Michael Yiqing Hu, Alvin Hong Yao Yan, Jialin Li
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 $Ω(1)$.