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SIAM Journal on Computing, 1991
Summary: This paper investigates the possibility of disposing of interaction between prover and verifier in a zero-knowledge proof if they share beforehand a short random string. Without any assumption, it is proven that noninteractive zero-knowledge proofs exist for some number-theoretic languages for which no efficient algorithm is known. If deciding
Manuel Blum +2 more
exaly +3 more sources
Summary: This paper investigates the possibility of disposing of interaction between prover and verifier in a zero-knowledge proof if they share beforehand a short random string. Without any assumption, it is proven that noninteractive zero-knowledge proofs exist for some number-theoretic languages for which no efficient algorithm is known. If deciding
Manuel Blum +2 more
exaly +3 more sources
Zero Knowledge and Circuit Minimization
Information and Computation, 2014 We show that every problem in the complexity class SZK (Statistical Zero Knowledge) is efficiently reducible to the Minimum Circuit Size Problem (MCSP). In particular Graph Isomorphism lies in RPMCSP. This is the first theorem relating the computational power of Graph Isomorphism and MCSP, despite the long history these problems share, as candidate NP ...
Eric Allender, Bireswar Das
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Fundamenta Informaticae, 1999
We show how a standard deck of playing cards can be used to implement a secure multiparty protocol to compute any boolean function. Our contribution to previous work: no identical copies of cards are needed, and the number of necessary cards is reduced.
Valtteri Niemi, Ari Renvall
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We show how a standard deck of playing cards can be used to implement a secure multiparty protocol to compute any boolean function. Our contribution to previous work: no identical copies of cards are needed, and the number of necessary cards is reduced.
Valtteri Niemi, Ari Renvall
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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science, 1995
Summary: We improve on the communication complexity of zero-knowledge proof systems. Let \({\mathcal C}\) be a Boolean circuit of size \(n\). Previous zero-knowledge proof systems for the satisfiability of \({\mathcal C}\) require the use of \(\Omega(kn)\) bit commitments in order to achieve a probability of undetected cheating below \(2^{-k}\). In the
Joan Boyar +2 more
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Summary: We improve on the communication complexity of zero-knowledge proof systems. Let \({\mathcal C}\) be a Boolean circuit of size \(n\). Previous zero-knowledge proof systems for the satisfiability of \({\mathcal C}\) require the use of \(\Omega(kn)\) bit commitments in order to achieve a probability of undetected cheating below \(2^{-k}\). In the
Joan Boyar +2 more
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Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98, 1998
Concurrent executions of a zero-knowledge protocol by a single prover (with one or more verifiers) may leak information and may not be zero-knowledge in toto . In this article, we study the problem of maintaining zero-knowledge.We introduce the notion of an (α, β) timing constraint : for any ...
Cynthia Dwork, Moni Naor, Amit Sahai
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Concurrent executions of a zero-knowledge protocol by a single prover (with one or more verifiers) may leak information and may not be zero-knowledge in toto . In this article, we study the problem of maintaining zero-knowledge.We introduce the notion of an (α, β) timing constraint : for any ...
Cynthia Dwork, Moni Naor, Amit Sahai
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44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings., 2004
We show how a polynomial-time prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof whether x /spl isin/ S or x /spl notin/ S, without revealing any knowledge beyond the verity of these membership assertions. Our method is non interactive.
Silvio Micali +2 more
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We show how a polynomial-time prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof whether x /spl isin/ S or x /spl notin/ S, without revealing any knowledge beyond the verity of these membership assertions. Our method is non interactive.
Silvio Micali +2 more
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Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing, 2006
We put forward the notion of Local Zero Knowledge and provide its first implementations in a variety of settings under standard complexity assumptions.Whereas the classical notion of Zero Knowledge guarantees the secrecy only of information that is hard to compute, the new one meaningfully guarantees the secrecy of any information (in case of perfect ...
Silvio Micali, Rafael Pass
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We put forward the notion of Local Zero Knowledge and provide its first implementations in a variety of settings under standard complexity assumptions.Whereas the classical notion of Zero Knowledge guarantees the secrecy only of information that is hard to compute, the new one meaningfully guarantees the secrecy of any information (in case of perfect ...
Silvio Micali, Rafael Pass
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Mathematische Semesterberichte, 1993
Mit Zero-Knowledge Protokollen kann eine Person A eine andere davon uberzeugen, ein Geheimnis zu haben, ohne das A das Geringste davon verraten mus. Diese Protokolle sind sowohl fur die Praxis auserst wichtig (elektronische Zugangskontrolle), als auch theoretisch sehr interessant, da in ihnen nichttriviale mathematische und komplexitatstheoretische ...
Beutelspacher, Albrecht, Schwenk, Jörg
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Mit Zero-Knowledge Protokollen kann eine Person A eine andere davon uberzeugen, ein Geheimnis zu haben, ohne das A das Geringste davon verraten mus. Diese Protokolle sind sowohl fur die Praxis auserst wichtig (elektronische Zugangskontrolle), als auch theoretisch sehr interessant, da in ihnen nichttriviale mathematische und komplexitatstheoretische ...
Beutelspacher, Albrecht, Schwenk, Jörg
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Zero-knowledge proofs of identity
Journal of Cryptology, 1987In this paper we extend the notion of interactive proofs of assertions to interactive proofs of knowledge. This leads to the definition of unrestricted input zero-knowledge proofs of knowledge in which the prover demonstrates possession of knowledge without revealing any computational information whatsover (not even the one bit revealed in zero ...
Uriel Feige, Amos Fiat, Adi Shamir
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