Good-case early-stopping latency of synchronous byzantine reliable broadcast: the deterministic case

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 good-case latency below the worst-case bound of \(t+1\) $t+1$ 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 \(\textsf{max} (2,t+3-c)\) $\mathsf{max}(2,t+3-c)$ rounds (or equivalently \(\textsf{max} (2,f+t+3-n)\) $\mathsf{max}(2,f+t+3-n)$ ), where t is the upper bound on the number of Byzantine processes, \(f\le t\) $f\le t$ the number of effectively Byzantine processes, and \(c=n-f\) $c=n-f$ the number of effectively correct processes. The proposed algorithm does not put any constraint on t, and assumes an authenticated setting, in which individual processes can sign the messages they send, and verify the authenticity of the signatures they receive.