Paper 2021/814

A New Way to Achieve Round-Efficient Byzantine Agreement

Matthias Fitzi and Chen-Da Liu-Zhang and Julian Loss

Abstract

Minimizing the round complexity of Byzantine Agreement (BA) protocols is a fundamental problem in distributed computing. The typical approach to achieve round efficient (randomized) BA is to have a weak form of BA, called graded consensus (GC), followed by a distributed coin, and to repeat this process until some termination condition is met---as introduced by Feldman and Micali (STOC'88). In this work, we revisit the question of building BA from GC, or, more precisely, from generalizations of GC. Concretely, for Monte Carlo style BA, where the protocol is run for a fixed number of rounds in function of the security parameter (in contrast to protocols with probabilistic termination), we demonstrate that this generalization helps to considerably reduce the round complexity of BA. In particular, assuming a setup for threshold signatures among the parties and corruption threshold $t<n/3$, we improve over the round complexity of the best known protocol by a factor of $1/2$, asymptotically; this is achieved by applying one single Feldman-Micali iteration consisting of one (generalized) GC instance and one round of coin tossing. Our technique also applies to the dishonest-minority case ($t<n/2$), yielding an improvement by a factor of $1/4$ (asymptotically) over the round complexity of the best known fixed-round protocol.