Not a COINcidence: Sub-Quadratic Asynchronous Byzantine Agreement WHP

Authors Shir Cohen, Idit Keidar, Alexander Spiegelman

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Author Details

Shir Cohen
  • Technion - Israel Institute of Technology, Haifa, Israel
Idit Keidar
  • Technion - Israel Institute of Technology, Haifa, Israel
Alexander Spiegelman
  • VMware Research, Herzliya, Israel


We thank Ittai Abraham, Dahlia Malkhi, Kartik Nayak and Ling Ren for insightful initial discussions.

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Shir Cohen, Idit Keidar, and Alexander Spiegelman. Not a COINcidence: Sub-Quadratic Asynchronous Byzantine Agreement WHP. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


King and Saia were the first to break the quadratic word complexity bound for Byzantine Agreement in synchronous systems against an adaptive adversary, and Algorand broke this bound with near-optimal resilience (first in the synchronous model and then with eventual-synchrony). Yet the question of asynchronous sub-quadratic Byzantine Agreement remained open. To the best of our knowledge, we are the first to answer this question in the affirmative. A key component of our solution is a shared coin algorithm based on a VRF. A second essential ingredient is VRF-based committee sampling, which we formalize and utilize in the asynchronous model for the first time. Our algorithms work against a delayed-adaptive adversary, which cannot perform after-the-fact removals but has full control of Byzantine processes and full information about communication in earlier rounds. Using committee sampling and our shared coin, we solve Byzantine Agreement with high probability, with a word complexity of Õ(n) and O(1) expected time, breaking the O(n²) bit barrier for asynchronous Byzantine Agreement.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Cryptographic primitives
  • Mathematics of computing → Probabilistic algorithms
  • shared coin
  • Byzantine Agreement
  • VRF
  • sub-quadratic consensus protocol


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