Perfectly secure message transmission for mobile networks

The problem of perfectly secure message transmission is to ensure that the adversary cannot obtain information about messages in the information theoretic sense. There are lots of studies about the interplay of network connectivity and perfectly secure message transmission under a Byzantine adversary that cannot corrupt at most t players. It is known that perfectly secure communication among any pair of players is possible if and only if the underlying synchronous wired network is (2t+1)-connected. This has been studied only on traditional wired networks, and perfectly secure message transmission on mobile networks has not been studied. Therefore we proposed a perfectly secure message transmission protocol and considered the interplay of mobile network connectivity and perfectly secure message transmission. We showed that the connectivity, (2T+1) on mobile networks, where T = t⌈K log n⌉, must be higher than the connectivity (2t+1)-of wired networks. It is proved by using an undirected graph as the communication model.