Constant Phase Bit Optimal Protocols for Perfectly Reliable and Secure Message Transmission
In this paper, we study the problem of perfectly reliable message transmission(PRMT) and perfectly secure message transmission(PSMT) between a sender S and a receiver R in a synchronous network, where S and R are connected by n vertex disjoint paths called wires, each of which facilitates bidirectional communication. We assume that atmost t of these wires are under the control of adversary. We present two-phase-bit optimal PRMT protocol considering Byzantine adversary as well as mixed adversary. We also present a three phase PRMT protocol which reliably sends a message containing l field elements by overall communicating O(l) field elements. This is a significant improvement over the PRMT protocol proposed in  to achieve the same task which takes log(t) phases. We also present a three-phase-bit-optimal PSMT protocol which securely sends a message consisting of t field elements by communicating O(t 2) field elements.
KeywordsReliable and Secure Communication Information Theoretic Security Communication Efficiency
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