On perfectly secure communication over arbitrary networks
We study the interplay of network connectivity and perfectly secure message transmission under the corrupting influence of generalized Byzantine adversaries. It is known that in the threshold adversary model, where the Byzantine adversary can corrupt upto and t among the n players (nodes), perfectly secure communication among any pair of players is possible if and only if the underlying synchronous network is (2t + 1)-connected. Strictly generalizing these results to the non-threshold setting, we show that perfectly secure communication among any pair of players is possible if and only if the union of no two sets in the adversary structure is a vertex cutset of the synchronous network. The computation and communication complexities of the transmission protocol are polynomial in the size of the network and the maximal basis of the adversary structure.
