Self-stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Traditional Byzantine resilient algorithms use 2f+1 vertex disjoint paths to ensure message deliveryin the presence of up to f Byzantine nodes. The question of how these paths are identified is related tothe fundamental problem of topology discovery.Distributed algorithms for topology discovery cope with a never ending task, dealing with frequentchanges in the network topology and unpredictable transient faults. Therefore, algorithms for topologydiscovery should be self-stabilizing to ensure convergence of the topology information following anysuch unpredictable sequence of events. We present the first such algorithm that can cope with Byzantinenodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node iseventually aware of all the other non-Byzantine nodes and their connecting communication links.Using the topology information, nodes can, for example, route messages across the network anddeliver messages from one end user to another. We present the first deterministic, cryptographic-assumptions-free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery andend-to-end message delivery. We also consider the task of r-neighborhood discovery for the case inwhich r and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facili-tates polynomial time, communication and space solutions for the above tasks.The obtained algorithms can be used to authenticate parties, in particular during the establishmentof private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of thecompromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on theestablished private secrets can be employed in between periodical re-establishments of the secrets.