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 $Ω(1)$.

翻译：拜占庭可靠广播（BRB）是分布式计算和密码系统中的基础原语。降低BRB协议的通信复杂度仍是一个重要的研究方向。然而，现有工作大多聚焦于同步网络，对更具挑战性的网络异步环境关注有限。实现亚二次通信复杂度的异步BRB通常需要采用概率性方法，且需牺牲最优的$f=\frac{n}{3}$容错性。本文提出一种面向异步网络的多轮BRB算法，通过一种尚未被充分发掘的技术——摊销——来维持最优容错性。我们的协议将BRB结构化为多轮执行，每一轮提供增量式累加保证。当这些初始轮次完成后，后续每个BRB实例仅需额外一轮即可完成。当消息规模足够大时，该摊销策略可实现渐进最优的$O(n|m|)$消息复杂度，最坏情况下轮次复杂度为$Ω(n)$。在有利条件下，乐观传递路径可将轮次复杂度降低至$Ω(1)$。