Byzantine-tolerant detection of causality: There is no holy grail

Abstract

Detecting causality or the “happened before” relation between events in an asynchronous distributed system is a widely used building block in distributed applications. To the best of our knowledge, this problem has not been examined in a system with Byzantine processes. We prove the following results for an asynchronous system with Byzantine processes. (1) We prove that it is impossible to determine causality between events in the presence of even a single Byzantine process when processes communicate by unicasting. (2) We also prove a similar impossibility result when processes communicate by broadcasting. (3) We also prove a similar impossibility result when processes communicate by multicasting. (4–5) In an execution where there exists a causal path between two events passing through only correct processes, we prove that it is possible to detect causality between such a pair of events when processes communicate by unicasting or broadcasting. (6) However, when processes communicate by multicasting and there exists a causal path between two events passing through only correct processes, we prove that it is impossible to detect causality between such a pair of events. (7–9) Even with the use of cryptography, we prove that the impossibility results of (1–3) for unicasts, broadcasts, and multicasts, respectively, hold. (10–12) With the use of cryptography, when there exists a causal path between two events passing through only correct processes, we prove it is possible to detect causality between such a pair of events, irrespective of whether the communication is by unicasts, broadcasts, or multicasts. Our results are significant because Byzantine systems mirror the real world.