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NonInteractive ZeroKnowledge Proofs of NonMembership
"... Abstract. Often, in privacysensitive cryptographic protocols, a party commits to a secret message m and later needs to prove thatm belongs to a language L or thatm does not belong to L (but does not want to reveal any further information). We present a method to prove in a noninteractive way that ..."
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introduced zeroknowledge proofs with witness elimination which enable to prove that a committed messagem belongs to a setL in such a way that the verifier accepts the interaction only ifm does not belong to a set determined by a public relation Q and some private input m ′ of the verifier. We show
Lower Bounds For Noninteractive Zeroknowledge
, 2007
"... We establish new lower bounds and impossibility results for noninteractive zeroknowledge proofs and arguments with setup assumptions. – For the common random string model, we exhibit a lower bound for the tradeoff between hardness assumptions and the length of the random string for noninteract ..."
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We establish new lower bounds and impossibility results for noninteractive zeroknowledge proofs and arguments with setup assumptions. – For the common random string model, we exhibit a lower bound for the tradeoff between hardness assumptions and the length of the random string for noninteractive
New Techniques for Noninteractive ZeroKnowledge
"... Noninteractive zeroknowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including CCA2secure cryptosystems, digital signatures, and various cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a bilin ..."
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Noninteractive zeroknowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including CCA2secure cryptosystems, digital signatures, and various cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a
Noninteractive ZeroKnowledge
 SIAM J. COMPUTING
, 1991
"... This paper investigates the possibility of disposing of interaction between prover and verifier in a zeroknowledge proof if they share beforehand a short random string. Without any assumption, it is proven that noninteractive zeroknowledge proofs exist for some numbertheoretic languages for which ..."
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Cited by 214 (18 self)
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This paper investigates the possibility of disposing of interaction between prover and verifier in a zeroknowledge proof if they share beforehand a short random string. Without any assumption, it is proven that noninteractive zeroknowledge proofs exist for some numbertheoretic languages
Efficient NonInteractive ZeroKnowledge Proofs of Circuit Satisfiability
 Institut for Matematik og Datalogi, Odense Universitet, Preprints 1994, Nr. 1, ISSN
, 1994
"... We show how to construct a "zeroknowledge proof" that a circuit of size m is satisfiable. The proof is a string of length O(m lg m) which is constructed (and can be verified) using a trusted random string of length O(m lg m). The probability of failure or of cheating is exponentially smal ..."
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Cited by 2 (1 self)
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of using it. Thus, these "proofs" are essentially noninteractive zeroknowledge proofs, with a couple of changes to the standard definition, though they can easily be modified to fit the standard definition. The techniques used yield more efficient "proofs" than those previously known
Efficient Cryptographic Primitives for NonInteractive ZeroKnowledge Proofs and Applications
, 2011
"... Noninteractive zeroknowledge (NIZK) proofs have enjoyed much interest in cryptography since they were introduced more than twenty years ago by Blum et al. [BFM88]. While quite useful when designing modular cryptographic schemes, until recently NIZK could be realized efficiently only using certain ..."
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Cited by 4 (0 self)
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Noninteractive zeroknowledge (NIZK) proofs have enjoyed much interest in cryptography since they were introduced more than twenty years ago by Blum et al. [BFM88]. While quite useful when designing modular cryptographic schemes, until recently NIZK could be realized efficiently only using certain
Short Noninteractive ZeroKnowledge Proofs
, 2010
"... Abstract. We show that probabilistically checkable proofs can be used to shorten noninteractive zeroknowledge proofs. We obtain publicly verifiable noninteractive zeroknowledge proofs for circuit satisfiability with adaptive and unconditional soundness where the size grows quasilinearly in the ..."
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Cited by 4 (1 self)
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Abstract. We show that probabilistically checkable proofs can be used to shorten noninteractive zeroknowledge proofs. We obtain publicly verifiable noninteractive zeroknowledge proofs for circuit satisfiability with adaptive and unconditional soundness where the size grows quasi
ZeroKnowledge Proofs and Arguments
, 1996
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
On Efficient ZeroKnowledge PCPs
"... Abstract. We revisit the question of ZeroKnowledge PCPs, studied by Kilian, Petrank, and Tardos (STOC ’97). A ZKPCP is defined similarly to a standard PCP, except that the view of any (possibly malicious) verifier can be efficiently simulated up to a small statistical distance. Kilian et al. obtai ..."
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. The existence of ZKPCPs for NP with efficient oracles and arbitrary polynomialtime malicious verifiers was left open. This question is motivated by the recent line of work on cryptography using tamperproof hardware tokens: an efficient ZKPCP (for any language) is equivalent to a statistical zeroknowledge
The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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for the languages of quadratic residuosity and quadratic nonresiduosity. These are the first examples of zeroknowledge proofs for languages not known to be efficiently recognizable.
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