On Optimal Secure Message Transmission by Public Discussion

In a secure message transmission (SMT) scenario, a sender wants to send a message in a private and reliable way to a receiver. Sender and receiver are connected by n wires, t of which can be controlled by an adaptive adversary with unlimited computational resources. In Eurocrypt 2008, Garay and Ostrovsky considered an SMT scenario where sender and receiver have access to a public discussion channel and showed that secure and reliable communication is possible when n ≥ t + 1. In this paper, we will show that a secure protocol requires at least three rounds of communication and two rounds invocation of the public channel and hence give a complete answer to the open question raised by Garay and Ostrovsky. We also describe a round optimal protocol that has constant transmission rate over the public channel.