Network Connection and Perfectly Secure Message Transmission on Wireless Mobile Networks

In this paper we proposed perfectly secure message transmission for reliable and secure communications in order to ensure that an adversary cannot obtain information (in the information theoretic sense) about messages. There are numerous studies about the interplay of network connectivity and perfectly secure message transmission under a Byzantine adversary capable of corrupting up to 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. But existing studies deal with traditional wired networks and neglect perfectly secure message transmission on mobile networks. Therefore, we proposed a perfectly secure message transmission protocol and analyzed the interplay of mobile network connectivity and perfectly secure message transmission. We considered that network connection takes priority over other factors for perfectly secure message transmission, and we showed that the number of paths needed to ensure mobile network connection is   n K n N log = in an undirected graph with n nodes. And, we proved that the connectivity (2T+1) on mobile networks with n nodes, where   n K t T log = , must be higher than the connectivity (2t+1) of wired networks.