Paper 2008/262

Statistically Reliable and Secure Message Transmission in Directed Networks

Arpita Patra, Ashish Choudhury, and C. Pandu Rangan

Abstract

Consider the following problem: a sender S and a receiver R are part of a directed synchronous network and connected through intermediate nodes. Specifically, there exists n node disjoint paths, also called as wires, which are directed from S to R and u wires, which are directed from R to S. Moreover, the wires from S to R are disjoint from the wires directed from R to S. There exists a centralized, static adversary who has unbounded computing power and who can control at most t wires between S and R in Byzantine fashion. S has a message m^S, which we wants to send to R. The challenge is to design a protocol, such that after interacting in phases as per the protocol, R should correctly output m^R = m^S, except with error probability 2^{-\Omega(\kappa)}, where \kappa is the error parameter. This problem is called as statistically reliable message transmission (SRMT). The problem of statistically secure message transmission (SSMT) has an additional requirement that at the end of the protocol, m^S should be information theoretically secure. Desmedt et.al have given the necessary and sufficient condition for the existence of SRMT and SSMT protocols in the above settings. They also presented an SSMT protocol, satisfying their characterization. Desmedt et.al claimed that their protocol is efficient and has polynomial computational and communication complexity. However, we show that it is not so. That is, we specify an adversary strategy, which may cause the protocol to have exponential computational and communication complexity. We then present new and efficient SRMT and SSMT protocols, satisfying the characterization of Desmedt et.al Finally we show that the our proposed protocols are communication optimal by deriving lower bound on the communication complexity of SRMT and SSMT protocols. As far our knowledge is concerned, our protocols are the first communication optimal SRMT and SSMT protocols in directed networks.