Byzantine-Tolerant Causal Ordering for Unicasts, Multicasts, and Broadcasts

Abstract

Byzantine fault-tolerant causal ordering of messages is useful to many applications. Causal ordering requires a property that we term strong safety, and liveness. In this paper, we use execution histories to prove that it is impossible to solve causal ordering -strong safety and liveness -in a deterministic manner for unicasts, multicasts, and broadcasts in an asynchronous system with one or more Byzantine processes. We also define a weaker version of strong safety termed weak safety. We prove that it is impossible to solve causal ordering -weak safety and liveness -in a deterministic manner for unicasts and multicasts, in an asynchronous system with one or more Byzantine processes. In view of these impossibility results, we propose the Sender-Inhibition algorithm and the Channel Sync algorithm to provide causal order -weak safety and liveness -of unicasts under the Byzantine failure model in synchronous systems, which have a known upper bound on message latency. The algorithms operate under the synchronous system model, but are inherently asynchronous and offer a high degree of concurrency as lock-step communication is not assumed. The two algorithms provide different trade-offs. We also indicate how the algorithms can be extended to multicasts.