Impossibility and feasibility results for zero knowledge with public keys

Abstract

In this paper, we continue the study of the round complexity of black-box zero knowledge in the bare public-key (BPK, for short) model previously started by Micali and Reyzin in [11]. Specifically we show the impossibility of 3-round concurrent (and thus resettable) black-box zero-knowledge argument systems with sequential soundness for non-trivial languages. In light of the previous state-of-the-art, our result completes the analysis of the round complexity of black-box zero knowledge in the BPK model with respect to the notions of soundness and black-box zero knowledge. Further we give sufficient conditions for the existence of a 3-round resettable zero-knowledge proof (in contrast to argument) system with concurrent soundness for NP in the upperbounded public-key model introduced in [14]. © International Association for Cryptologic Research 2005.