Causal Ordering Properties of Byzantine Reliable Broadcast Primitives

Abstract

In this paper, we examine the inherent properties of the Byzantine Reliable Broadcast (BRB) primitive as pertain to the ability to provide causal ordering. We prove the following results. First, we analyze Bracha’s BRB algorithm and show that under the failure-free model, safety is guaranteed across broadcasts. Second, we also prove that Bracha’s BRB algorithm guarantees safety across broadcasts under the crash failure model tolerating any number of crash failures. Third, we prove that Bracha’s BRB algorithm cannot provide weak or strong safety under the Byzantine failure model. Fourth, we prove that neither the Imbs-Raynal BRB protocol nor any (2,*)-round BRB protocol can provide causal order even if all processes are correct, and they must incur additional latency to causally order messages at a higher layer. The inherent causal ordering properties of Bracha’s BRB can be of use under favourable circumstances in practical applications, given the widespread adoption of the protocol.