Efficient zero knowledge on the internet

Abstract

The notion of concurrent zero knowledge has been introduced by Dwork et al. [STOC 1998] motivated by the growing use of asynchronous networks as the Internet. In this paper we show a transformation that, for any language L admitting a Σ-protocol, produces a 4-round concurrent zero-knowledge argument system with concurrent soundness in the bare public-key (BPK, for short) model. The transformation only adds O(1) modular exponentiations, and uses standard number-theoretic assumptions and polynomial-time simulation. A tool that we construct and use for our main result is that of efficient concurrent equivocal commitments. We give an efficient construction of this gadget in the BPK model that can be of independent interest. © Springer-Verlag Berlin Heidelberg 2006.