Self-Stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Traditional Byzantine resilient algorithms use $2f + 1$ vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually 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 and deliver messages from one end user to another. We present the first deterministic, cryptographic-assumptions-free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which $r$ and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical re-establishments of the secrets

Communication in networks with random dependent faults

The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p ≤ 1/c log n. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1/n 1/2, and does not when p ∈ 1/O(n 1/2). Furthermore, a network built of tori is designed, with the same fault-tolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ∈ 1/O(n 1/d). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults. Keywords: Fault-tolerance, dependent faults, communication, crash faults, network connectivity

Communication in random geometric radio networks with positively correlated random faults

We study the feasibility and time of communication in random geometric radio networks, where nodes fail randomly with positive correlation. We consider a set of radio stations with the same communication range, distributed in a random uniform way on a unit square region. In order to capture fault dependencies, we introduce the ranged spot model in which damaging events, called spots, occur randomly and independently on the region, causing faults in all nodes located within distance s from them. Node faults within distance 2s become dependent in this model and are positively correlated. We investigate the impact of the spot arrival rate on the feasibility and the time of communication in the fault-free part of the network. We provide an algorithm which broadcasts correctly with probability 1 - ε in faulty random geometric radio networks of diameter D in time O(D + log1/ε)

FAST BROADCASTING WITH BYZANTINE FAULTS

Abstract: We construct and analyze a fast broadcasting algorithm working in the presence of Byzantine component faults. Such faults are particularly difficult to deal with, as faulty components may behave arbitrarily (even maliciously) as transmitters, by either blocking, rerouting, or altering transmitted messages in a way most detrimental to the broadcasting process. We assume that links and nodes of a communication network are subject to Byzantine failures, and that faults are distributed randomly and independently, with link failure probability p and node failure probability q, these parameters satisfying the inequality (1 − p) 2 (1−q)> 1/2. A broadcasting algorithm, working in an n-node network, is called almost safe if the probability of its correctness is at least 1 − 1/n, for sufficiently large n. Thus the robustness of the algorithm grows with the size of the network. Our main result is the design and analysis of an almost safe broadcasting algorithm working in time O(log 2 n) and using O(n log n) messages in n-node networks. The novelty of our algorithm is that it can cope with the most difficult type of faults, potentially affecting all components of the network (both its links and nodes), and that it is simultaneously robust and efficient. Copyright (c) 2004 IFA