Distributed Causal Memory in the Presence of Byzantine Servers

Abstract

We study distributed causal shared memory (or distributed read/write objects) in the client-server model over asynchronous message-passing networks in which some servers may suffer Byzantine failures. Since Ahamad et al. proposed causal memory in 1994, there have been abundant research on causal storage. Lately, there is a renewed interest in enforcing causal consistency in large-scale distributed storage systems (e.g., COPS, Eiger, Bolt-on). However, to the best of our knowledge, the fault-tolerance aspect of causal memory is not well studied, especially on the tight resilience bound. In our prior work, we showed that 2 f+1 servers is the tight bound to emulate crash-tolerant causal shared memory when up to f servers may crash. In this paper, we adopt a typical model considered in many prior works on Byzantine-tolerant storage algorithms and quorum systems. In the system, up to f servers may suffer Byzantine failures and any number of clients may crash. We constructively present an emulation algorithm for Byzantine causal memory using 3 f+1 servers. We also prove that 3 f+1 is necessary for tolerating up to f Byzantine servers. In other words, we show that 3 f+1 is a tight bound. For evaluation, we implement our algorithm in Golang and compare their performance with two state-of-the-art fault-tolerant algorithms that ensure atomicity in the Google Cloud Platform.