Byzantine Reliable Broadcast (BRB) is a fundamental primitive in distributed computing and cryptographic systems; reducing the communication cost of BRB thus remains an important research direction. However, most existing works either focus strictly on the synchronous network model or utilize computationally impractical erasure codes. Therefore, to achieve a practical yet network-robust algorithm, one must turn toward committee sampling techniques. However, Committee sampling techniques often forgo optimal resilience ($f < \lfloor\frac{n}{3} \rfloor$) in the face of asynchrony. This work produces two interesting results: Firstly, we propose a \textit{randomly asynchronous} BRB protocol that can achieve both optimal resilience and asymptotically optimal communication complexity ($O(n|m|)$) through an underutilized technique: \textit{amortization}; and does not utilize computationally expensive \textit{erasure codes}. Next, we show that an optimally resilient BRB protocol utilizing sampled committees cannot exist in a \textit{fully asynchronous} network.

翻译：拜占庭可靠广播（Byzantine Reliable Broadcast, BRB）是分布式计算与密码系统中的基础原语，降低BRB的通信成本始终是重要研究方向。然而，现有工作大多严格限定于同步网络模型，或采用计算代价高昂的纠删码。为实现兼具实用性与网络鲁棒性的算法，必须转向委员会采样技术。但委员会采样技术通常无法在异步环境下维持最优弹性（$f < \lfloor\frac{n}{3} \rfloor$）。本文取得两项重要成果：首先，我们提出一种\textit{随机异步}BRB协议，通过利用一项被低估的技术——\textit{分摊（amortization）}——实现了最优弹性与渐近最优通信复杂度（$O(n|m|)$），且无需采用计算昂贵的\textit{纠删码}。其次，我们证明在\textit{完全异步}网络中，任何基于采样委员会的BRB协议均无法达到最优弹性。