Time-Free Authenticated Byzantine Consensus

International audienceThis paper presents a simple protocol that solves the authenticated ByzantineConsensus problem in asynchronous distributed systems. To circumvent the FLP impossibility result in a deterministic way, synchrony assumptions should be added. In the context of Byzantine failures for systems where at most t processes may exhibit a Byzantine behavior and where not all the system is assumed eventually synchronous, Moumen et al. provide the main result. They assume at least one correct process, called 2t-bisource, connected with 2t privileged neighbors with eventually timely outgoing and incoming links. The present paper shows that a deterministic solution for the authenticated byzantine consensus problem is possible if the system model satisfies an additional assumption that does not rely on physical time but on the pattern of messages that are exchanged. The basic message exchange between processes is the query-response mechanism. To solve the Consensus problem, we assume a correct process p, called eventual 2t-winning process, and a set Q of 2t processes such that, eventually, for each query issued by p, any process q of Q receives a response from p among the (n-t) first responses to that query. The processes in the set Q can exhibit a Byzantine behavior and this set may change over time. Whereas many time-free solutions have been designed for the consensus problem in the crash model, this is, to our knowledge, the first time-free deterministic solution to the Byzantine consensus problem.Cet article présente un protocole de consensus dans un système asynchrone où un certain nombre de processus (au plus t) peuvent exhiber un comportement byzantin. Il est connu que ce problème n'a pas de solution dans un tel contexte c'est pour cela qu'il faut renforcer le système asynchrone de base avec des contraintes temporelles ou structurelles qui puisse rendre le problème décidable. La démarche choisie dans cet article puisque c'est la première fois que la contrainte rajoutée n'est pas temorelles mais repose sur la pattern de message échangé par les processus

Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems

In this paper, we show that the protocol complex of a Byzantine synchronous system can remain $(k - 1)$-connected for up to $\lceil t/k \rceil$ rounds, where $t$ is the maximum number of Byzantine processes, and $t \ge k \ge 1$. This topological property implies that $\lceil t/k \rceil + 1$ rounds are necessary to solve $k$-set agreement in Byzantine synchronous systems, compared to $\lfloor t/k \rfloor + 1$ rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine $k$-set agreement in exactly $\lceil t/k \rceil + 1$ synchronous rounds, at least when $n$ is suitably large compared to $t$. In conclusion, we see how Byzantine failures can potentially require one extra round to solve $k$-set agreement, and, for $n$ suitably large compared to $t$, at most that