Signature-Free Asynchronous Binary Byzantine Consensus with t<<n/3, O(n²) Messages, and O(1) Expected Time

International audienceThis paper is on broadcast and agreement in asynchronous message-passing systems made up of n processes, and where up to t processes may have a Byzantine Behavior. Its first contribution is a powerful , yet simple, all-to-all broadcast communication abstraction suited to binary values. This abstraction, which copes with up to t < n/3 Byzantine processes, allows each process to broadcast a binary value, and obtain a set of values such that (1) no value broadcast only by Byzantine processes can belong to the set of a correct process, and (2) if the set obtained by a correct process contains a single value v, then the set obtained by any correct process contains v. The second contribution of the paper is a new round-based asynchronous consensus algorithm that copes with up to t < n/3 Byzantine processes. This algorithm is based on the previous binary broadcast abstraction and a weak common coin. In addition of being signature-free and optimal with respect to the value of t, this consensus algorithm has several noteworthy properties: the expected number of rounds to decide is constant; each round is composed of a constant number of communication steps and involves O(n²) messages; each message is composed of a round number plus a constant number of bits. Moreover , the algorithm tolerates message reordering by the adversary (i.e., the Byzantine processes)

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 réduction du consensus multivalué au consensus binaire en présence d'asynchronisme, de t < n/3 processus byzantins, avec un temps constant, O(n 2) messages, et pas de signatures Résumé : Cet article présente un algorithme réparti qui, dans un système asynchrone de n processus qui communiquent par passage de messages, et qui comprend jusqu'à t processus byzantins, ramène le problème du consensus multivalué au problème du consensus binaire. Cette réduction est optimale par rapport à t (t < n/3), requiert un temps constant et O(n 2) messages, et n'utilise aucun élément cryptographique (i.e., pas de signatures). Elle considère donc un adversaire donc la la puissance de calcul peut être illimitée

Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(n²) Messages, O(1) Time, and no Signature

International audienceThis paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asyn-chronous 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(n²) 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(n²) 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(n²) 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 reordering by Byzantine processes