Perfect NIZK with Adaptive Soundness

Abstract. This paper presents a very simple and efficient adaptivelysound perfect NIZK argument system for any NP-language. In contrast to recently proposed schemes by Groth, Ostrovsky and Sahai, our scheme does not pose any restriction on the statements to be proven. Besides, it enjoys a number of desirable properties: it allows to re-use the common reference string (CRS), it can handle arithmetic circuits, and the CRS can be set-up very efficiently without the need for an honest party. We then show an application of our techniques in constructing efficient NIZK schemes for proving arithmetic relations among committed secrets, whereas previous methods required expensive generic NP-reductions. The security of the proposed schemes is based on a strong non-standard assumption, an extended version of the so-called Knowledge-of-Exponent Assumption (KEA) over bilinear groups. We give some justification for using such an assumption by showing that the commonly-used approach for proving NIZK...

• Type: Conference
• Year: 2007
• Where: TCC
• Authors: Masayuki Abe, Serge Fehr
• Keywords: Cryptography, Nizk Arguments, Non-standard Assumption, Strong Non-standard Assumption, TCC 2007