Brief Announcement: A Leader-free Byzantine Consensus Algorithm

We consider the consensus problem in a partially synchronous system with Byzantine faults. In a distributed system of n processes, where each process has an initial value, Byzantine consensus is the problem of agreeing on a common value, even though some of the processes may fail in arbitrary, even malicious, ways. It is shown in [11] that — in a synchronous system — 3t + 1 processes are needed to solve the Byzantine consensus problem without signatures, where t is the maximum number of Byzantine processes. In an asynchronous system, Fischer, Lynch and Peterson [7] proved that no deterministic asynchronous consensus protocol can tolerate even a single non-Byzantine (= crash) failure. The problem can however be solved using randomization for benign and Byzantine faults. For Byzantine faults, Ben-Or [2] and Rabin [12] showed that this requires 5t + 1 processes. Later, Bracha [3] increased the resiliency of the randomized algorithm to 3t+ 1. In 1988, Dwork, Lynch and Stockmeyer [6], considered an asynchronous system that eventually becomes synchronous (called partially synchronous system). The consensus algorithms proposed in [6], ensure safety in all executions, while guaranteeing liveness only if there exists a period of synchrony. Recently, several papers have considered the partially synchronous system model for Byzantine consensus [4,10,8,1,5]. However, [1,5] point out a potential weakness of these Byzantine consensus algorithms, namely that they suffer from “performance failure”. According to [1], a performance failure occurs when messages are sent slowly by a Byzantine leader, but without triggering protocol timeouts, and the paper points out that the PBFT leader-based algorithm [4] is vulnerable to such an attack. Interestingly, all deterministic Byzantine consensus algorithms for non-synchronous systems are leader-based. This raises the following fundamental question: is it possible to design a deterministic Byzantine consensus algorithm for a partially synchronous system that is not leader-based? With such an algorithm, performance failure of Byzantine processes might be harmless.