations",
"from",
"round",
"r",
".",
"Then",
"the",
"preferred",
"branch",
"algorithm",
"will",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"push",
"all",
"nodes",
"onto",
"the",
"most",
"popular",
"ledge",
"##r",
"L",
".",
"Thus",
"in",
"the",
"next",
"round",
"all",
"nodes",
"will",
"valid",
"##ate",
"a",
"child",
"of",
"L",
".",
"If",
"messages",
"sent",
"during",
"del",
"##iber",
"##ation",
"are",
"delivered",
"s",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
",",
"then",
"all",
"nodes",
"see",
"the",
"same",
"proposals",
"from",
"round",
"1",
"and",
"either",
"all",
"exit",
"del",
"##iber",
"##ation",
"with",
"the",
"same",
"ledge",
"##r",
"(",
"if",
"some",
"transaction",
"set",
"is",
"shared",
"with",
"80",
"%",
"of",
"the",
"nodes",
"in",
"X",
")",
"or",
"else",
"build",
"their",
"proposal",
"for",
"round",
"2",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"from",
"the",
"same",
"prop",
"##os",
"-",
"al",
"##s",
"from",
"round",
"1",
",",
"so",
"all",
"nodes",
"propose",
"the",
"same",
"set",
"of",
"transactions",
"in",
"round",
"2",
",",
"and",
"all",
"nodes",
"leave",
"del",
"##iber",
"##ation",
"with",
"the",
"same",
"set",
"of",
"transactions",
".",
"Thus",
"every",
"node",
"submit",
"##s",
"a",
"valid",
"##ation",
"for",
"the",
"same",
"ledge",
"##r",
",",
"and",
"all",
"nodes",
"fully",
"valid",
"##ate",
"that",
"ledge",
"##r",
".",
"5",
"Con",
"##c",
"##lusion",
"We",
"have",
"given",
"a",
"detailed",
"description",
"and",
"thorough",
"analysis",
"of",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
",",
"which",
"is",
"a",
"protocol",
"for",
"reaching",
"consensus",
"without",
"universal",
"agreement",
"of",
"network",
"participants",
".",
"Our",
"work",
"correct",
"##s",
"prior",
"analysis",
"in",
"[",
"10",
",",
"1",
"]",
".",
"We",
"show",
"in",
"theorem",
"8",
"that",
"roughly",
">",
"90",
"%",
"agreement",
"on",
"participants",
"is",
"needed",
"to",
"ensure",
"network",
"safety",
".",
"In",
"the",
"restricted",
"case",
"of",
"a",
"single",
"expanding",
"UN",
"##L",
"with",
"leaves",
",",
"theorem",
"11",
"shows",
"we",
"can",
"always",
"make",
"forward",
"progress",
"during",
"periods",
"when",
"no",
"nodes",
"are",
"fault",
"##y",
"and",
"network",
"messages",
"are",
"delivered",
"with",
"bounded"
] | Analysis of the XRP Ledger Consensus Protocol | 197 |
e atomic broadcast is a variant of consensus, by the FLP result [5] we
cannot guarantee forward progress in the presence of arbitrary asynchrony and
faulty nodes. Instead, we assume a form of "weak asynchrony": safety should
hold under arbitrary asynchrony, but censorship resilience is only guaranteed to
hold under the assumption that the network is eventually civil, meaning that
messages are delivered within some protocol-specified maximum delay bound
and no nodes are faulty.
In order to help enforce th | [
797,
197,
135,
186,
1182,
117,
21902,
1169,
3106,
9221,
2193,
149,
1112,
1218,
119,
4516,
1122,
1110,
1579,
2276,
1115,
21902,
1209,
2028,
3106,
9221,
2193,
170,
1207,
21340,
1197,
117,
1177,
21902,
2834,
1243,
5342,
119,
15840,
16996,
1429,
119,
15463,
8661,
6787,
1111,
1155,
15029,
1103,
7414,
2162,
186,
11848,
5697,
1110,
1383,
1106,
183,
25532,
100,
113,
183,
25532,
122,
114,
120,
180,
100,
1111,
1199,
18157,
180,
119,
161,
20336,
149,
13113,
2834,
1243,
5342,
1107,
170,
2443,
4721,
1104,
170,
1423,
2675,
118,
1852,
7414,
2162,
161,
1104,
2060,
1120,
1655,
180,
1373,
1114,
1126,
16439,
1295,
1104,
7404,
9221,
11664,
119,
5096,
10008,
119,
1370,
1251,
7404,
9221,
6579,
21902,
117,
11437,
134,
197,
161,
197,
116,
122,
132,
1290,
186,
1182,
134,
197,
161,
197,
116,
122,
25532,
100,
113,
197,
161,
197,
116,
122,
25532,
122,
114,
120,
180,
100,
134,
197,
161,
197,
116,
122,
25532,
100,
197,
161,
197,
120,
180,
100,
127,
197,
161,
197,
117,
1118,
5837,
12917,
1275,
1122,
28117,
3101,
18117,
1106,
1437,
1115,
2335,
6379,
2834,
1243,
5342,
119,
4516,
6699,
1175,
1110,
170,
1423,
2675,
118,
1852,
7414,
2162,
3190,
119,
15463,
8661,
6787,
1107,
1199,
1668,
187,
1155,
9221,
1891,
7416,
1132,
4653,
1976,
1536,
1177,
1115,
8377,
3300,
118,
2912,
3486,
1105,
1451,
14372,
5302,
1451,
1168,
14372,
112,
188,
9221,
6006,
1121,
1668,
187,
119,
1599,
1103,
6349,
3392,
9932,
1209,
1260,
2083,
25685,
5668,
2716,
4684,
1155,
15029,
2135,
1103,
1211,
1927,
21340,
1197,
149,
119,
4516,
1107,
1103,
1397,
1668,
1155,
15029,
1209,
9221,
2193,
170,
2027,
1104,
149,
119,
1409,
7416,
1850,
1219,
3687,
24851,
1891,
1132,
4653,
188,
27250,
8167,
23038,
1361,
1193,
117,
1173,
1155,
15029,
1267,
1103,
1269,
10698,
1121,
1668,
122,
1105,
1719,
1155,
6300,
3687,
24851,
1891,
1114,
1103,
1269,
21340,
1197,
113,
1191,
1199,
13618,
1383,
1110,
3416,
1114,
2908,
110,
1104,
1103,
15029,
1107,
161,
114,
1137,
1950,
3076,
1147,
5835,
1111,
1668,
123,
1260,
2083,
25685,
5668,
2716,
1121,
1103,
1269,
21146,
2155,
118,
2393,
1116,
1121,
1668,
122,
117,
1177,
1155,
15029,
17794,
1103,
1269,
1383,
1104,
14409,
1107,
1668,
123,
117,
1105,
1155,
15029,
1817,
3687,
24851,
1891,
1114,
1103,
1269,
1383,
1104,
14409,
119,
4516,
1451,
14372,
12295,
1116,
170,
9221,
1891,
1111,
1103,
1269,
21340,
1197,
117,
1105,
1155,
15029,
3106,
9221,
2193,
1115,
21340,
1197,
119,
126,
16752,
1665,
17855,
1284,
1138,
1549,
170,
6448,
6136,
1105,
17213,
3622,
1104,
1103,
161,
20336,
18657,
2895,
16752,
3792,
14410,
17580,
117,
1134,
1110,
170,
11309,
1111,
3634,
10923,
1443,
8462,
3311,
1104,
2443,
6635,
119,
3458,
1250,
5663,
1116,
2988,
3622,
1107,
164,
1275,
117,
122,
166,
119,
1284,
1437,
1107,
10384,
129,
1115,
4986,
135,
3078,
110,
3311,
1113,
6635,
1110,
1834,
1106,
4989,
2443,
3429,
119,
1130,
1103,
7458,
1692,
1104,
170,
1423,
9147,
7414,
2162,
1114,
2972,
117,
10384,
1429,
2196,
1195,
1169,
1579,
1294,
1977,
5070,
1219,
6461,
1165,
1185,
15029,
1132,
6088,
1183,
1105,
2443,
7416,
1132,
4653,
1114,
10350
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
19,
20,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1,
2,
2,
2,
5,
6,
6,
5,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | [
"β²",
"|",
">",
"q",
"##i",
",",
"Pi",
"can",
"fully",
"valid",
"##ate",
"L",
"as",
"well",
".",
"Thus",
"it",
"is",
"always",
"true",
"that",
"Pi",
"will",
"eventually",
"fully",
"valid",
"##ate",
"a",
"new",
"ledge",
"##r",
",",
"so",
"Pi",
"cannot",
"get",
"stuck",
".",
"Theo",
"##rem",
"11",
".",
"Su",
"##pp",
"##ose",
"for",
"all",
"nodes",
"the",
"UN",
"##L",
"q",
"##uo",
"##rum",
"is",
"set",
"to",
"n",
"##β",
"[UNK]",
"(",
"n",
"##β",
"1",
")",
"/",
"k",
"[UNK]",
"for",
"some",
"integer",
"k",
".",
"X",
"##RP",
"L",
"##CP",
"cannot",
"get",
"stuck",
"in",
"a",
"network",
"consisting",
"of",
"a",
"single",
"agreed",
"-",
"upon",
"UN",
"##L",
"X",
"of",
"size",
"at",
"least",
"k",
"along",
"with",
"an",
"arbitrary",
"number",
"of",
"leaf",
"valid",
"##ators",
".",
"Pro",
"##of",
".",
"For",
"any",
"leaf",
"valid",
"##ator",
"Pi",
",",
"ni",
"=",
"|",
"X",
"|",
"+",
"1",
";",
"since",
"q",
"##i",
"=",
"|",
"X",
"|",
"+",
"1",
"##β",
"[UNK]",
"(",
"|",
"X",
"|",
"+",
"1",
"##β",
"1",
")",
"/",
"k",
"[UNK]",
"=",
"|",
"X",
"|",
"+",
"1",
"##β",
"[UNK]",
"|",
"X",
"|",
"/",
"k",
"[UNK]",
"6",
"|",
"X",
"|",
",",
"by",
"le",
"##mma",
"10",
"it",
"su",
"##ff",
"##ices",
"to",
"show",
"that",
"complete",
"networks",
"cannot",
"get",
"stuck",
".",
"Thus",
"suppose",
"there",
"is",
"a",
"single",
"agreed",
"-",
"upon",
"UN",
"##L",
"##X",
".",
"Su",
"##pp",
"##ose",
"in",
"some",
"round",
"r",
"all",
"valid",
"##ation",
"messages",
"are",
"delivered",
"quickly",
"enough",
"so",
"that",
"Byzantine",
"account",
"-",
"ability",
"holds",
"and",
"every",
"node",
"sees",
"every",
"other",
"node",
"'",
"s",
"valid",
"##ations",
"from",
"round",
"r",
".",
"Then",
"the",
"preferred",
"branch",
"algorithm",
"will",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"push",
"all",
"nodes",
"onto",
"the",
"most",
"popular",
"ledge",
"##r",
"L",
".",
"Thus",
"in",
"the",
"next",
"round",
"all",
"nodes",
"will",
"valid",
"##ate",
"a",
"child",
"of",
"L",
".",
"If",
"messages",
"sent",
"during",
"del",
"##iber",
"##ation",
"are",
"delivered",
"s",
"##ync",
"##hr",
"##ono",
"##us",
"##ly",
",",
"then",
"all",
"nodes",
"see",
"the",
"same",
"proposals",
"from",
"round",
"1",
"and",
"either",
"all",
"exit",
"del",
"##iber",
"##ation",
"with",
"the",
"same",
"ledge",
"##r",
"(",
"if",
"some",
"transaction",
"set",
"is",
"shared",
"with",
"80",
"%",
"of",
"the",
"nodes",
"in",
"X",
")",
"or",
"else",
"build",
"their",
"proposal",
"for",
"round",
"2",
"de",
"##ter",
"##mini",
"##stic",
"##ally",
"from",
"the",
"same",
"prop",
"##os",
"-",
"al",
"##s",
"from",
"round",
"1",
",",
"so",
"all",
"nodes",
"propose",
"the",
"same",
"set",
"of",
"transactions",
"in",
"round",
"2",
",",
"and",
"all",
"nodes",
"leave",
"del",
"##iber",
"##ation",
"with",
"the",
"same",
"set",
"of",
"transactions",
".",
"Thus",
"every",
"node",
"submit",
"##s",
"a",
"valid",
"##ation",
"for",
"the",
"same",
"ledge",
"##r",
",",
"and",
"all",
"nodes",
"fully",
"valid",
"##ate",
"that",
"ledge",
"##r",
".",
"5",
"Con",
"##c",
"##lusion",
"We",
"have",
"given",
"a",
"detailed",
"description",
"and",
"thorough",
"analysis",
"of",
"the",
"X",
"##RP",
"Led",
"##ger",
"Con",
"##sen",
"##sus",
"Protocol",
",",
"which",
"is",
"a",
"protocol",
"for",
"reaching",
"consensus",
"without",
"universal",
"agreement",
"of",
"network",
"participants",
".",
"Our",
"work",
"correct",
"##s",
"prior",
"analysis",
"in",
"[",
"10",
",",
"1",
"]",
".",
"We",
"show",
"in",
"theorem",
"8",
"that",
"roughly",
">",
"90",
"%",
"agreement",
"on",
"participants",
"is",
"needed",
"to",
"ensure",
"network",
"safety",
".",
"In",
"the",
"restricted",
"case",
"of",
"a",
"single",
"expanding",
"UN",
"##L",
"with",
"leaves",
",",
"theorem",
"11",
"shows",
"we",
"can",
"always",
"make",
"forward",
"progress",
"during",
"periods",
"when",
"no",
"nodes",
"are",
"fault",
"##y",
"and",
"network",
"messages",
"are",
"delivered",
"with",
"bounded"
] | Analysis of the XRP Ledger Consensus Protocol | 198 |
e bounded delay in the XRP ledger implemen-
tation, several heuristics are used to identify lagging nodes, prevent excessive
flooding of messages and route traffic through the network. Protocol parameters
also define maximum delays on different trusted messages in an attempt to aid
liveness. Although we ignore these details to simplify the presentation below, we
stress that they are important practical considerations in the actual implemen-
tation and control the real world performance of the algorithm. T | [
8513,
119,
1130,
1103,
1167,
1704,
1692,
1114,
1256,
3137,
19855,
1104,
6635,
117,
1195,
2834,
11865,
1115,
1103,
2443,
2228,
1977,
5070,
119,
1135,
1110,
1126,
1501,
2304,
2480,
1103,
6664,
19235,
3879,
1107,
10384,
129,
1169,
1129,
4725,
1118,
170,
1167,
6448,
9486,
1104,
1103,
3496,
22411,
1104,
1103,
2443,
119,
138,
1167,
8277,
3879,
1115,
1674,
1136,
2566,
1321,
1154,
3300,
3111,
15868,
19235,
1116,
1133,
1145,
1103,
1236,
1107,
1134,
7416,
4235,
18814,
1194,
1103,
2443,
1547,
1138,
3209,
1111,
2368,
170,
1167,
10515,
3879,
1111,
11865,
1158,
3429,
119,
18872,
117,
1195,
1547,
1129,
1682,
1106,
24228,
1103,
3496,
2401,
1406,
1106,
1618,
4137,
2740,
1165,
3687,
24851,
1891,
1169,
8693,
117,
1134,
1107,
1885,
1547,
2621,
170,
1167,
16686,
4287,
1113,
1977,
5070,
119,
1966,
1195,
1138,
2602,
1115,
161,
20336,
149,
13113,
1110,
5250,
2497,
4999,
2914,
1114,
1103,
1954,
1105,
1485,
118,
2174,
2443,
4413,
117,
1107,
1126,
2661,
1106,
27295,
1199,
1104,
1157,
1603,
118,
1909,
1116,
117,
1107,
1103,
26563,
2526,
164,
127,
166,
1195,
1675,
1126,
4174,
10923,
11309,
1270,
3291,
26443,
119,
12250,
1106,
161,
20336,
149,
13113,
117,
3291,
26443,
1169,
1145,
1129,
1215,
1107,
6379,
1115,
2960,
6029,
3311,
1113,
6635,
1137,
3496,
117,
1133,
2228,
1977,
5070,
1120,
170,
6386,
2603,
1107,
1103,
2915,
1104,
4177,
21073,
1181,
8377,
21688,
1105,
170,
26281,
1182,
118,
189,
23728,
1112,
27250,
8167,
10031,
119,
1135,
1178,
2993,
135,
2539,
110,
19235,
1106,
1801,
1103,
161,
20336,
149,
13113,
3429,
15745,
1116,
119,
3291,
26443,
1145,
1144,
1317,
1168,
4625,
1115,
1294,
1122,
17633,
1106,
19774,
1103,
2332,
1104,
6379,
1107,
2415,
119,
1370,
1292,
3672,
1195,
2059,
3291,
26443,
5149,
1126,
11653,
2447,
1111,
1256,
3407,
2174,
11858,
4412,
2734,
1104,
1103,
161,
20336,
2443,
119,
138,
2158,
2728,
10481,
1174,
14294,
1116,
119,
4514,
1128,
1106,
11679,
10649,
1158,
12786,
1105,
2419,
24539,
1111,
1884,
1233,
118,
5530,
3798,
1113,
1103,
1346,
5251,
1104,
1142,
1844,
119,
1284,
1145,
6243,
1681,
17834,
1105,
8882,
1819,
1111,
3558,
5616,
10508,
1105,
8815,
117,
1105,
3352,
23287,
2042,
6473,
1111,
5784,
10620,
119,
1284,
1314,
1193,
6243,
1155,
1412,
8304,
1120,
155,
9717,
7136,
1111,
1147,
1619,
119,
1188,
1250,
1108,
6264,
1118,
155,
9717,
7136,
119,
19714,
1116,
164,
122,
166,
5291,
9866,
1377,
24446,
1377,
1673,
9817,
117,
144,
16481,
9995,
152,
119,
14069,
3263,
117,
138,
13160,
7666,
2328,
2268,
6919,
117,
13359,
1389,
2158,
1192,
11553,
2087,
117,
1105,
10129,
18933,
2511,
119,
155,
9717,
7136,
131,
3278,
7334,
1105,
25059,
119,
1130,
4623,
1105,
4623,
13849,
20463,
131,
5192,
1570,
3047,
117,
157,
2069,
13329,
1942,
1410,
117,
5096,
118,
172,
11394,
5018,
117,
5097,
19207,
782,
7967,
119,
18919,
1570,
7045,
117,
1410,
119,
2282,
4087,
118,
124,
118,
1955,
1580,
118,
24618,
23435,
118,
125,
119,
9465,
131,
1275,
119,
1620,
1559,
120,
4087,
118,
124,
118,
1955,
1580,
118,
24618,
23435,
118,
125,
1275,
119,
164,
123,
166,
159,
119,
1252,
9866,
1179,
1105,
159,
119,
14672,
119,
27950,
1103
] | [
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
0,
13,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
13,
0,
1,
0
] | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
11,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
21,
0,
0,
0,
0,
0,
0,
0,
23,
24,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
6,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5,
6,
6,
0,
0,
1,
2,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
0,
13,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
13,
14,
14,
0,
0,
0,
13,
0,
1,
0
] | [
"delay",
".",
"In",
"the",
"more",
"general",
"case",
"with",
"even",
"minor",
"disagreement",
"of",
"participants",
",",
"we",
"cannot",
"guarantee",
"that",
"the",
"network",
"makes",
"forward",
"progress",
".",
"It",
"is",
"an",
"open",
"question",
"whether",
"the",
"sufficient",
"overlap",
"condition",
"in",
"theorem",
"8",
"can",
"be",
"improved",
"by",
"a",
"more",
"detailed",
"consideration",
"of",
"the",
"trust",
"topology",
"of",
"the",
"network",
".",
"A",
"more",
"complicated",
"condition",
"that",
"does",
"not",
"simply",
"take",
"into",
"account",
"pair",
"##wise",
"overlap",
"##s",
"but",
"also",
"the",
"way",
"in",
"which",
"messages",
"flow",
"indirectly",
"through",
"the",
"network",
"might",
"have",
"potential",
"for",
"giving",
"a",
"more",
"precise",
"condition",
"for",
"guarantee",
"##ing",
"safety",
".",
"Likewise",
",",
"we",
"might",
"be",
"able",
"to",
"leverage",
"the",
"trust",
"structure",
"20",
"to",
"better",
"explain",
"cases",
"when",
"del",
"##iber",
"##ation",
"can",
"fail",
",",
"which",
"in",
"turn",
"might",
"allow",
"a",
"more",
"refined",
"understanding",
"on",
"forward",
"progress",
".",
"Although",
"we",
"have",
"shown",
"that",
"X",
"##RP",
"L",
"##CP",
"is",
"pro",
"##va",
"##bly",
"safe",
"with",
"the",
"current",
"and",
"near",
"-",
"future",
"network",
"structures",
",",
"in",
"an",
"attempt",
"to",
"alleviate",
"some",
"of",
"its",
"short",
"-",
"coming",
"##s",
",",
"in",
"the",
"sibling",
"paper",
"[",
"6",
"]",
"we",
"present",
"an",
"alternative",
"consensus",
"protocol",
"called",
"Co",
"##balt",
".",
"Similar",
"to",
"X",
"##RP",
"L",
"##CP",
",",
"Co",
"##balt",
"can",
"also",
"be",
"used",
"in",
"networks",
"that",
"lack",
"uniform",
"agreement",
"on",
"participants",
"or",
"trust",
",",
"but",
"makes",
"forward",
"progress",
"at",
"a",
"steady",
"rate",
"in",
"the",
"presence",
"of",
"maximum",
"tolerate",
"##d",
"Byzantine",
"faults",
"and",
"a",
"##rb",
"##i",
"-",
"t",
"##rary",
"as",
"##ync",
"##hr",
"##ony",
".",
"It",
"only",
"needs",
">",
"60",
"%",
"overlap",
"to",
"match",
"the",
"X",
"##RP",
"L",
"##CP",
"safety",
"tolerance",
"##s",
".",
"Co",
"##balt",
"also",
"has",
"several",
"other",
"properties",
"that",
"make",
"it",
"simpler",
"to",
"analyze",
"the",
"health",
"of",
"networks",
"in",
"practice",
".",
"For",
"these",
"reasons",
"we",
"believe",
"Co",
"##balt",
"represents",
"an",
"encouraging",
"direction",
"for",
"even",
"greater",
"future",
"decent",
"##ral",
"##ization",
"of",
"the",
"X",
"##RP",
"network",
".",
"A",
"##ck",
"##no",
"##wl",
"##ed",
"##gment",
"##s",
".",
"Thank",
"you",
"to",
"Ha",
"##ox",
"##ing",
"Du",
"and",
"Joseph",
"McGee",
"for",
"co",
"##l",
"-",
"labor",
"##ating",
"on",
"the",
"early",
"stages",
"of",
"this",
"research",
".",
"We",
"also",
"thank",
"David",
"Schwartz",
"and",
"Stefan",
"Thomas",
"for",
"providing",
"useful",
"discussions",
"and",
"guidance",
",",
"and",
"Rome",
"Reg",
"##ine",
"##lli",
"for",
"careful",
"editing",
".",
"We",
"last",
"##ly",
"thank",
"all",
"our",
"colleagues",
"at",
"R",
"##ip",
"##ple",
"for",
"their",
"support",
".",
"This",
"work",
"was",
"funded",
"by",
"R",
"##ip",
"##ple",
".",
"Reference",
"##s",
"[",
"1",
"]",
"Fred",
"##eri",
"##k",
"Arm",
"##k",
"##ne",
"##cht",
",",
"G",
"##has",
"##san",
"O",
".",
"Kara",
"##me",
",",
"A",
"##vik",
"##ars",
"##ha",
"Man",
"##dal",
",",
"Fr",
"##an",
"##ck",
"You",
"##sse",
"##f",
",",
"and",
"Erik",
"Zen",
"##ner",
".",
"R",
"##ip",
"##ple",
":",
"Over",
"##view",
"and",
"outlook",
".",
"In",
"Trust",
"and",
"Trust",
"##worthy",
"Computing",
":",
"8th",
"International",
"Conference",
",",
"T",
"##R",
"##US",
"##T",
"2015",
",",
"Pro",
"-",
"c",
"##eed",
"##ings",
",",
"pages",
"163",
"β",
"180",
".",
"Springer",
"International",
"Publishing",
",",
"2015",
".",
"ISBN",
"978",
"-",
"3",
"-",
"31",
"##9",
"-",
"228",
"##46",
"-",
"4",
".",
"doi",
":",
"10",
".",
"100",
"##7",
"/",
"978",
"-",
"3",
"-",
"31",
"##9",
"-",
"228",
"##46",
"-",
"4",
"10",
".",
"[",
"2",
"]",
"V",
".",
"But",
"##eri",
"##n",
"and",
"V",
".",
"Griffith",
".",
"Casper",
"the"
] | Analysis of the XRP Ledger Consensus Protocol | 199 |