We present new protocols for Byzantine state machine replication and
Byzantine agreement in the synchronous and authenticated setting. The
celebrated PBFT state machine replication protocol tolerates f Byzantine
faults in an asynchronous setting using 3f+1 replicas, and has since been
studied or deployed by numerous works. In this work, we improve the Byzantine
fault tolerance threshold to n=2f+1 by utilizing a relaxed synchrony
assumption. We present a synchronous state machine replication protocol that
commits a decision every 3 rounds in the common case. The key challenge is to
ensure quorum intersection at one honest replica. Our solution is to rely on
the synchrony assumption to form a post-commit quorum of size 2f+1, which
intersects at f+1 replicas with any pre-commit quorums of size f+1. Our
protocol also solves synchronous authenticated Byzantine agreement in expected
8 rounds. The best previous solution (Katz and Koo, 2006) requires expected 24
rounds. Our protocols may be applied to build Byzantine fault tolerant systems
or improve cryptographic protocols such as cryptocurrencies when synchrony can
be assumed
