Reliable broadcast with respect to topology knowledge

Abstract

We study the Reliable Broadcast problem in incomplete networks against a Byzantine adversary. We examine the problem under the locally bounded adversary model of Koo (2004) and the general adversary model of Hirt and Maurer (1997) and explore the tradeoff between the level of topology knowledge and the solvability of the problem.We refine the local pair-cut technique of Pelc and Peleg (2005) in order to obtain impossibility results for every level of topology knowledge and any type of corruption distribution. On the positive side we devise protocols that match the obtained bounds and thus, exactly characterize the classes of graphs in which Reliable Broadcast is possible.Among others, we show that Koo's Certified Propagation Algorithm (CPA) is unique against locally bounded adversaries in ad hoc networks, that is, it can tolerate as many local corruptions as any other non-faulty algorithm; this settles an open question posed by Pelc and Peleg. We also provide an adaptation of CPA against general adversaries and show its uniqueness in this case too. To the best of our knowledge this is the first optimal algorithm for Reliable Broadcast in generic topology ad hoc networks against general adversaries.

Broadcast using certified propagation algorithm in presence of Byzantine faults

“…The condition in [7] is indeed equivalent to our condition (condition in Theorem 1) in undirected graphs. Therefore, it is NP-hard to examine whether a given graph satisfies our condition or not.…”

“…Complexity Pagourtzis et al [7] proved that it is NP-hard to examine whether CPA is correct in a given undirected graph. The condition in [7] is indeed equivalent to our condition (condition in Theorem 1) in undirected graphs.…”

“…Koo [6], Bhandari and Vaidya [1], Pelc and Peleg [8], Ichimura and Shigeno [5], Pagourtzis et al [7] also explored this fault model. Yet, to the best of our knowledge, the tight necessary and sufficient conditions for the correctness of CPA in directed networks under f -local fault model have not been developed previously.…”

“…Ichimura and Shigeno [5] provided another condition that can approximate (within a factor of 2) the largest f for which CPA is correct in a given graph. Independently, Pagourtzis et al [7] presented the tight condition in undirected graphs. Similar condition under other contexts are also discovered by other researchers [9,3].…”

“…We assume an f -locally bounded model, in which at most f Byzantine faults occur in the neighborhood of every fault-free node [6]. In particular, we are interested in the necessary and sufficient condition on the underlying communication network topology for the correctness of the Certified Propagation Algorithm (CPA) -the CPA algorithm has been analyzed in prior work [6,1,8,5,7].…”