On the Versatility of Bracha's Byzantine Reliable Broadcast Algorithm

G. Bracha presented in 1987 a simple and efficient reliable broadcast algorithm for [Formula: see text]-process asynchronous message-passing systems, which tolerates up to [Formula: see text] Byzantine processes. Following an idea recently introduced by Hirt, Kastrato and Liu-Zhang (OPODIS 2020), instead of considering the upper bound on the number of Byzantine processes [Formula: see text], the present short article considers two types of Byzantine behavior: the ones that can prevent the safety property from being satisfied, and the ones that can prevent the liveness property from being satisfied (a Byzantine process can exhibit only one or both types of failures). This Byzantine differentiated failure model is captured by two associated upper bounds denoted [Formula: see text] (for safety) and [Formula: see text] for liveness). The article shows that only the threshold values used in the predicates of Bracha’s algorithm must be modified to obtain an algorithm that works with this differentiated Byzantine failure model.