Proofs of knowledge for non-monotone discrete-log formulae and applications

Abstract

This paper addresses the problem ofdefining and providing proofs of knowledge for a general class of exponentiation-based formulae. We consider general predicates built from modular exponentiations ofsecret values, combined by products and connected with the logical operators “AND”, “OR”, “NOT”. We first show how to deal with non-linear combination ofsecret exponents. Next,we extend the work by Brands [4] to a strictly larger class ofpredicates, allowing a more liberal use ofthe logical operator “NOT”. We sketch two applications by which we enhance group signatures schemes with revocation ofiden tity and multi-signer features. Such features can be useful to protect privacy or for collaborative use of group signatures, respectively.