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The knowledge complexity of quadratic residuosity languages
1994
Theoretical Computer Science
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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]
1994
Lecture Notes in Computer Science
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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]
1991
Lecture Notes in Computer Science
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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
1995
Information and Computation
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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
1998
Proceedings of the 5th ACM conference on Computer and communications security - CCS '98
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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
1997
Theoretical Computer Science
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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
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
, 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
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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
1994
SIAM journal on computing (Print)
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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]
1986
Theoretical Aspects of Reasoning About Knowledge
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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
2005
SIAM Journal on Discrete Mathematics
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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
1988
Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88
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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]
1996
Lecture Notes in Computer Science
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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]
2022
arXiv
pre-print
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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]
2006
Lecture Notes in Computer Science
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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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