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Paper

Analysis of Some Natural Variants of the PKP AlgorithmTopics: Applied Cryptography; Authentication; Identification, Authentication and Non-Repudiation; Security Information Systems Architecture and Design and Security Patterns

Keyword(s):Public-key Cryptography, Identification Scheme, Zero Knowledge, Permuted Kernel Problem.

Related
Ontology
Subjects/Areas/Topics:Applied Cryptography
;
Authentication
;
Cryptographic Techniques and Key Management
;
Data Engineering
;
Databases and Data Security
;
Identification, Authentication and Non-Repudiation
;
Information and Systems Security
;
Obstacles
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Security in Information Systems
;
Security Information Systems Architecture and Design and Security Patterns
;
Sensor Networks

Abstract: In 1989, (Shamir, 1989) proposed a new zero-knowledge identification scheme based on a NP-complete problem
called PKP for Permuted Kernel Problem. For a given prime p, a given matrix A and a given vector V, the
problem is to find a permutation p such that the permuted vector Vp verifies A·Vp = 0 mod p. This scheme
is still in 2011 known as one of the most efficient identification scheme based on a combinatorial problem.
However, we will see in this paper that it is possible to improve this scheme significantly by combining new
ideas in order to reduce the total number of computations to be performed and to improve very efficiently the
security against side channel attacks using precomputations. We will obtain like this a new scheme that we
have called SPKP. Moreover, if we use precomputed values in the scheme SPKP, then the prover will need to
perform no computations (i.e. only selection and transmission of precomputed values). This is very interesting
for security against side channel attacks because our scheme is zero-knowledge and we don’t perform any
computations using the key during the identification so we prove that any attacker (even using side channel
attacks) being successfully identified implies that he has a solution to the NP-complete problem PKP.(More)

In 1989, (Shamir, 1989) proposed a new zero-knowledge identification scheme based on a NP-complete problem called PKP for Permuted Kernel Problem. For a given prime p, a given matrix A and a given vector V, the problem is to find a permutation p such that the permuted vector Vp verifies A·Vp = 0 mod p. This scheme is still in 2011 known as one of the most efficient identification scheme based on a combinatorial problem. However, we will see in this paper that it is possible to improve this scheme significantly by combining new ideas in order to reduce the total number of computations to be performed and to improve very efficiently the security against side channel attacks using precomputations. We will obtain like this a new scheme that we have called SPKP. Moreover, if we use precomputed values in the scheme SPKP, then the prover will need to perform no computations (i.e. only selection and transmission of precomputed values). This is very interesting for security against side channel attacks because our scheme is zero-knowledge and we don’t perform any computations using the key during the identification so we prove that any attacker (even using side channel attacks) being successfully identified implies that he has a solution to the NP-complete problem PKP.

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Guests can use SciTePress Digital Library without having a SciTePress account. However, guests have limited access to downloading full text versions of papers and no access to special options.

Lampe, R. and Patarin, J. (2012). Analysis of Some Natural Variants of the PKP Algorithm.In Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2012) ISBN 978-989-8565-24-2, pages 209-214. DOI: 10.5220/0004012202090214

@conference{secrypt12, author={Rodolphe Lampe. and Jacques Patarin.}, title={Analysis of Some Natural Variants of the PKP Algorithm}, booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2012)}, year={2012}, pages={209-214}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0004012202090214}, isbn={978-989-8565-24-2}, }

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2012) TI - Analysis of Some Natural Variants of the PKP Algorithm SN - 978-989-8565-24-2 AU - Lampe, R. AU - Patarin, J. PY - 2012 SP - 209 EP - 214 DO - 10.5220/0004012202090214