Best-Case Complexity of Asynchronous Byzantine Consensus

This paper establishes the first theorem relating resilience, time complexity and authentication in distributed computing. We study consensus algorithms that tolerate Byzantine failures and arbitrary long periods of asynchrony. We measure the ability of processes to reach a consensus decision in a minimal number of rounds of information exchange, as a function of (a) their ability to use authentication and (b) the number of actual process failures in those rounds, as well as of (c) the total number of failures tolerated and (d) the system constellation. The constellations considered distinguish different roles of processes, such that we can directly derive a meaningful bound on the time complexity of implementing robust general services using several replicas coordinated through consensus. To prove our theorem, we establish certain lower bounds and we give algorithms that match these bounds. The algorithms are all variants of the same generic asynchronous Byzantine consensus algorithm, which is interesting in its own right.

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