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In this paper, we investigate a communication abstraction, called Set-Constrained Delivery Broadcast (SCD-Broadcast) and its optimal resilience in a message-passing system prone to Byzantine failures. SCD-Broadcast is a communication abstraction that offers an ordering property among a set of messages. This abstraction allows each process to broadcast messages and to deliver sets of received messages such that if a process delivers a set containing a message m before a set containing a message m', then no other process can deliver a set containing m' before a set containing m. The first implementation of SCD-Broadcast was designed for crash-prone distributed systems. Afterward, a new implementation of SCD-Broadcast called Byzantine-Tolerant Set-Constrained Delivery Broadcast (BSCD-Broadcast) was adapted to a context prone to Byzantine failures. The resilience of this implementation is t < n/4 (where t is the maximal number of processes that may be Byzantine and n is the total number of processes). This paper presents a new algorithm that implements the Byzantine SCD-Broadcast abstraction with an optimal resilience t < n/3.
Vincent et al. (Mon,) studied this question.