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 arguments sound does not allow for adaptively-sound statistical NIZK arguments (unless NP is in P/poly). Furthermore, we show that the assumption used in our construction holds with respect to generic adversaries that do not exploit the specific representation of the group elements. We also discuss how to avoid the non-standard assumption in a pre-processing model.Category / Keywords: cryptographic protocols / NIZK, adaptive soundness, KEA Publication Info: Full version of TCC 07 paper. Date: received 16 Nov 2006 Contact author: Serge Fehr at cwi nl Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Version: 20061119:194617 (All versions of this report) Short URL: ia.cr/2006/423 Discussion forum: Show discussion | Start new discussion