$\diamondsuit {\mathcal P}_{mute}$-BASED CONSENSUS for ASYNCHRONOUS BYZANTINE SYSTEMS

This paper presents a consensus protocol for asynchronous distributed systems made up of n processes, where up to f<n/4 processes can behave arbitrarily (Byzantine processes). The protocol assumes that the underlying system is equipped with an unreliable failure detector of the class [Formula: see text]. The failure detectors of the class [Formula: see text] ensure that (1) all mute processes are detected (a mute process is a process that, after some time, stops sending protocol messages), and (2) after some unknown but finite time, no correct process is suspected (mute processes are a subset of the Byzantine processes). The proposed protocol enjoys the following properties. It is based on the round coordinator paradigm and its design principle is particularly simple. Its message complexity is O(n2) per round. In addition to a round number, the message size is O(1), except for one message per round (sent by the round coordinator) whose size is O(n). The protocol does not use message "proofs", certificates, or application level signatures. When no process is faulty, all processes propose the same value, and the failure detector makes no mistake, the processes decide in one round (4 communication steps). Finally, when a process decides, it only needs a simple unreliable broadcast mechanism to prevent the other processes from deadlocking. All these features make the protocol attractive to cope with the net effect of Byzantine failures and asynchrony.

EFFICIENT SOLUTION TO UNIFORM ATOMIC BROADCAST

Chandra and Toueg proposed in 1993 a new approach to overcome the impossibility of reaching deterministically Consensus — and by corollary Atomic Broadcast — in asynchronous systems subject to crash failures. They augment the asynchronous system with a possibly Unreliable Failure Detector which provides some information about the operational state of processes. In this paper, we present an extension of the Consensus problem that we call Uniform Prefix Agreement. This extension enables all the processes to propose a flow of messages during an execution — instead of one as in the Consensus problem — and uses all these proposed messages to compose the decision value. Prefix Agreement is based on an Unreliable Failure Detector. We use repeated executions of Prefix Agreement to build an efficient Uniform Atomic Broadcast algorithm. This paper describes the Uniform Prefix Agreement and Uniform Atomic Broadcast algorithms, and provides proofs of their correctness.