Byzantine Fault-Tolerant Causal Broadcast on Incomplete Graphs

Causal ordering of broadcasts is a widely used requirement in collaborative distributed software systems. We consider Byzantine-tolerant causal ordering of broadcasts in a replicated data store implemented over an incomplete graph network topology, wherein messages of the broadcast are sent via flooding. We propose two protocols to achieve this. The incomplete graph topology also occurs naturally in wireless networks and in overlay peer-to-peer networks. We identify four properties – safety, liveness, no impersonation, and no avatars – that a Byzantine-tolerant causal broadcast algorithm for a replicated data store over an incomplete graph must satisfy. We also reformulate the traditional properties – validity, integrity, self-delivery, and reliability (or termination) – specified for a complete graph in the literature for a replicated data store system over an incomplete graph topology. We then analyze whether Byzantine processes can mount attacks on these properties in our two protocols. We show results for the classical communication model and the local broadcast model.