Causal Ordering in the Presence of Byzantine Processes

Causal ordering of messages in distributed systems is important for capturing application-level semantics. To the best of our knowledge, Byzantine fault-tolerant causal ordering has not been attempted for point-to-point communication in an asynchronous setting. In this paper, we first prove that it is impossible to causally order messages under point-to-point communication in an asynchronous system with one or more Byzantine processes. In the face of this impossibility, we then present an algorithm that can causally order messages under point-to-point communication in the face of Byzantine failures, assuming the network provides a known upper bound on the message latency. We also prove that it is impossible to causally order multicasts in an asynchronous setting with one or more Byzantine processes. We then give an extension of our algorithm for unicasts to provide Byzantine fault-tolerant causal ordering of multicasts under the assumption of a known upper bound on the message latency.