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2019 | OriginalPaper | Buchkapitel

Bitcoin Security Under Temporary Dishonest Majority

verfasst von : Georgia Avarikioti, Lukas Käppeli, Yuyi Wang, Roger Wattenhofer

Erschienen in: Financial Cryptography and Data Security

Verlag: Springer International Publishing

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Abstract

We prove Bitcoin is secure under temporary dishonest majority. We assume the adversary can corrupt a specific fraction of parties and also introduce crash failures, i.e., some honest participants are offline during the execution of the protocol. We demand a majority of honest online participants on expectation. We explore three different models and present the requirements for proving Bitcoin’s security in all of them: we first examine a synchronous model, then extend to a bounded delay model and last we consider a synchronous model that allows message losses.

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Vorheriges Kapitel VeriSolid: Correct-by-Design Smart Contracts for Ethereum

Nächstes Kapitel VAPOR: A Value-Centric Blockchain that is Scale-out, Decentralized, and Flexible by Design

The Chain-Growth Property in [7] is defined slightly different: ...it holds that for any s rounds, there are at least \(\tau \cdot s\) blocks added to the chain of P. Considering the proof for Theorem 1 (of [2]), one can see, why we use \(s+1\) instead of s. It follows by the fact that the sum in Lemma 13 (of [2]) only goes from \(i=r\) to \(s-1\) and not to s.

The statement (d) uses different factors as [7]. The problem is, that it’s even not possible to prove the bounds from [7] with their theorems, lemmas and assumptions.

According to Theorem 11 of [12], the parameter \(\varDelta \) has to be known by the honest parties to achieve state machine replication, e.g. achieving consensus.

One might notice that our lower bound of \(\delta \) differs from the lower bound from [7]. First of all, they provided two different values for \(\delta \), where both of them are wrong in the sense that they are too small in order to prove the needed bounds.

Note that \(\delta \) is dependent on \(E[X_i]\), which is again dependent on s. If we would remove this dependency, the results would be at most 2% better than the actual results shown in Fig. 1.

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Titel: Bitcoin Security Under Temporary Dishonest Majority
verfasst von: Georgia Avarikioti
Lukas Käppeli
Yuyi Wang
Roger Wattenhofer
Verlag: Springer International Publishing
Buch: Financial Cryptography and Data Security
Print ISBN: 978-3-030-32100-0

Electronic ISBN: 978-3-030-32101-7

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-32101-7_28

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