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In this paper we extend the notion of zero knowledge proofs of membership (which reveal one bit of information) to zero knowledge proofs of knowledge (which reveal no information whatsoever). After formally defining this notion, we show its relevance to identification schemes, in which parties prove their identity by demonstrating their knowledge rather than by proving the validity of assertions. We describe a novel scheme which is provably secure if factoring is difficult and whose practical implementations are about two orders of magnitude faster than RSA-based identification schemes. In the last part of the paper we consider the question of sequential versus parallel executions of zero knowledge protocols, define a new notion of “transferable information”, and prove that the parallel version of our identification scheme (which is not known to be zero knowledge) is secure since it reveals no transferable information.