Randomized byzantine agreement protocol with constant expected time and guaranteed termination in optimal (deterministic) time

Abstract

This paper presents a randomized Byzantine agreement protocol for t = Ω(n) that runs in constant expected number of rounds, and uses polynomial messages. In the worst case all correct processors terminate in min{f + 2, t + 1} rounds where t is an a priori upper bound on the number of faulty processors and f is the number of actual faults. Hence our protocol is time optimal both on average and in the worst cast simultaneously. This result improves on the previous almost optimal protocol of Goldreich and Petrank, where optimality on average requires an extra O(log t) rounds in the worst case. To obtain this result we present a new technique of random choice of a deterministic protocol: First we look for a family of deterministic protocols, each one of the same worst case running time, and then we use random coin to choose on the fly one them. Since every one of the considered deterministic protocol ensures reaching Byzantine agreement in optimal time, we get that in the worst case, the running time of the obtained (randomized) protocols is similar to that of deterministic protocols; In the average case, the processors terminate after a small (constant) number of rounds, since for every possible strategy of the adversary, it holds that if it 'works' against one particular deterministic protocol, it will fail against a lot of other protocols.