On the Optimal Communication Complexity of Multiphase Protocols for Perfect Communication

In the perfectly secure message transmission (PSMT) problem, two synchronized non-faulty players (or processors), the Sender S and the Receiver R are connected by n wires (each of which facilitates 2-way communication); S has a message, represented by a sequence oft elements from a finite field, that he wishes to send to R; after exchanging messages in phases R should correctly obtain S ´s message, while an adversary listening on and actively controlling any set of t (or less) wires should have no information about S ´s message. Similarly, in the problem of perfect reliable message transmission (PRMT), the receiver R should correctly obtain S´s message, in spite of the adversary actively controlling any set oft (or less) wires.