COOL Is Optimal in Error-Free Asynchronous Byzantine Agreement

TL;DR

This paper introduces OciorACOOL, an asynchronous Byzantine agreement protocol that maintains optimal communication complexity and security, adapting the synchronous COOL protocol to asynchronous networks with minimal rounds.

Contribution

It presents the first asynchronous variant of COOL, achieving optimal resilience, low communication, and single binary BA invocation, while preserving error-correction features.

Findings

Achieves $O( ext{max}\{n ext{l}, n t ext{log} q ight") communication complexity.

Operates in $O(1)$ rounds in asynchronous settings.

Maintains error correction with $(n, k)$ codes, where $k=t/3$."

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 $O(\max\{n\ell, nt \log q\})$ 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 $O(\max\{n\ell, n t \log q\})$ 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 $k=t/3$.