On the possibility of one-message weak zero-knowledge

Abstract

We investigate whether it is possible to obtain any meaningful type of zero-knowledge proofs using a one-message (i.e., noninteractive) proof system. We show that, under reasonable (although not standard) assumptions, there exists a one-message proof system for every language in NP that satisfies the following relaxed form of zero knowledge: 1. The soundness condition holds only against cheating provers that run in uniform (rather than non-uniform) probabilistic polynomialtime. 2. The zero-knowledge condition is obtained using a simulator that runs in quasi-polynomial (rather than polynomial) time. We note that it is necessary to introduce both relaxations to obtain a one-message system for a non-trivial language. We stress that our result is in the plain model, and in particular we do not assume any setup conditions (such as the existence of a shared random string). We also discuss the validity of our assumption, and show two conditions that imply it. In addition, we show that an assumption of a similar kind is necessary in order to obtain a one-message system that satisfies some sort of meaningful zero-knowledge and soundness conditions. © Springer-Verlag 2004.