|Title:||PROOFS THAT YIELD ~OTHING BUT THEIR VALIDITY or ALL LANGUAGES IN NP HAVE ZERO-KNOWLEDGE PROOF SYSTEMS (Revised Version oŁ TR~ 498 & 544)
|Authors:||o. Goldreich, S. Micali, and A. Wigderson
|Abstract:||In this paper we demonstrate the generality and wide applicability of zero-knowledge proofs, a notion introduced by Goldwasser, Micali and Rackoff. 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 NPrlCoNP. Under the assumption that secure encryption functions exist or by using "physical means for hiding infonnation", we show that all languages in NP have zero-knowledge proofs. Loosely speaking, it is possible to demonstrate that a CNF fonnula is satisfiable without revealing any other property of the fonnula. In particular, without yielding neither a satisfying assignment nor properties such as whether there is a satisfying assignment in which xl=x3 etc. We also demonstrate that zero-knowledge proofs exist "outside the domain of cryptography and number theory". Using no assumptions, we show that both graph isomorphism and graph non-isomorphism have 7..ero-knowledge interactive proofs. The mere existence of an interactive proof for graph non-isomorphism is interesting, since graph non-isomorphism is not known to be in NP and hence no efficient proofs were known before for demonstrating that two graphs are not isomorphic.|
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