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Optimal Error-Free Multi-Valued Byzantine Agreement

Author Jinyuan Chen

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LIPIcs.DISC.2021.17.pdf
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Jinyuan Chen
  • Louisiana Tech University, Ruston, LA, USA

Funding

  • Chen, Jinyuan: This work was supported in part by the NSF under Grant OIA-1946231 and in part by the Louisiana Board of Regents under Grant 32-4121-40336.

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Jinyuan Chen. Optimal Error-Free Multi-Valued Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.17

Abstract

Byzantine agreement (BA) is a distributed consensus problem where n processors want to reach agreement on an 𝓁-bit message or value, but up to t of the processors are dishonest or faulty. The challenge of this BA problem lies in achieving agreement despite the presence of dishonest processors who may arbitrarily deviate from the designed protocol. In this work by using coding theory, together with graph theory and linear algebra, we design a coded BA protocol (termed as COOL) that achieves consensus on an 𝓁-bit message with optimal resilience, asymptotically optimal round complexity, and asymptotically optimal communication complexity when 𝓁 ≥ t log t, simultaneously. The proposed COOL is a deterministic BA protocol that is guaranteed to be correct in all executions (error free) and does not rely on cryptographic technique such as signatures, hashing, authentication and secret sharing (signature free). It is secure against computationally unbounded adversary who takes full control over the dishonest processors (information-theoretic secure). The main idea of the proposed COOL is to use a carefully-crafted error correction code that provides an efficient way of exchanging "compressed" information among distributed nodes, while keeping the ability of detecting errors, masking errors, and making a consistent and validated agreement at honest distributed nodes. We show that our results can also be extended to the setting of Byzantine broadcast, aka Byzantine generals problem, where the honest processors want to agree on the message sent by a leader who is potentially dishonest. The results reveal that coding is an effective approach for achieving the fundamental limits of Byzantine agreement and its variants. Our protocol analysis borrows tools from coding theory, graph theory and linear algebra.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Byzantine agreement
  • information-theoretic security
  • error correction codes

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