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The knowledge complexity of quadratic residuosity languages

1994
*
Theoretical Computer Science
*

Persiano,

doi:10.1016/0304-3975(94)90237-2
fatcat:fpx55wr4pjhyrov7a43gjweeli
*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*. ...##
###
Secret Sharing and Perfect Zero Knowledge
[chapter]

1994
*
Lecture Notes in Computer Science
*

In this work, we show that a large class

doi:10.1007/3-540-48329-2_7
fatcat:yz3roml4qve4dcfputzne7453m
*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. ...##
###
Public-Randomness in Public-Key Cryptography
[chapter]

1991
*
Lecture Notes in Computer Science
*

We propose

doi:10.1007/3-540-46877-3_5
fatcat:kksw4dij4vgxdaadfjpnjm424e
*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*...##
###
Zero-Knowledge Arguments and Public-Key Cryptography

1995
*
Information and Computation
*

Building on this result, we show that all

doi:10.1006/inco.1995.1121
fatcat:tlixnbmghbglzawq2eqt3joj7q
*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. ...##
###
Communication-efficient anonymous group identification

1998
*
Proceedings of the 5th ACM conference on Computer and communications security - CCS '98
*

We extend this scheme to

doi:10.1145/288090.288110
dblp:conf/ccs/SantisCP98
fatcat:6gdfimpo55ekbm5apyjicm7jrq
*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*. ...##
###
Practical proofs of knowledge without relying on theoretical proofs of membership on languages

1997
*
Theoretical Computer Science
*

A four-move protocol for

doi:10.1016/s0304-3975(96)00277-0
fatcat:yswo7wkljbcsdekcgdcpiabeyy
*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. ...##
###
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

2010
*
Electronic Commerce Research
*

uses

doi:10.1007/s10660-010-9057-x
fatcat:egud4tft6fcxbfjd4gzbwzinpy
*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 ...##
###
The Complexity of Decision Versus Search

1994
*
SIAM journal on computing (Print)
*

We indicate that

doi:10.1137/s0097539792228289
fatcat:5h53wc3gsbeqjaneurwasrqa5a
*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 ...##
###
Knowledge and Efficient Computation
[chapter]

1986
*
Theoretical Aspects of Reasoning About Knowledge
*

We informally discuss "

doi:10.1016/b978-0-934613-04-0.50029-6
fatcat:u346nlp46zcl3mdx6gla5aam3a
*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. ...##
###
On the Power of Nonlinear Secret-Sharing

2005
*
SIAM Journal on Discrete Mathematics
*

Most previously known secret-sharing schemes belonged to a class

doi:10.1137/s0895480102412868
fatcat:5es4ktqclbfgziq67gg7ucb7bi
*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}. ...##
###
Non-interactive zero-knowledge and its applications

1988
*
Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88
*

We use this result to construct

doi:10.1145/62212.62222
dblp:conf/stoc/BlumFM88
fatcat:rat6mg6h3zfazcidzcfynqctpa
*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. ...##
###
Proving Without Knowing: On Oblivious, Agnostic and Blindfolded Provers
[chapter]

1996
*
Lecture Notes in Computer Science
*

As part

doi:10.1007/3-540-68697-5_15
fatcat:dj4zam77knb73o4hbm6lwsd47i
*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. ...##
###
Zero-Knowledge Authentication
[article]

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. ...

##
###
Concurrent Zero Knowledge Without Complexity Assumptions
[chapter]

2006
*
Lecture Notes in Computer Science
*

To our best

doi:10.1007/11681878_1
fatcat:qb5hsghfj5gkdkxdrmqbrtbpd4
*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*. ...
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