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Near-Optimal Communication Byzantine Reliable Broadcast Under a Message Adversary

Authors Timothé Albouy , Davide Frey , Ran Gelles , Carmit Hazay , Michel Raynal , Elad Michael Schiller , François Taïani , Vassilis Zikas

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Author Details

Timothé Albouy
  • Univ Rennes, Inria, CNRS, IRISA, 35042 Rennes-cedex, France
Davide Frey
  • Univ Rennes, Inria, CNRS, IRISA, 35042 Rennes-cedex, France
Ran Gelles
  • Bar-Ilan University, Ramat Gan, Israel
Carmit Hazay
  • Bar-Ilan University, Ramat Gan, Israel
Michel Raynal
  • Univ Rennes, Inria, CNRS, IRISA, 35042 Rennes-cedex, France
Elad Michael Schiller
  • Chalmers University of Technology, Gothenburg, Sweden
François Taïani
  • Univ Rennes, Inria, CNRS, IRISA, 35042 Rennes-cedex, France
Vassilis Zikas
  • Georgia Institute of Technology, Atlanta, GA, USA

Funding

This work was partially supported by the French ANR projects ByBloS (ANR-20-CE25-0002-01) and PriCLeSS (ANR-10-LABX-07-81), devoted to the modular design of building blocks for large-scale Byzantine-tolerant multi-users applications. Research supported in part by the United States-Israel Binational Science Foundation (BSF) through Grant No. 2020277.

Acknowledgements

R. Gelles would like to thank Paderborn University and CISPA - Helmholtz Center for Information Security for hosting him while part of this research was done.

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Timothé Albouy, Davide Frey, Ran Gelles, Carmit Hazay, Michel Raynal, Elad Michael Schiller, François Taïani, and Vassilis Zikas. Near-Optimal Communication Byzantine Reliable Broadcast Under a Message Adversary. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 14:1-14:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.14

Abstract

We address the problem of Reliable Broadcast in asynchronous message-passing systems with n nodes, of which up to t are malicious (faulty), in addition to a message adversary that can drop some of the messages sent by correct (non-faulty) nodes. We present a Message-Adversary-Tolerant Byzantine Reliable Broadcast (MBRB) algorithm that communicates O(|m|+nκ) bits per node, where |m| represents the length of the application message and κ = Ω(log n) is a security parameter. This communication complexity is optimal up to the parameter κ. This significantly improves upon the state-of-the-art MBRB solution (Albouy, Frey, Raynal, and Taïani, TCS 2023), which incurs communication of O(n|m|+n²κ) bits per node. Our solution sends at most 4n² messages overall, which is asymptotically optimal. Reduced communication is achieved by employing coding techniques that replace the need for all nodes to (re-)broadcast the entire application message m. Instead, nodes forward authenticated fragments of the encoding of m using an erasure-correcting code. Under the cryptographic assumptions of threshold signatures and vector commitments, and assuming n > 3t+2d, where the adversary drops at most d messages per broadcast, our algorithm allows at least 𝓁 = n - t - (1 + ε)d (for any arbitrarily low ε > 0) correct nodes to reconstruct m, despite missing fragments caused by the malicious nodes and the message adversary.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Asynchronous message-passing
  • Byzantine fault-tolerance
  • Message adversary
  • Reliable broadcast
  • Erasure-correction codes
  • {Threshold} signatures
  • {Vector commitments}

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