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Proofs that Yield Nothing But Their Validity or All Languages Proof Systems in NP Have Zero-Knowledge ODED GOLDREICH Technion, Haifa, Israel SILVIO MICALI Institute of Technology, Catnbridge, Massachusetts Massachusetts AND AVI WIGDERSON Hebrew University, Jerusalem, Israel Abstract. In this paper the generality and wide applicability of Zero-knowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without conveying any additional knowledge. All previously known zero-knowledge proofs were only for number-theoretic languages in NP fl CONP. Under the assumption that secure encryption functions exist or by using physical means for hiding information, it is shown that all languages in NP have zero-knowledge proofs. Loosely speaking, it is possible to demonstrate that a CNF formula is satisfiable without revealing any other property of the formula, in particular, without yielding neither a satis@ing assignment nor properties such as whether there is a satisfying assignment in which xl = X3 etc. It is also demonstrated that zero-knowledge proofs exist outside the domain of cryptography and number theory. Using no assumptions. it is shown that both graph isomorphism and
Journal of the ACM (JACM) – Association for Computing Machinery
Published: Jul 1, 1991
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