Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(n 2 ) Messages, O(1) Time, and no Signature

This paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asynchronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes t < n/3 (and is consequently optimal from a resilience point of view), uses O(n 2) messages, has a constant time complexity, and does not use signatures. The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values such that, if the set of a non-faulty process contains a single value, then this value belongs to the set of any non-faulty process. Both communication abstractions have an O(n 2) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with O(n 2) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to t < n/3 Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm tolerates message re-ordering by Byzantine processes. Une reduction du consensus multivalue au consensus binaire en presence d'asynchronisme, de t < n/3 processus byzantins, avec un temps constant, O(n 2) messages, et pas de signatures Resume : Cet article presente un algorithme reparti qui, dans un systeme asynchrone de n processus qui communiquent par passage de messages, et qui comprend jusqu'a t processus byzantins, ramene le probleme du consensus multivalue au probleme du consensus binaire. Cette reduction est optimale par rapport a t (t < n/3), requiert un temps constant et O(n 2) messages, et n'utilise aucun element cryptographique (i.e., pas de signatures). Elle considere donc un adversaire donc la la puissance de calcul peut etre illimitee.