Byzantine-tolerant causal broadcast.

• In this paper, we provide a formal definition of a causal broadcast abstraction in the presence of Byzantine processes. • We present a simple causal broadcast algorithm that implements this specification in the presence of Byzantine processes. • We prove our algorithm to be correct under the specification we have provided. • One difficulty consists in proving that an adversary cannot destroy the causality between broadcasts of correct processes. • We illustrate how our algorithm can help implement a money transfer object, with potential application to cryptocurrencies. Causal broadcast is a communication abstraction built on top of point-to-point send/receive networks that ensures that any two messages whose broadcasts are causally related (as captured by Lamport's "happened before" relation) are delivered in their sending order. Several causal broadcast algorithms have been designed for failure-free and crash-prone asynchronous message-passing systems. This article first gives a formal definition of a causal broadcast abstraction in the presence of Byzantine processes, in the form of two equivalent characterizations, and then presents a simple causal broadcast algorithm that implements it. The main difficulty in the design and the proof of this algorithm comes from the very nature of Byzantine faults: Byzantine processes may have arbitrary behavior, and the algorithm must ensure that correct processes (i) maintain a coherent view of causality and (ii) are never prevented from communicating between themselves. To this end, the algorithm is built modularly, namely it works on top of any Byzantine-tolerant reliable broadcast algorithm. Due to this modularity, the proposed algorithm is easy to understand and inherits the computability assumptions (notably the maximal number of processes that may be Byzantine) and the message/time complexities of the underlying reliable broadcast on top of which it is built. [ABSTRACT FROM AUTHOR]