Byzantine Fault Tolerant Causal Ordering

TL;DR

This paper investigates the challenge of achieving causal message ordering in asynchronous distributed systems with Byzantine faults, proving impossibility results and proposing algorithms under certain network assumptions.

Contribution

It introduces the first algorithms for Byzantine fault-tolerant causal ordering of point-to-point communication in asynchronous systems with message delay bounds.

Findings

Existing algorithms fail under Byzantine faults.

Impossibility of causal ordering with Byzantine faults in pure asynchrony.

Proposed algorithms work when message transmission time is bounded.

Abstract

Causal ordering in an asynchronous system has many applications in distributed computing, including in replicated databases and real-time collaborative software. Previous work in the area focused on ordering point-to-point messages in a fault-free setting, and on ordering broadcasts under various fault models. 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 show that existing algorithms for causal ordering of point-to-point communication fail under Byzantine faults. We then prove that it is impossible to causally order messages under point-to-point communication in an asynchronous system with one or more Byzantine failures. We then present two algorithms that can causally order messages under Byzantine failures, where the network provides an upper bound on the message transmission time. The proofs of correctness for these algorithms show that it is possible to achieve causal ordering for point-to-point communication under a stronger asynchrony model where the network provides an upper bound on message transmission time. We also give extensions of our two algorithms for Byzantine fault-tolerant causal ordering of multicasts.