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Optimal Probabilistic Synchronous Byzantine Agreement

1988; Feldman, Micali

  • Reference work entry
Encyclopedia of Algorithms

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Keywords and Synonyms

Distributed consensus; Byzantine generals problem          

Problem Definition

The Byzantine agreement problem (BA) is concerned with multiple processors (parties, “players”) all starting with some initial value, agreeing on a common value, despite the possible disruptive or even malicious behavior of some them. BA is a fundamental problem in fault-tolerant distributed computing and secure multi-party computation.

The problem was introduced by Pease, Shostak and Lamport in [18], who showed that the number of faulty processors must be less than a third of the total number of processors for the problem to have a solution. They also presented a protocol matching this bound, which requires a number of communication rounds proportional to the number of faulty processors—exactly \( { t+1 } \), where t is the number of faulty processors. Fischer and Lynch [10] later showed that this number of rounds is necessary in the worst-case run of any deterministic BA protocol. Furthermore,...

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Notes

  1. 1.

    Karlin and Yao [14] showed that the maximum number of faulty processors for probabilistic BA is also \( { t < \frac{n}{3} } \), where n is the total number of processors.

  2. 2.

    Indeed, it was shown by Dwork and Moses [7] that at least \( { t+1 } \) rounds are necessary for simultaneous termination. In [13], Goldreich and Petrank combine “the best of both worlds” by showing a BA protocol running in expected constant number of rounds which always terminates within \( { t+O(\log t) } \) rounds.

Recommended Reading

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Authors and Affiliations

  1. Bell Labs, Murray Hill, NJ, USA

    Juan Garay

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  1. Juan Garay
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Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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Garay, J. (2008). Optimal Probabilistic Synchronous Byzantine Agreement. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_269

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