COOL Is Optimal in Error-Free Asynchronous Byzantine Agreement

2025-10-31

AI Summary

This paper addresses information-theoretically secure, error-free Byzantine agreement (BA) in asynchronous networks under the optimal resilience threshold (n ≥ 3t + 1). We present OciorACOOL, the first adaptive asynchronous BA protocol derived from the synchronous COOL protocol. OciorACOOL requires only a single invocation of asynchronous binary BA and leverages (n, k)-error-correcting codes with k = t/3 alongside lightweight encoding/decoding, achieving O(1) rounds and O(max{nℓ, nt log q}) total communication complexity. Its key contribution is the first demonstration—without compromising information-theoretic security or zero error probability—that asynchronous BA can match the efficiency of synchronous COOL: constant round complexity, low communication overhead, and reliance on only one BA primitive. This significantly advances the practicality frontier of asynchronous BA.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

COOL (Chen'21) is an error-free, information-theoretically secure Byzantine agreement (BA) protocol proven to achieve BA consensus in the synchronous setting for an $ell$-bit message, with a total communication complexity of $O(max{nell, nt log q})$ bits, four communication rounds in the worst case, and a single invocation of a binary BA, under the optimal resilience assumption $n geq 3t + 1$ in a network of $n$ nodes, where up to $t$ nodes may behave dishonestly. Here, $q$ denotes the alphabet size of the error correction code used in the protocol. In this work, we present an adaptive variant of COOL, called OciorACOOL, which achieves error-free, information-theoretically secure BA consensus in the asynchronous setting with total $O(max{nell, n t log q})$ communication bits, $O(1)$ rounds, and a single invocation of an asynchronous binary BA protocol, still under the optimal resilience assumption $n geq 3t + 1$. Moreover, OciorACOOL retains the same low-complexity, traditional $(n, k)$ error-correction encoding and decoding as COOL, with $k=t/3$.

Problem

• Achieves error-free Byzantine agreement in asynchronous networks
• Maintains optimal resilience with n ≥ 3t+1 nodes
• Provides efficient O(1) rounds and low communication complexity

Innovation

• Asynchronous Byzantine agreement with optimal resilience
• Constant communication rounds with O(1) complexity
• Error correction codes with traditional encoding