Relay Protocol for Approximate Byzantine Consensus

Approximate byzantine consensus is a fundamental problem of distributed computing. This paper presents a novel algorithm for approximate byzantine consensus, called Relay-ABC. The algorithm allows machines to achieve approximate consensus to arbitrary exactness in the presence of byzantine failures. The algorithm relies on the usage of a relayed messaging system and signed messages with unforgeable signatures that are unique to each node. The use of signatures and relays allows the strict necessary network conditions of traditional approximate byzantine consensus algorithms to be circumvented. We also provide theoretical guarantees of validity and convergence for Relay-ABC. To do this, we utilize the idea that the iteration of states in the network can be modeled by a sequence of transition matrices. We extend previous methods, which use transition matrices to prove ABC convergence, by having each state vector model not just one iteration, but a set of $D$ iterations, where $D$ is a diameter property of the graph. This allows us to accurately model the delays of messages inherent within the relay system.