This paper presents an algorithm, called BCM-Broadcast, for the implementation of causal broadcast in distributed mobile systems in the presence of Byzantine failures. The BCM-Broadcast algorithm simultaneously focuses on three critical challenges in distributed systems: Byzantine failures, Causality, and Mobility. We first present a hierarchical architecture for BCM-Broadcast. Then, we define twelve properties for BCM-Broadcast, including validity, integrity, termination, and causality. We then show that BCM-Broadcast satisfies all these properties. We also prove the safety of BCM-Broadcast; i.e., no healthy process delivers a message from any Byzantine process, assuming that the number of Byzantine processes is less than a third of the total number of mobile nodes. Subsequently, we show that the message complexity of BCM-Broadcast is linear. Finally, using the Poisson process, we analyze the probability of the violation of the safety condition under different mobility scenarios.

翻译：本文提出了一种名为BCM-Broadcast的算法，用于在存在拜占庭故障的分布式移动系统中实现因果广播。该算法同时聚焦于分布式系统的三个关键挑战：拜占庭故障、因果性和移动性。我们首先提出了BCM-Broadcast的分层架构，随后定义了其十二项属性，包括有效性、完整性、终止性和因果性，并证明BCM-Broadcast满足所有这些属性。我们还验证了算法的安全性，即假设拜占庭进程数量小于移动节点总数的三分之一时，任何健康进程都不会从拜占庭进程处接收消息。进而表明BCM-Broadcast的消息复杂度呈线性。最后，基于泊松过程，我们分析了不同移动场景下违反安全条件的概率。