Synchronous consensus protocols, by definition, have a worst-case commit latency that depends on the bounded network delay. The notion of optimistic responsiveness was recently introduced to allow synchronous protocols to commit instantaneously when some optimistic conditions are met. In this work, we revisit this notion of optimistic responsiveness and present optimal latency results. We present a lower bound for Byzantine Broadcast that relates the latency of optimistic and synchronous commits when the designated sender is honest and while the optimistic commit can tolerate some faults. We then present two matching upper bounds for tolerating f faults out of n = 2f + 1 parties. Our first upper bound result achieves optimal optimistic and synchronous commit latency when the designated sender is honest and the optimistic commit can tolerate at least one fault. We experimentally evaluate this protocol and show that it achieves throughput comparable to state-of-the-art synchronous and partially synchronous protocols and under optimistic conditions achieves latency better than the state-of-the-art. Our second upper bound result achieves optimal optimistic and synchronous commit latency when the designated sender is honest but the optimistic commit does not tolerate any faults. The presence of matching lower and upper bound results make both of the results tight for n = 2f + 1. Our upper bound results are presented in a state machine replication setting with a steady-state leader who is replaced with a view-change protocol when they do not make progress. For this setting, we also present an optimistically responsive protocol where the view-change protocol is optimistically responsive too. CCS CONCEPTS • Security and privacy → Distributed systems security.

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FaB Paxos [5] sets a lower bound of 5f + 1 replicas for any two-step consensus protocols tolerating f byzantine failures. Yet, hBFT[3] promises a two-step consensus protocol with only 3f + 1 replicas. As a result, it violates safety property of a consensus protocol. In this note, we review the lower bound set by FaB Paxos and present a simple execution scenario that produces a safety violation in hBFT. To demonstrate the scenario, we require a relatively simple setup with only 4 replicas and one view-change.

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BFT protocols in the synchronous setting rely on a strong assumption: every message sent by a party will arrive at its destination within a known bounded time. To allow some degree of asynchrony while still tolerating a minority corruption, recently, in Crypto'19, a weaker synchrony assumption called mobile sluggish faults was introduced. In this work, we investigate the support for mobile sluggish faults in existing synchronous protocols such as Dfinity, Streamlet, Sync HotStuff, OptSync and the optimal latency BFT protocol. We identify key principles that can be used to "compile" these synchronous protocols to tolerate mobile sluggish faults. CCS CONCEPTS• Security and privacy → Distributed systems security.