Good-case Latency of Byzantine Broadcast: a Complete Categorization

This paper explores the problem good-case latency of Byzantine fault-tolerant broadcast, motivated by the real-world latency and performance of practical state machine replication protocols. The good-case latency measures the time it takes for all non-faulty parties to commit when the designated broadcaster is non-faulty. We provide a complete characterization of tight bounds on good-case latency, in the authenticated setting under synchrony, partial synchrony and asynchrony. Some of our new results may be surprising, e.g., 2-round PBFT-style partially synchronous Byzantine broadcast is possible if and only if $ngeq 5f-1$, and a tight bound for good-case latency under $n/3<f<n/2$ under synchrony is not an integer multiple of the delay bound.