In this paper we focus on sender-anonymous channels (a.k.a. Dining Cryptographers networks) and present a construction requiring a very low (constant) number of rounds of interaction while tolerating actively malicious behavior by some of the participants (up to less than half of them). Our construction is unconditionally secure (meaning that no bounds are placed on the computational power of the adversary), makes black-box use of a verifiable secret sharing (VSS) protocol, and is based on a special-purpose secure multiparty computation protocol implementing the method of "throwing darts;" its round complexity is essentially equal to that of the VSS protocol.

In the problem of secure message transmission in the public discussion model (SMT-PD), a sender wants to send a message$M_{{\cal S}}\in\{0,1\}^{\ell}$to a receiver privately and reliably. Sender and receiver are connected by$n$channels, also known as simple wires, up to$t