Efficient Byzantine Reliable Broadcast in the Failure Case

Reliable broadcast is a fundamental primitive in distributed computing that is widely used in various applications. Several new reliable broadcast algorithms have been presented in recent years, primarily focusing on reducing the communication complexity, which is the total number of exchanged bits in the worst case. While significant progress has been achieved, all proposed algorithms share a common weakness. Executions may fail, i.e., no message is ever delivered, while incurring a communication complexity equal or nearly equal to the communication complexity of executions where a message is delivered. In fact, a single Byzantine node, acting as the dedicated sender, is sufficient to trigger such executions, causing all nodes to consume bandwidth in vain. This paper introduces the novel concept of a reliable broadcast detector, a distributed algorithm that can be coupled with a reliable broadcast algorithm to minimize the communication complexity of failed executions. Two concrete detectors are presented with different requirements and properties. Additionally, reliable broadcast algorithms that utilize detectors are introduced, the main algorithm guaranteeing an overhead factor, compared to an ideal failure-free execution, that tends to 2 as the network size increases. Furthermore, a lower bound is proven that an overhead factor of 5/3 is inevitable when the sender initially broadcasts the message, as is the case for the proposed algorithm. Therefore, it achieves a bound that is close to optimal for any algorithm with this property.