Secure Message Transmission by Public Discussion: A Brief Survey

Abstract

In the problem of Secure Message Transmission in the public discussion model (SMT-PD), a Sender wants to send a message to a Receiver privately and reliably. Sender and Receiver are connected by n channels, up to t < n of which may be maliciously controlled by a computationally unbounded adversary, as well as one public channel, which is reliable but not private. The SMT-PD abstraction has been shown instrumental in achieving secure multi-party computation on sparse networks, where a subset of the nodes are able to realize a broadcast functionality, which plays the role of the public channel. In this short survey paper, after formally defining the SMT-PD problem, we overview the basic constructions starting with the first, rather communication-inefficient solutions to the problem, and ending with the most efficient solutions known to-date--optimal private communication and sublinear public communication. These complexities refer to resource use for a single execution of an SMT-PD protocol. We also review the amortized complexity of the problem, which would arise in natural use-case scenarios where S and R must send several messages back and forth, where later messages depend on earlier ones.