Constant Phase Bit Optimal Protocols for Perfectly Reliable and Secure Message Transmission Tolerating

We study the fundamental problem of perfectly secure message transmission (PSMT), where two non-faulty players, the sender S and the receiver R are part of a synchronous network modeled as an undirected graph, a part of which may be under the influence of a malicious unbounded computational powerful adversary who can disrupt the communication in variety of ways. S intends to transmit a message m to R using some protocol such that after interacting in phases 1 as per the protocol R should correctly obtain S’s message while adversary should be completely ignorant about the same. The problem of perfectly reliable message transmission (PRMT), requires only correctness of the message received by R. However, unlike most of the literature on the problem, we assume the adversary modeling the faults is mixed (and can corrupt different set of nodes in Byzantine, failstop and passive fashion simultaneously) and thus versatile enough to disrupt the information flow in the network in variety of ways. The mixed adversary can be either static or mobile. The communication complexity of multiphase interactive PRMT and PSMT protocols is one of their most important complexity measure. In this work we look into the optimal communication complexity of PRMT and PSMT problem considering static and mobile mixed adversary. We observ