Byzantine fault-tolerant (BFT) state machine replication (SMR) has been studied for over 30 years. Recently it has received more attention due to its application in permissioned blockchain systems. A sequence of research efforts focuses on improving the commit latency of the SMR protocol in the common good case, including PBFT with $3$-round latency and $ngeq 3f+1$ and FaB with $2$-round latency and $ngeq 5f+1$. In this paper, we propose an authenticated protocol that solves $2$-round BFT SMR with only $ngeq 5f-1$ replicas, which refutes the optimal resiliency claim made in FaB for needing $n geq 5f+1$ for $2$-round PBFT-style BFT protocols. For the special case when $f=1$, our protocol needs only $4$ replicas, and strictly improves PBFT by reducing the latency by one round (even when one backup is faulty).
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