Asynchronous Byzantine Agreement with Optimal Resilience and Linear Complexity

TL;DR

This paper introduces a new asynchronous Byzantine agreement protocol that achieves optimal resilience with linear expected running time, significantly improving previous quadratic-time solutions.

Contribution

It presents a protocol that reaches agreement in expected linear time under optimal fault tolerance, improving upon prior quadratic-time algorithms.

Findings

Achieves agreement in O(t) expected time for n > 3t+1

Improves previous O(n^2) time complexity

Provides faster agreement when n is close to 3t

Abstract

Given a system with $n > 3t + 1$ processes, where $t$ is the tolerated number of faulty ones, we present a fast asynchronous Byzantine agreement protocol that can reach agreement in $O(t)$ expected running time. This improves the $O(n^2)$ expected running time of Abraham, Dolev, and Halpern [PODC 2008]. Furthermore, if $n = (3 + \varepsilon) t$ for any $\varepsilon > 0$, our protocol can reach agreement in $O (1 / \varepsilon)$ expected running time. This improves the result of Feldman and Micali [STOC 1988] (with constant expected running time when $n > 4 t$).