This paper addresses the problem of defining and providing proofs of knowledge for a general class of exponentiation-based formulae. We consider general predicates built from modular exponentiations of secret values, combined by products and connected with the logical operators "AND", "OR", "NOT". We first show how to deal with non-linear combination of secret exponents. Next,we extend the work by Brands [4] to a strictly larger class of predicates, allowing a more liberal use of the logical

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... rator "NOT". We sketch two applications by which we enhance group signatures schemes with revocation of identity and multi-signer features. Such features can be useful to protect privacy or for collabrative use of group signatures, respectively.