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Round-Optimal Byzantine Agreement

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

Byzantine agreement is a fundamental primitive in cryptography and distributed computing, and minimizing its round complexity is of paramount importance. It is long known that any randomized r-round protocol must fail with probability at least \((c\cdot r)^{-r}\), for some constant c, when the number of corruptions is linear in the number of parties, \(t = \theta (n)\). On the other hand, current protocols fail with probability at least \(2^{-r}\). Whether we can match the lower bound agreement probability remains unknown.

In this work, we resolve this long-standing open question. We present a protocol that matches the lower bound up to constant factors. Our results hold under a (strongly rushing) adaptive adversary that can corrupt up to \(t = (1-\epsilon )n/2\) parties, and our protocols use a public-key infrastructure and a trusted setup for unique threshold signatures. This is the first protocol that decreases the failure probability (overall) by a super-constant factor per round.

V. Goyal and C.-D. Liu-Zhang—Supported in part by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Notes

  1. 1.

    All parties simultaneously terminate in the same round.

  2. 2.

    This is a bulletin-board PKI, where the keys from corrupted parties can be chosen adversarially. See [BCG21] for a nice discussion.

  3. 3.

    Note that \(\frac{x}{x+a} \le \frac{x+b}{x+a+b}\) for any positive real numbers x, a and b.

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Author information

Authors and Affiliations

  1. ETH Zurich, Zürich, Switzerland

    Diana Ghinea

  2. Carnegie Mellon University and NTT Research, Pittsburgh, USA

    Vipul Goyal

  3. Carnegie Mellon University, Pittsburgh, USA

    Chen-Da Liu-Zhang

Authors
  1. Diana Ghinea
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  2. Vipul Goyal
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  3. Chen-Da Liu-Zhang
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Correspondence to Chen-Da Liu-Zhang .

Editor information

Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Ghinea, D., Goyal, V., Liu-Zhang, CD. (2022). Round-Optimal Byzantine Agreement. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_4

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  • DOI: https://doi.org/10.1007/978-3-031-06944-4_4

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