  This paper studies the {\em good-case latency} of {\em unauthenticated}
Byzantine fault-tolerant broadcast, which measures the time it takes for all
non-faulty parties to commit given a non-faulty broadcaster. For both
asynchrony and synchrony, we show that $n\geq 4f$ is the tight resilience
threshold that separates good-case 2 rounds and 3 rounds. For asynchronous
Byzantine reliable broadcast (BRB), we also investigate the {\em bad-case
latency} for all non-faulty parties to commit when the broadcaster is faulty
but some non-faulty party commits. We provide matching upper and lower bounds
on the resilience threshold of bad-case latency for BRB protocols with optimal
good-case latency of 2 rounds. In particular, we show 2 impossibility results
and propose 4 asynchronous BRB protocols.

Distributed, Parallel, and Cluster Computing;Cryptography and Security