  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.
