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

Authors Guy Goren , Yoram Moses , Alexander Spiegelman

Thumbnail PDF


  • Filesize: 0.52 MB
  • 4 pages

Document Identifiers

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

Cite AsGet BibTex

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)


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
  • Indistinguishability
  • probabilistic lower bounds
  • Byzantine agreement


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Hagit Attiya and Faith Ellen. Impossibility results for distributed computing. Synthesis Lectures on Distributed Computing Theory, 5(1):1-162, 2014. Google Scholar
  2. Michael Ben-Or. Another advantage of free choice (extended abstract) completely asynchronous agreement protocols. In Proceedings of the second annual ACM symposium on Principles of distributed computing, pages 27-30, 1983. Google Scholar
  3. Pesech Feldman and Silvio Micali. An optimal probabilistic protocol for synchronous byzantine agreement. SIAM Journal on Computing, 26(4):873-933, 1997. Google Scholar
  4. Faith Fich and Eric Ruppert. Hundreds of impossibility results for distributed computing. Distributed computing, 16(2-3):121-163, 2003. Google Scholar
  5. Michael J. Fischer, Nancy A. Lynch, and Michael S. Paterson. Impossibility of distributed consensus with one faulty process. JACM, 1985. Google Scholar
  6. Guy Goren, Yoram Moses, and Alexander Spiegelman. Probabilistic indistinguishability and the quality of validity in byzantine agreement, 2020. URL:
  7. Jonathan Katz and Chiu-Yuen Koo. On expected constant-round protocols for byzantine agreement. In Annual International Cryptology Conference, pages 445-462. Springer, 2006. Google Scholar
  8. Nancy A Lynch. Distributed algorithms. Elsevier, 1996. Google Scholar
  9. Amir Pnueli. On the extremely fair treatment of probabilistic algorithms. In Proceedings of the fifteenth annual ACM symposium on Theory of computing, pages 278-290, 1983. Google Scholar
  10. Michael O Rabin. Probabilistic algorithms in finite fields. SIAM Journal on computing, 9(2):273-280, 1980. Google Scholar
  11. Michael O Rabin. Randomized byzantine generals. In 24th Annual Symposium on Foundations of Computer Science (sfcs 1983), pages 403-409. IEEE, 1983. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail