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，现有工作主要关注同步网络，对更具挑战性的网络异步场景关注有限。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，但这会牺牲最优的$f=\frac{n}{3}$容错性。本文提出一种适用于异步网络的多轮次BRB算法，通过一种未充分利用的技术——摊销——维持最优容错性。我们的协议将BRB划分为多个轮次进行结构化设计，每轮提供递增的累加保证。当初始轮次完成后，每个后续BRB实例仅需额外一轮即可完成。这种摊销策略在消息足够大时实现了渐近最优的$O(n|m|)$消息复杂度，最坏情况下轮次复杂度为$\Omega(n)$。在有利条件下，一种乐观交付路径可将轮次复杂度降至$\Omega(1)$。