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Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement

Authors Guy Goren , Yoram Moses , Alexander Spiegelman



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Author Details

Guy Goren
  • The Viterbi Faculty of Electrical & Computer Engineering, Technion, Haifa, Israel
Yoram Moses
  • The Viterbi Faculty of Electrical & Computer Engineering, Technion, Haifa, Israel
Alexander Spiegelman
  • Novi Research, USA

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Guy Goren, Yoram Moses, and Alexander Spiegelman. Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 57:1-57:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.57

Abstract

Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply to deterministic algorithms only. Probabilistic protocols have been around for at least four decades and are receiving a lot of attention with the emergence of blockchain systems. Nonetheless, we are aware of only a handful of randomized lower bounds. In this work we provide a formal framework for reasoning about randomized distributed algorithms. We generalize the notion of indistinguishability, the most useful tool in deterministic lower bounds, to apply to a probabilistic setting. We apply this framework to prove a result of independent interest. Namely, we completely characterize the quality of decisions that protocols for a randomized multi-valued Consensus problem can guarantee in an asynchronous environment with Byzantine faults. We use the new notion to prove a lower bound on the guaranteed probability that honest parties will not decide on a possibly bogus value proposed by a malicious party. Finally, we show that the bound is tight by providing a protocol that matches it. This brief announcement consists of an introduction to the full paper [Guy Goren et al., 2020] by the same title. The interested reader is advised to consult the full paper for a detailed exposition.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Security and privacy → Distributed systems security
Keywords
  • Indistinguishability
  • probabilistic lower bounds
  • Byzantine agreement

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References

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