Consensus protocols for asynchronous networks are usually complex and inefficient, leading practical systems to rely on synchronous protocols. The invention proposes an approach to simplify asynchronous consensus by building it atop a novel threshold logical clock abstraction, allowing the consensus protocol to operate in “virtual synchrony.” Leveraging accountable state machine techniques to detect and suppress Byzantine nodes, and verifiable secret sharing for random leader election, we obtain simple and efficient protocols for asynchronous Byzantine consensus.