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A Note on Constant-Round Zero-Knowledge Proofs for NP [chapter]

Alon Rosen
2004 Lecture Notes in Computer Science  
We consider the problem of constructing a constant-round zero-knowledge proof system for all languages in N P.  ...  Following recent works on concurrent zero-knowledge, we propose an alternative solution that admits a considerably simpler analysis.  ...  I would like to thank Oded Goldreich, Yehuda Lindell and Moni Naor for helpful conversations on the subject.  ... 
doi:10.1007/978-3-540-24638-1_11 fatcat:mosmwb7y7bco7jzkcrsh25mqgy

On the Round Complexity of Zero-Knowledge Proofs Based on One-Way Permutations [chapter]

S. Dov Gordon, Hoeteck Wee, David Xiao, Arkady Yerukhimovich
2010 Lecture Notes in Computer Science  
We also give strong evidence that we are unlikely to find fully black-box constructions of constant-round zero knowledge proofs for NP, even without this restriction on adaptivity.  ...  Specifically, we show that only languages in coAM have constant-round zero-knowledge proofs of this kind.  ...  This raises the following intriguing open problem: Can we base constant-round zero-knowledge proofs for NP on the existence of one-way permutations?  ... 
doi:10.1007/978-3-642-14712-8_12 fatcat:pxbk5jgmjff6rdeqrmfsdr7yii

On Round-Efficient Argument Systems [chapter]

Hoeteck Wee
2005 Lecture Notes in Computer Science  
Next, we relate the existence of non-trivial 2-round argument systems to that of hard-on-average search problems in NP and that of efficient public-coin zero-knowledge arguments for NP.  ...  We consider the problem of constructing round-efficient public-coin argument systems, that is, interactive proof systems that are only computationally sound with a constant number of rounds.  ...  We note that the existence of a 2-round public-coin universal argument of knowledge secure against subexponential-sized circuits yields a 4-round public-coin zero-knowledge argument for NP with negligible  ... 
doi:10.1007/11523468_12 fatcat:x3k2vjcelzct5oggyjy2kujd3y

On constant-round zero-knowledge proofs of knowledge for NP-relations

HongDa Li, HaiXia Xu, Bao Li, DengGuo Feng
2010 Science China Information Sciences  
Keywords zero-knowledge proof, proof of knowledge, constant-round, NP-relation Citation Li H D, Xu H X, Li B, et al. On constant-round zero-knowledge proofs of knowledge for NP-relations.  ...  This paper considers the existence of constant-round zero-knowledge proofs of knowledge for NP under standard assumptions.  ...  Zero-knowledge strong proofs of knowledge with non-constant round-complexity exist for NP-relations if one-way functions exist [4] . It is worth noting that Barak et al.  ... 
doi:10.1007/s11432-010-0071-3 fatcat:22uxo53h7jdolbjwwcaxdl26b4

Lower bounds for non-black-box zero knowledge

Boaz Barak, Yehuda Lindell, Salil Vadhan
2006 Journal of computer and system sciences (Print)  
There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP-complete language.  ...  There does not exist a constant-round public-coin proof system for a nontrivial language that is resettable zero knowledge.  ...  Acknowledgements We thank Oded Goldreich, Silvio Micali and Luca Trevisan for helpful discussions, and the anonymous FOCS and JCSS referees for useful comments.  ... 
doi:10.1016/j.jcss.2005.06.010 fatcat:hllc2tom6zgrrapoftgdz5hdqy

Round-optimal zero-knowledge proofs of knowledge for NP

HongDa Li, DengGuo Feng, Bao Li, HaiXia Xue
2012 Science China Information Sciences  
This paper focuses on the existence of constant-round (black-box) zero-knowledge proofs of knowledge for NP under general cryptographic assumptions.  ...  Our main results Note that all the known constructions of constant-round black-box zero-knowledge proof are not proofs of knowledge.  ...  Our goal in this section is to construct a constant-round zero-knowledge proof of knowledge for HC.  ... 
doi:10.1007/s11432-011-4379-4 fatcat:ncgh2ze4nfgbll3g4iykkaouvi

Constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP

HongDa Li, DengGuo Feng
2014 Science China Information Sciences  
This paper focuses on this problem and gives a positive answer by presenting a construction of constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP. convinces  ...  Some known constant-round construction of ZKP for NP, such as ones in [5, 6] , are not proofs of knowledge.  ...  To construct a zero-knowledge proof of knowledge for an NP-relation R with a strict polynomial-time (non-black-box) knowledge extractor, we need a constant-round statistically binding commit-with-extract  ... 
doi:10.1007/s11432-013-5044-x fatcat:wglgnxmnnnhe3ks5rmzagoj3om

A Constant-Round Resettably-Sound Resettable Zero-Knowledge Argument in the BPK Model

2012 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
That results in a constant-round resettably-sound and resettable zero-knowledge argument system for all NP languages in the BPK model.  ...  This paper gives a first constant-round argument system for all NP languages in the BPK model that is both resettably-sound and resettable zero-knowledge.  ...  Constant-Round Resettably-Sound Arguments It is known that there exists a constant-round public-coin zero-knowledge argument for all NP languages assuming collision-resistant hash-functions [1] .  ... 
doi:10.1587/transfun.e95.a.1390 fatcat:zahfwyhiqzh7dhaznkgxwa5zoa

Page 5542 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
This is the best one can obtain, unless Q-RES € BPP, as constant-round zero-knowledge proofs of Arthur-Merlin type or 3-round zero-knowledge proofs of general type exist only for languages in BPP [O.  ...  In this paper, we show that if we let the verifier hide his random bits from the prover, it is possible to give a 4- round perfect zero-knowledge proof system of membership (A,B) for Q-RES.  ... 

Which Languages Have 4-Round Zero-Knowledge Proofs?

Jonathan Katz
2010 Journal of Cryptology  
We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, thenL ∈ MA.  ...  Assuming the polynomial hierarchy does not collapse, this means, in particular, that NP-complete languages do not have 4-round zero-knowledge proofs (at least with respect to black-box simulation).  ...  Acknowledgments Thanks to Dov Gordon and Arkady Yerukhimovich for helpful discussions, and to Arkady for reading and commenting on a preliminary version of this manuscript.  ... 
doi:10.1007/s00145-010-9081-y fatcat:2tge2wse5zbalf7qvjz47nxfxa

Private Coins versus Public Coins in Zero-Knowledge Proof Systems [chapter]

Rafael Pass, Muthuramakrishnan Venkitasubramaniam
2010 Lecture Notes in Computer Science  
zero-knowledge proofs; the same holds for constant-round fully black-box zero-knowledge arguments with sublinear verifier communication complexity.  ...  showed that only languages in BPP have constant-round public-coin black-box zero-knowledge protocols.  ...  Acknowledgements We would like to thank the anonymous TCC reviewers for their helpful comments, and Iftach Haitner for pointing out the connection to the work of [14] .  ... 
doi:10.1007/978-3-642-11799-2_35 fatcat:znie35oq35fvfhvd7k6pteh2vy

Simulatable Commitments and Efficient Concurrent Zero-Knowledge [chapter]

Daniele Micciancio, Erez Petrank
2003 Lecture Notes in Computer Science  
Using simulatable commitments, we show how to efficiently transform any public coin honest verifier zero knowledge proof system into a proof system that is concurrent zero-knowledge with respect to any  ...  term is close to optimal (for black box simulation): only ω(log n) additional rounds, and ω(log n) additional public key operations for each round of the original protocol, where n is a security parameter  ...  We thank the anonymous referees for their deep remarks. References  ... 
doi:10.1007/3-540-39200-9_9 fatcat:dlt4wczhprg2jn6t3jyuxfv5uy

Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems

Oded Goldreich, Silvio Micali, Avi Wigderson
1991 Journal of the ACM  
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.  ...  Special thanks to Gilles Brassard, Ariel Kahn, Hugo Krawczyk, Eyal Kushilevitz, Yair Oren, and the anonymous referees for their remarks on earlier versions of this manuscript.  ... 
doi:10.1145/116825.116852 fatcat:snodcvveqnez3c2zc5fqcyrmsm

Witness indistinguishable and witness hiding protocols

U. Feige, A. Shamir
1990 Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90  
Introduction A two party protocol in which party A uses one of several secret witnesses to an NP assertion is witness indistinguishable if party B cannot tell which witness A is actually using.  ...  Special thanks to Oded Goldreich for his colorful and very useful comments on an earlier version of this manuscript.  ...  Acknowledgements We thank Mihir Bellare and Shaft Goldwasser for discussions concerning their signature scheme.  ... 
doi:10.1145/100216.100272 dblp:conf/stoc/FeigeS90 fatcat:zsg4g67tzrbjpfekhg2lt6n2ui

On Constant-Round Precise Zero-Knowledge [chapter]

Ning Ding, Dawu Gu
2012 Lecture Notes in Computer Science  
-We present a constant-round precise zero-knowledge argument for any language in NP with respect to our definition, assuming the existence of collision-resistant hash function families (against all n O  ...  Though there are some constructions of precise zero-knowledge, constant-round constructions are unknown to exist. This paper is towards constant-round constructions of precise zero-knowledge.  ...  The authors are grateful to the reviewers of ICICS 2012 for their useful comments.  ... 
doi:10.1007/978-3-642-34129-8_16 fatcat:zjfdo2ettnflvdmc7dr6m36qg4
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