In the Secure Message Transmission (SMT) problem, Alice is connected to Bob through n node-disjoint communication paths, called wires, at most t of which can be captured by an adversary with unlimited computational power. The goal of an SMT protocol is to send a message reliably and privately. A perfectly secure message transmission (PSMT) guarantees that Bob always correctly receives the sent message (perfect reliability) and the adversary does not learn anything about the message (perfect privacy). A PSMT protocol can have one or more rounds. Messages are delivered to the recipient of a round before the next round starts. Dolev et al. showed that 2-round PSMT is possible iff there are n ≥ 2t + 1 wires . An important measure of efficiency for SMT protocols is transmission rate which is the ratio of the total communication to the size of the messages that is transmitted. It was shown that the transmission rate for 2 or more round PSMT is lower bounded by Ω( n n−2t)  and so when n = (2 + ɛ)t, the lower bound on the communication rate is Ω(1). A PSMT protocol which achieves the lower bound on the transmission rate is termed an optimal PSMT protocol
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