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Brief Announcement: Towards 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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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Asynchronous message-passing
  • Byzantine fault-tolerance
  • Message adversary
  • Reliable Broadcast

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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 an almost optimal amount of O(|m|+n²κ) bits per node, where |m| represents the length of the application message and κ = Ω(log n) is a security parameter. This 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 PKI and collision-resistant hash, 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 ε > 0) correct nodes to reconstruct m, despite missing fragments caused by the malicious nodes and the message adversary.

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Timothé Albouy, Davide Frey, Ran Gelles, Carmit Hazay, Michel Raynal, Elad Michael Schiller, François Taïani, and Vassilis Zikas. Brief Announcement: Towards Optimal Communication Byzantine Reliable Broadcast Under a Message Adversary. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 41:1-41:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.41

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
  • Purdue University, West Lafayette, IN, 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.

References

  1. Timothé Albouy, Davide Frey, Ran Gelles, Carmit Hazay, Michel Raynal, Elad Michael Schiller, François Taïani, and Vassilis Zikas. Towards optimal communication Byzantine reliable broadcast under a message adversary. CoRR, abs/2312.16253, 2023. URL: https://doi.org/10.48550/arXiv.2312.16253.
  2. Timothé Albouy, Davide Frey, Michel Raynal, and François Taïani. Asynchronous Byzantine reliable broadcast with a message adversary. Theor. Comput. Sci., 978:114110, 2023. URL: https://doi.org/10.1016/J.TCS.2023.114110.
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