Self-Healing Algorithms of Byzantine Faults

Recent years have seen significant interest in designing networks that are self-healing in the sense that they can automatically recover from adversarial attacks. Previous work shows that it is possible for a network to automatically recover, even when an adversary repeatedly deletes nodes in the network. However, there have not yet been any algorithms that self-heal in the case where an adversary takes over nodes in the network. In this paper, we address this gap. In particular, we describe a communication network over n nodes that ensures the following properties, even when an adversary controls up to t <= (1/8 - \epsilon)n nodes, for any non-negative \epsilon. First, the network provides a point-to-point communication with bandwidth and latency costs that are asymptotically optimal. Second, the expected total number of message corruptions is O(t(log* n)^2) before the adversarially controlled nodes are effectively quarantined so that they cause no more corruptions. Empirical results show that our algorithm can reduce the bandwidth cost by up to a factor of 70.