You can prove so many things in zero-knowledge

Abstract

We present a short survey of known notions of zero-knowledge proof systems in the interactive model and main results about these notions, We then introduce a new notion, an extension of proofs of knowledge, which we call Proofs of Non-Zero Knowledge, as they allow a prover to convince a verifier that he knows a secret satisfying some relation, without revealing any new information about the secret or even the relation that the secret satifies with the common input. We prove a number of basic results about proofs of non-zero knowledge, and, in the process, revisit previously studied protocols, described as 'proofs of partial knowledge', which are particular cases of proofs of non-zero knowledge. © Springer-Verlag Berlin Heidelberg 2005.