Amortized Asynchronous Byzantine Reliable Broadcast with Optimal Resilience

2026-05-11

AI Summary

This work addresses the challenge of achieving both optimal fault tolerance (with $ f = \lfloor (n-1)/3 \rfloor $) and low communication complexity in asynchronous Byzantine reliable broadcast (BRB). The paper proposes a novel multi-round asynchronous BRB protocol that, for the first time, maintains optimal fault tolerance while amortizing the cost across multiple broadcast instances. The initial round provides incremental confirmation guarantees, enabling subsequent instances to complete in just one communication round. Combined with optimizations in asynchronous message passing, the protocol achieves asymptotically optimal message complexity of $ O(n|m|) $ when the message length $ |m| $ is sufficiently large. Its round complexity is $ O(n) $ in the worst case but reduces to $ O(1) $ under favorable conditions, thereby overcoming the sub-quadratic communication bottleneck inherent in prior probabilistic approaches.

Abstract

Byzantine Reliable Broadcast (BRB) is a fundamental primitive in distributed computing and cryptographic systems. Reducing the communication complexity of BRB protocols remains an important research direction. However, most work focuses on synchronous networks, with limited attention to the more challenging setting of network \textit{asynchrony}. Achieving sub-quadratic communication for asynchronous BRB typically requires probabilistic approaches that sacrifice optimal $f=\frac{n}{3}$ resilience. In this work, we present a multi-shot BRB algorithm for asynchronous networks that maintains optimal resilience through an underutilized technique: \textit{amortization}. Our protocol structures BRB across multiple rounds, where each round provides incremental additive guarantees. Once these initial rounds complete, each subsequent BRB instance requires only a single additional round. This amortization strategy achieves asymptotic optimal $O(n|m|)$ message complexity when messages are sufficiently large, with $Ω(n)$ round complexity in the worst case. Under favorable conditions, an optimistic delivery path reduces the round complexity to $Ω(1)$.

Problem

• Byzantine Reliable Broadcast
• asynchronous networks
• optimal resilience
• communication complexity
• amortization

Innovation

• amortization
• asynchronous Byzantine Reliable Broadcast
• optimal resilience
• sub-quadratic communication
• multi-shot BRB