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 being constant and 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. Under a stronger assumption on failure probability parameters, namely (1 - p)2(1 - q)2 > 1/2, our algorithm can be modified to work in time O( log 2 n/ log log n), also using O(n log n) messages. 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.