Linear Consistency for Proof-of-Stake Blockchains Article Swipe

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Erica Blum , Aggelos Kiayias , Cristopher Moore , Saad Quader , Alexander Russell ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1911.10187

The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $Θ(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $Θ(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.

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Computer Science

Theoretical Computer Science

Mathematics

Discrete Mathematics

Martingale (Probability Theory)

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Correctness Consistency (knowledge bases) Axiom Liveness Computer science Generality Theoretical computer science Mathematics Strong consistency Quadratic equation Protocol (science) Discrete mathematics Martingale (probability theory) Algorithm Applied mathematics Medicine Psychotherapist Psychology Geometry Statistics Estimator Pathology Alternative medicine

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1911.10187
PDF: https://arxiv.org/pdf/1911.10187
OA Status: green
References: 17
Related Works: 20
OpenAlex ID: https://openalex.org/W2991400344

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DOI: https://doi.org/10.48550/arxiv.1911.10187

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Title: Linear Consistency for Proof-of-Stake Blockchains

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Language: en

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Publication year: 2019

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Publication date: 2019-11-22

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Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander Russell

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Landing page: https://arxiv.org/abs/1911.10187

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Concepts: Correctness, Consistency (knowledge bases), Axiom, Liveness, Computer science, Generality, Theoretical computer science, Mathematics, Strong consistency, Quadratic equation, Protocol (science), Discrete mathematics, Martingale (probability theory), Algorithm, Applied mathematics, Medicine, Psychotherapist, Psychology, Geometry, Statistics, Estimator, Pathology, Alternative medicine

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abstract_inverted_index.$k$:	66
abstract_inverted_index.Such	18
abstract_inverted_index.been	108
abstract_inverted_index.both	196
abstract_inverted_index.data	2
abstract_inverted_index.from	33, 61
abstract_inverted_index.give	125, 180
abstract_inverted_index.only	84
abstract_inverted_index.open	111
abstract_inverted_index.rely	118
abstract_inverted_index.rule	139
abstract_inverted_index.show	163
abstract_inverted_index.such	103
abstract_inverted_index.tail	193
abstract_inverted_index.that	86, 132, 164
abstract_inverted_index.this	92, 189
abstract_inverted_index.tool	14
abstract_inverted_index.with	46
abstract_inverted_index.(PoS)	58
abstract_inverted_index.2018)	77
abstract_inverted_index.Praos	75
abstract_inverted_index.While	39
abstract_inverted_index.about	136
abstract_inverted_index.broad	143
abstract_inverted_index.chain	26
abstract_inverted_index.depth	32, 52, 87, 148
abstract_inverted_index.error	47, 154
abstract_inverted_index.first	160
abstract_inverted_index.match	168
abstract_inverted_index.order	150
abstract_inverted_index.their	31
abstract_inverted_index.these	67
abstract_inverted_index.time,	161
abstract_inverted_index.2017),	73, 82
abstract_inverted_index.Sleepy	79
abstract_inverted_index.blocks	23, 50
abstract_inverted_index.bounds	194
abstract_inverted_index.chain.	38
abstract_inverted_index.derive	192
abstract_inverted_index.i.i.d.	197
abstract_inverted_index.issues	102
abstract_inverted_index.linear	172
abstract_inverted_index.theory	128
abstract_inverted_index.urgent	110
abstract_inverted_index.$O(k)$,	53
abstract_inverted_index.$Θ(k)$	145
abstract_inverted_index.(Crypto	72
abstract_inverted_index.Bitcoin	43
abstract_inverted_index.Whether	91
abstract_inverted_index.achieve	20, 152
abstract_inverted_index.analyze	175
abstract_inverted_index.further	117
abstract_inverted_index.permits	133
abstract_inverted_index.suffers	60
abstract_inverted_index.$2^{-k}$	48
abstract_inverted_index.achieve,	141
abstract_inverted_index.analysis	41
abstract_inverted_index.critical	186
abstract_inverted_index.deployed	114
abstract_inverted_index.dynamics	131
abstract_inverted_index.function	29
abstract_inverted_index.powerful	12
abstract_inverted_index.process,	179, 190
abstract_inverted_index.protocol	122
abstract_inverted_index.relation	183
abstract_inverted_index.rigorous	134
abstract_inverted_index.settings	200
abstract_inverted_index.$2^{-k}$.	155
abstract_inverted_index.$Θ(k^2)$	88
abstract_inverted_index.Consensus	80
abstract_inverted_index.Ouroboros	71, 74
abstract_inverted_index.PoS---due	100
abstract_inverted_index.axiomatic	127
abstract_inverted_index.consensus	16
abstract_inverted_index.establish	85
abstract_inverted_index.intrinsic	97
abstract_inverted_index.protocols	166, 170
abstract_inverted_index.quadratic	63, 93
abstract_inverted_index.question,	112
abstract_inverted_index.reasoning	135
abstract_inverted_index.recursive	182
abstract_inverted_index.structure	3
abstract_inverted_index.(Asiacrypt	81
abstract_inverted_index.(Eurocrypt	76
abstract_inverted_index.algorithms	19
abstract_inverted_index.associated	177, 202
abstract_inverted_index.blockchain	1, 130
abstract_inverted_index.dependence	64, 146
abstract_inverted_index.functions.	204
abstract_inverted_index.generating	203
abstract_inverted_index.guarantees	44
abstract_inverted_index.limitation	98
abstract_inverted_index.maintained	4
abstract_inverted_index.martingale	199
abstract_inverted_index.protocols,	68
abstract_inverted_index.stochastic	178
abstract_inverted_index.algorithmic	13
abstract_inverted_index.algorithms.	17
abstract_inverted_index.blockchains	59, 116
abstract_inverted_index.consistency	21, 45, 120, 153
abstract_inverted_index.exemplified	69
abstract_inverted_index.functionals	187
abstract_inverted_index.generality,	144
abstract_inverted_index.particular,	157
abstract_inverted_index.sufficient.	90
abstract_inverted_index.Bitcoin---is	10
abstract_inverted_index.consistency.	173
abstract_inverted_index.correctness.	123
abstract_inverted_index.longest-chain	7, 138
abstract_inverted_index.problem---has	107
abstract_inverted_index.proof-of-work	169
abstract_inverted_index.proof-of-stake	57
abstract_inverted_index.nothing-at-stake	106
abstract_inverted_index.state-of-the-art	55
abstract_inverted_index.rule---popularized	8
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	5
citation_normalized_percentile