Byzantine-tolerant causal broadcast

Causal broadcast is a communication abstraction built on top of point-to-point send/receive networks that ensures any two messages whose broadcasts are causally related (as captured by Lamport's “happened before” relation) delivered in their sending order. Several causal algorithms have been designed for failure-free and crash-prone asynchronous message-passing systems. This article first gives formal definition the presence Byzantine processes, form equivalent characterizations, then presents simple algorithm implements it. The main difficulty design proof this comes from very nature faults: processes may arbitrary behavior, must ensure correct (i) maintain coherent view causality (ii) never prevented communicating between themselves. To end, modularly, namely it works Byzantine-tolerant reliable algorithm. Due to modularity, proposed easy understand inherits computability assumptions (notably maximal number be Byzantine) message/time complexities underlying which built.