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The knowledge complexity of quadratic residuosity languages

Alfredo De Santis, Giovanni Di Crescenzo, Guiseppe Persiano
1994 Theoretical Computer Science  
Persiano, The knowledge complexity of quadratic residuosity languages, Theoretical Computer Science 132 (1994) 291-317.  ...  Acknowledgment We thank an anonymous referee for careful reading and useful remarks on the paper.  ...  More precisely, we give a protocol for the language of thresholds of quadratic residuosity.  ... 
doi:10.1016/0304-3975(94)90237-2 fatcat:fpx55wr4pjhyrov7a43gjweeli

Secret Sharing and Perfect Zero Knowledge [chapter]

A. De Santis, G. Di Crescenzo, G. Persiano
1994 Lecture Notes in Computer Science  
In this work, we show that a large class of languages related to quadratic residuosity admits non-interactive perfect zero-knowledge proofs.  ...  In fact, since the introduction of the non-interactive model for zero knowledge, the only perfect zero-knowledge proof known was for quadratic non residues.  ...  In the non-interactive model the only perfect zero-knowledge proof has been given in [5] for the language of quadratic non residuosity modulo Regalar(2) integers.  ... 
doi:10.1007/3-540-48329-2_7 fatcat:yz3roml4qve4dcfputzne7453m

Public-Randomness in Public-Key Cryptography [chapter]

Alfredo De Santis, Giuseppe Persiano
1991 Lecture Notes in Computer Science  
We propose the jirs~ implementation of non-interactive nature for Perfect Zero-Knowledge in the dual model of Brassard, Crbpeau, and Chaum for all NP-languages.  ...  In this work WC investigate the power of Public Randomness in the context of Public-key cryptosystcms.  ...  Thcir implementation is based on a complexity assumption related to the Discrete Logarithm problem (thc Diffie-Nellman assumption [DH]), whereas OUT implementation is based on the Quadratic Residuosity  ... 
doi:10.1007/3-540-46877-3_5 fatcat:kksw4dij4vgxdaadfjpnjm424e

Zero-Knowledge Arguments and Public-Key Cryptography

A. Desantis, G. Dicrescenzo, G. Persiano
1995 Information and Computation  
Building on this result, we show that all languages in NP have Perfect Zero-Knowledge Arguments in the PKPR model. De nition 1.  ...  The 1-out-of-2 condition is inspired by the notion of security of 33]. Here, we do not let Key Generator 0 and Receive 0 receive the strings s 0 ; s 1 ; s 2 ; s 3 as inputs.  ...  The third author would like to thank Michael Rabin for his constant support.  ... 
doi:10.1006/inco.1995.1121 fatcat:tlixnbmghbglzawq2eqt3joj7q

Communication-efficient anonymous group identification

Afredo De Santis, Giovanni Di Crescenzo, Giuseppe Persiano
1998 Proceedings of the 5th ACM conference on Computer and communications security - CCS '98  
We extend this scheme to the case of groups oft >1 users and obtain a protocol that improves on the communication complexity of previous protocoh even q Dipartimento d] Informatica ed Appliczioni, Univer-sit  ...  Assuming factoring Blum integers is hard, we construct a secure and anonymous group identification scheme having communication complexity @ (m+n), where m is the size of the group and n is the security  ...  H we replace the non-interactive version of the hashing procedure with the interactive one (as in [15]), we can prove that there suiting scheme is rdso perfect zer~knowledge.  ... 
doi:10.1145/288090.288110 dblp:conf/ccs/SantisCP98 fatcat:6gdfimpo55ekbm5apyjicm7jrq

Practical proofs of knowledge without relying on theoretical proofs of membership on languages

Kouichi Sakurai
1997 Theoretical Computer Science  
A four-move protocol for quadratic residuosity is proposed and a new notion of practical soundness is introduced based on its application to a cryptographic identification scheme.  ...  Recently, Bellare and Goldreich [3] gave rigorous definitions of proofs of knowledge and introduced the following weaker version of the knowledge proof Pro0j.i of' kno\cledge should be dejined in the case  ...  Acknowledgements This work was inspired by the discussion while the author was writing his thesis under the supervision of Kazuo Iwama.  ... 
doi:10.1016/s0304-3975(96)00277-0 fatcat:yswo7wkljbcsdekcgdcpiabeyy

Page 6942 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
, Giuseppe] (1-HRV-C; Cambridge, MA) The knowledge complexity of quadratic residuosity languages.  ...  The new noninteractive perfect zero-knowledge proofs are for problems based on quadratic residuosity. This expands the very small set of known noninteractive perfect zero-knowledge proofs.  ... 

On server trust in private proxy auctions

Giovanni Di Crescenzo, Javier Herranz, Germán Sáez
2010 Electronic Commerce Research  
uses the random oracle assumption, and another based on quadratic residuosity that only uses standard intractability assumptions but is less efficient.  ...  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  ...  We note that every language in N P has a non-interactive computational zero-knowledge proof system under the hardness of deciding quadratic residuosity [5] or even more general complexity assumptions  ... 
doi:10.1007/s10660-010-9057-x fatcat:egud4tft6fcxbfjd4gzbwzinpy

The Complexity of Decision Versus Search

Mihir Bellare, Shafi Goldwasser
1994 SIAM journal on computing (Print)  
We indicate that the answer is negative: under a complexity assumption that deterministic and non-deterministic double-exponential time are unequal we construct a language in NP for which search does not  ...  Under similar assumptions we present languages in NP for which it is harder to prove membership interactively than it is to decide this membership, and languages in NP which are not checkable.  ...  We thank Oded Goldreich for many helpful comments on the paper. We thank Satish Thate for  ... 
doi:10.1137/s0097539792228289 fatcat:5h53wc3gsbeqjaneurwasrqa5a

Knowledge and Efficient Computation [chapter]

Silvio Micali
1986 Theoretical Aspects of Reasoning About Knowledge  
We informally discuss "knowledge complexity": a measure for the amount of knowledge that can be feasibly extracted from a communication.  ...  We sympathize with the readers who are distressed by the level of informality of this short abstract. Most of the material is contained in the reference [GMR].  ...  We believe that knowledge complexity is one of the fundamental parameters of a language or, equivalently, of a theorem-proving procedure.  ... 
doi:10.1016/b978-0-934613-04-0.50029-6 fatcat:u346nlp46zcl3mdx6gla5aam3a

On the Power of Nonlinear Secret-Sharing

Amos Beimel, Yuval Ishai
2005 SIAM Journal on Discrete Mathematics  
Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure.  ...  A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n.  ...  The circuit complexity of NQR is the same, up to an O(n) difference, as that of the language {(w, u) : |w| = |u| and w is a quadratic residue modulo u}.  ... 
doi:10.1137/s0895480102412868 fatcat:5es4ktqclbfgziq67gg7ucb7bi

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 use this result to construct the first publickey cryptosystem secure against chosen ciphertext attack.  ...  We show that interaction in any zero-knowledge proof can be replaced by sharing a common, short, random string.  ...  For instance, in complexity theory, via results of fortnow [F] and Boppana and Hastad [BH] , zero-knowledge provides us an avenue to convince ourselves that certain languages are not NP-complete.  ... 
doi:10.1145/62212.62222 dblp:conf/stoc/BlumFM88 fatcat:rat6mg6h3zfazcidzcfynqctpa

Proving Without Knowing: On Oblivious, Agnostic and Blindfolded Provers [chapter]

Markus Jakobsson, Moti Yung
1996 Lecture Notes in Computer Science  
As part of the agnostic protocol, and perhaps of independent interest, we exhibit an efficient zero-knowledge proof of knowledge (possession) of both a base and an exponent of an element of a finite group  ...  Finally, we show a perfect agnostic riiinimuni-knowledge decision proof protocol for quxlratic residuosity modulo Blurn iiitegers.  ...  for proving quadratic residuosity and non-residuosity modulo Bliim integers.  ... 
doi:10.1007/3-540-68697-5_15 fatcat:dj4zam77knb73o4hbm6lwsd47i

Zero-Knowledge Authentication [article]

Jakob Povsic, Andrej Brodnik
2022 arXiv   pre-print
The system uses the zero-knowledge proof (ZKP) system as a password verification mechanism. The ZKP protocol used is based on the quadratic residuosity problem.  ...  The authentication system is defined as a method in the extensible authentication protocol (EAP).  ...  ZKP System for the Quadratic Residuosity Problem The first ZKP system defined [25] is for the quadratic residuosity problem. The quadratic residuosity problem is much older than ZKPs.  ... 
arXiv:2205.05847v1 fatcat:7fqu3nusczcgbf2xkwljkohdim

Concurrent Zero Knowledge Without Complexity Assumptions [chapter]

Daniele Micciancio, Shien Jin Ong, Amit Sahai, Salil Vadhan
2006 Lecture Notes in Computer Science  
To our best of knowledge, these are the first constructions of concurrent zero-knowledge protocols in the asynchronous model (without timing assumptions) that do not require complexity assumptions (such  ...  The problems include Graph Isomorphism, Graph Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a restricted version of Statistical Difference, and approximate versions of the (coNP forms  ...  The language Quadratic Nonresiduosity is the complement of Quadratic Residuosity.  ... 
doi:10.1007/11681878_1 fatcat:qb5hsghfj5gkdkxdrmqbrtbpd4
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