This paper considers the good-case latency of Byzantine Reliable Broadcast (BRB), i.e., the time taken by correct processes to deliver a message when the initial sender is correct. This time plays a crucial role in the performance of practical distributed systems. Although significant strides have been made in recent years on this question, progress has mainly focused on either asynchronous or randomized algorithms. By contrast, the good-case latency of deterministic synchronous BRB under a majority of Byzantine faults has been little studied. In particular, it was not known whether a goodcase latency below the worst-case bound of t + 1 rounds could be obtained. This work answers this open question positively and proposes a deterministic synchronous Byzantine reliable broadcast that achieves a good-case latency of max(2, t + 3 -- c) rounds, where t is the upper bound on the number of Byzantine processes and c the number of effectively correct processes.

翻译：本文考虑拜占庭可靠广播（BRB）的好情形延迟，即当初始发送方正确时，正确进程投递消息所需的时间。这一时间对实际分布式系统的性能至关重要。尽管近年来在该问题上取得了显著进展，但相关工作主要集中于异步或随机算法。相比之下，在多数拜占庭故障条件下，确定性同步BRB的好情形延迟鲜有研究。特别地，此前尚不清楚能否获得低于最坏情况界限 t+1 轮的好情形延迟。本文肯定了该开放问题，并提出一种确定性同步拜占庭可靠广播算法，其好情形延迟为 max(2, t+3−c) 轮，其中 t 为拜占庭进程数量的上界，c 为实际正确进程的数量。