Byzantine Fault Detectors for Solving Consensus

Abstract

Unreliable fault detectors can be defined in terms of completeness and accuracy properties and can be used to solve the consensus problem in asynchronous distributed systems that are subject to crash faults. We extend this result to asynchronous distributed systems that are subject to Byzantine faults. First, we define and categorize Byzantine faults. We then define two new completeness properties, eventual strong completeness and eventual weak completeness. We use these completeness properties and previously defined accuracy properties to define four new classes of unreliable Byzantine fault detectors. Next, we present an algorithm that uses a Byzantine fault detector to solve the consensus problem in an asynchronous distributed system of $n$ processes in which the number $k$ of Byzantine faults satisfies $k\leq \lfloor (n-1)/3\rfloor$. We also give algorithms that implement a Byzantine fault detector in a model of partial synchrony. Finally, we prove the correctness of the consensus algorithm and analyze its complexity.