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Strong Efficiency Lower Bounds for Byzantine Agreement

Authors Clément Ducros , Julian Loss , Matthieu Rambaud

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LIPIcs.DISC.2026.41.pdf
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Subject Classification

ACM Subject Classification
  • Security and privacy → Distributed systems security
Keywords
  • Byzantine agreement
  • Byzantine broadcast
  • communication complexity

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Abstract

Understanding the complexity of Byzantine agreement (BA) is a fundamental problem in distributed computing and cryptography. Existing round- or communication lower bounds either restrict the class of protocols they apply to in terms of communication, setup assumptions, or determinism. Another class of lower bounds holds only with respect to a very powerful (arguably unrealistic) adaptive adversary that can delete undelivered messages sent by a newly corrupted party while it was still honest. On the other hand, many popular BA protocols including the consensus protocol underlying the Algorand cryptocurrency assume only a standard adaptive adversary which cannot perform after-the-fact message removals. In this work, we aim to further narrow the gap between existing upper and lower bounds. We first show that unauthenticated BA has Ω(t²) messages complexity under an adaptive adversary even assuming randomization. This removes the restriction to multicast-based protocols in Abraham et al PODC'19. We then consider the restricted model of Dolev-Reischuk (J. ACM'85) where each signature counts as one and where signatures cannot be aggregated nor thresholdized. In this model, we show that partially synchronous consensus under an adaptive adversary requires that honest players send Ω(nt) signatures. We allow randomization, whereas Dolev-Reischuk proved an analogous bound under synchrony for deterministic protocols only.
As a technical contribution, we present a cryptographic formalization of the restricted model of Dolev-Reischuk, which may be of independent interest. We finally turn to the round complexity of randomized BA protocols in which only a subset of parties may speak. We show that such protocols must either rely on erasures or allow a party’s decision whether to speak for the first time to depend on its input. We discuss in detail how both of these design paradigms have been used in prior work and how they lead to efficiency and design-related issues for practical BA protocols.

Cite As Get BibTex

Clément Ducros, Julian Loss, and Matthieu Rambaud. Strong Efficiency Lower Bounds for Byzantine Agreement. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.41

Author Details

Clément Ducros
  • CISPA - Helmholtz Center for Information Security, Saarbrücken, Germany
Julian Loss
  • Ruhr University Bochum, Germany
Matthieu Rambaud
  • Télécom Paris, Institut Polytechnique de Paris, France

Funding

  • Rambaud, Matthieu: ANR-21-CE39-0009-BARRACUDA

References

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