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Efficient Zero-Knowledge Proofs of Knowledge without Intractability Assumptions [chapter]

Ronald Cramer, Ivan Damgård, Philip MacKenzie
2000 Lecture Notes in Computer Science  
None of our results rely on intractability assumptions.  ...  We initiate the investigation of the class of relations that admit extremely efficient perfect zero knowledge proofs of knowledge: constant number of rounds, communication linear in the length of the statement  ...  In this paper we characterize a class of relations where such a zero-knowledge proof of knowledge can be built without making any computational assumptions, and at negligible extra cost (communication  ... 
doi:10.1007/978-3-540-46588-1_24 fatcat:hipqekvb45hyfhmk65nwrwqgyu

Improved Efficient Arguments [chapter]

Joe Kilian
1995 Lecture Notes in Computer Science  
We introduce new techniques for implementing very efficient zero-knowledge arguments.  ...  We consider complexity of perfect zero-knowledge arguments [4]. Let T denote the time needed to (deterministically) check a proof and let L denote an appropriate security parameter.  ...  Dan Spielman provided early and invaluable information on his work with Polishchuk, which greatly improved the results of an earlier version of this manuscript.  ... 
doi:10.1007/3-540-44750-4_25 fatcat:v45yljjhjbf2lcl2fhxdmnjyjq

Efficient Concurrent Zero-Knowledge in the Auxiliary String Model [chapter]

Ivan Damgård
2000 Lecture Notes in Computer Science  
We also show that a wide range of known efficient proofs of knowledge using specialized assumptions can be modified to work in this model with no essential loss of efficiency.  ...  Finally, we point out that in a model with preprocessing (and no auxiliary string) proposed earlier, concurrent zero-knowledge for NP can be based on any one-way function.  ...  Based on standard intractability assumptions such as hardness of discrete log or RSA root extraction, very efficient trapdoor commitment schemes can be built, see e.g. [6] .  ... 
doi:10.1007/3-540-45539-6_30 fatcat:rss4erl52rgbhddv6bieedan4e

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments

Rafael Pass
2016 Computational Complexity  
We present barriers to provable security of two fundamental (and well-studied) cryptographic primitives perfect non-interactive zero knowledge (NIZK), and non-malleable commitments: • Black-box reductions  ...  based on any "standard" intractability assumptions.  ...  " assumption (simular to the "knowledge-of-exponent" assumption of [Dam91] ), as opposed to a computational-intractability assumption.  ... 
doi:10.1007/s00037-016-0122-2 fatcat:b4bkyiddbzhbzcgo5l7jaeqcve

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments [chapter]

Rafael Pass
2013 Lecture Notes in Computer Science  
We present barriers to provable security of two fundamental (and well-studied) cryptographic primitives perfect non-interactive zero knowledge (NIZK), and non-malleable commitments: • Black-box reductions  ...  based on any "standard" intractability assumptions.  ...  " assumption (simular to the "knowledge-of-exponent" assumption of [Dam91] ), as opposed to a computational-intractability assumption.  ... 
doi:10.1007/978-3-642-36594-2_19 fatcat:vogdn6q7dfdeld6gst6enntmea

A Note on Security Proofs in the Generic Model [chapter]

Marc Fischlin
2000 Lecture Notes in Computer Science  
Building on this lower bound, Shoup and subsequently Schnorr and Jakobsson proved other discrete-log-based protocols to be intractable in the generic model.  ...  Here, we discuss pitfalls when applying the generic model to other schemes than the discrete-log problem and when interpreting such lower bounds as security proofs for these schemes.  ...  Why does our result not contradict the lower bound in [13] for the round complexity of zero-knowledge proofs?  ... 
doi:10.1007/3-540-44448-3_35 fatcat:yskoogoeivaotevr3xrx6lvce4

Page 3141 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
“In this paper we present the first constructions of proof systems that are concurrent zero-knowledge without relying on unproven complexity assumptions.  ...  Summary: “Zero-knowledge proofs are a powerful tool for the construction of several types of cryptographic protocols.  ... 

How to construct constant-round zero-knowledge proof systems for NP

Oded Goldreich, Ariel Kahan
1996 Journal of Cryptology  
Constant-round zero-knowledge proof systems for every language in A/'7 9 are presented, assuming the existence of a collection of claw-free functions.  ...  In particular, it follows that such proof systems exist assuming the intractability of either the Discrete Logarithm Problem or the Factoring Problem for Blum integers.  ...  construct zero-knowledge proof systems for every NP statement (using a general intractability assumption) [10, Theorem 5] .  ... 
doi:10.1007/bf00208001 fatcat:ykta3ianerbhvhsw7jy34ecshm

A Relationship between One-Wayness and Correlation Intractability [chapter]

Satoshi Hada, Toshiaki Tanaka
1999 Lecture Notes in Computer Science  
of 3-round auxiliary-input zero-knowledge Arthur-Merlin proofs without making any assumptions.  ...  The notion of correlation intractability was introduced in an attempt to capture the "unpredictability" property of random oracles: It is assumed that if R is a random oracle then it is infeasible to find  ...  We would like to thank Rafail Ostrovsky for answering our questions regarding the results of [OW93] . We also thank Masahiro Wada and Kenji Suzuki for their encouragement.  ... 
doi:10.1007/3-540-49162-7_7 fatcat:3vyclvb6efe2pe5fjuqbnjztja

Page 4263 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
zero-knowledge proofs.  ...  Under the certified discrete log assumption, the protocol is perfect zero-knowledge.  ... 

On Correctness and Privacy in Distributed Mechanisms [chapter]

Felix Brandt, Tuomas Sandholm
2006 Lecture Notes in Computer Science  
We propose models with and without a center that guarantee correctness and preserve the privacy of preferences relying on diverse assumptions such as the trustworthiness of the center or the hardness of  ...  For one, it provides privacy without relying on a trusted third-party. Second, it enables the provably correct execution of randomized mechanisms (which is not the case in the centralized model).  ...  By applying zero-knowledge proofs to the commitment values, we essentially get computational privacy for free, i.e., without having to make further assumptions. Theorem 1.  ... 
doi:10.1007/11888727_16 fatcat:6wcgdlw4vzcuhfhe5cdts6ym7a

Fast and Secure Immunization Against Adaptive Man-in-the-Middle Impersonation [chapter]

Ronald Cramer, Ivan Damgård
1997 Lecture Notes in Computer Science  
Though zero-knowledge or witness hiding protocols are known to withstand attacks of the first kind, all such protocols previously proposed suffer from a weakness observed by Bengio et al. : a malicious  ...  Moreover, the required primitive protocols can efficiently be constructed under the factoring or discrete logarithm assumptions. ~~  ...  Using a three-move public coin protocol that is collision intractable (without knowing the private key, it is infeasible to pass the protocol) and honest verifier zero knowledge we build a witness-hiding  ... 
doi:10.1007/3-540-69053-0_7 fatcat:lujiiytcv5fg3cuk6uxu4r7l6e

Non-interactive zero-knowledge and its applications

Manuel Blum, Paul Feldman, Silvio Micali
1988 Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88  
We show that interaction in any zero-knowledge proof can be replaced by sharing a common, short, random string.  ...  , zero-knowledge proofs.  ...  The proof of zero knowledge is quite delicate. We restrict ourselves to merely outlining its high level steps, without further details.  ... 
doi:10.1145/62212.62222 dblp:conf/stoc/BlumFM88 fatcat:rat6mg6h3zfazcidzcfynqctpa

On server trust in private proxy auctions

Giovanni Di Crescenzo, Javier Herranz, Germán Sáez
2010 Electronic Commerce Research  
The main ingredients of our scheme are two minimal-round implementations of zero-knowledge proofs for proving lower bounds on encrypted values: one based on discrete logarithms that is more efficient but  ...  uses the random oracle assumption, and another based on quadratic residuosity that only uses standard intractability assumptions but is less efficient.  ...  Since this proof is zero-knowledge, it does not allow an efficient algorithm to compute the bidder's maximum value better than without access to the lower-bound proof.  ... 
doi:10.1007/s10660-010-9057-x fatcat:egud4tft6fcxbfjd4gzbwzinpy

The Complexity of Zero Knowledge [chapter]

Salil Vadhan
2007 Lecture Notes in Computer Science  
We give an informal introduction to zero-knowledge proofs, and survey their role both in the interface between complexity theory and cryptography and as objects of complexity-theoretic study in their own  ...  The main motivation of [BGKW] was to find a model in which zero-knowledge protocols for all of NP could be obtained without any complexity assumption (in contrast to Theorem 2.4).  ...  the study of zero-knowledge proofs.  ... 
doi:10.1007/978-3-540-77050-3_5 fatcat:3pfho3mpzrgx5i6zxepjni6m4a
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