Bounds and constructions for 1-round (0,δ)-secure message transmission against generalized adversary

Abstract

In the Secure Message Transmission (SMT) problem, a sender S is connected to a receiver R through n node-disjoint paths in the network, a subset of which are controlled by an adversary with unlimited computational power. S wants to send a message m to R in a private and reliable way. Constructing secure and efficient SMT protocols against a threshold adversary who can corrupt at most t out of n wires, has been extensively researched. However less is known about SMT problem for a generalized adversary who can corrupt one out of a set of possible subsets. In this paper we focus on 1-round (0,δ)-SMT protocols where privacy is perfect and the chance of protocol failure (receiver outputting NULL) is bounded by δ. These protocols are especially attractive because of their possible practical applications. We first show an equivalence between secret sharing with cheating and canonical 1-round (0, δ)-SMT against a generalized adversary. This generalizes a similar result known for threshold adversaries. We use this equivalence to obtain a lower bound on the communication complexity of canonical 1-round (0, δ)-SMT against a generalized adversary. We also derive a lower bound on the communication complexity of a general 1-round (0, 0)-SMT against a generalized adversary. We finally give a construction using a linear secret sharing scheme and a special type of hash function. The protocol has almost optimal communication complexity and achieves this efficiency for a single message (does not require block of message to be sent). © 2012 Springer-Verlag.