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 \(n\) vertex disjoint paths, referred to as 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 \(n \geq t+1\). In this paper we will show that a secure protocol requires at least 3 rounds of communication and 2 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 \emph{constant} transmission rate over the public channel.