Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes

Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink pr...

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Detalhes bibliográficos
Autores: Couvreur, Alain, Gaborit, Philippe, Gauthier-Umaña, Valérie, Otmani, Ayoub, Tillich, Jean-Pierre
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Colombia
Recursos:Universidad del Rosario
Repositorio:Repositorio EdocUR - U. Rosario
Idioma:inglés
OAI Identifier:oai:repository.urosario.edu.co:10336/23845
Acesso em linha:https://doi.org/10.1007/s10623-014-9967-z
https://repository.urosario.edu.co/handle/10336/23845
Access Level:acceso abierto
Palavra-chave:Matrix algebra
Public key cryptography
Recovery
Reed-Solomon codes
Code-based cryptography
Distinguishers
Generalized reed-solomon codes
Ho-momorphic encryptions
Key-recovery
Codes (symbols)
Distinguisher
Generalized Reed-Solomon codes
Homomorphic encryption
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spelling Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codesCouvreur, AlainGaborit, PhilippeGauthier-Umaña, ValérieOtmani, AyoubTillich, Jean-PierreMatrix algebraPublic key cryptographyRecoveryReed-Solomon codesCode-based cryptographyDistinguishersGeneralized reed-solomon codesHo-momorphic encryptionsKey-recoveryCodes (symbols)Code-based cryptographyDistinguisherGeneralized Reed-Solomon codesHomomorphic encryptionKey-recoveryBecause of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York.Kluwer Academic Publishers20142020-05-26T00:05:58Zinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.1007/s10623-014-9967-z0925102215737586https://repository.urosario.edu.co/handle/10336/23845reponame:Repositorio EdocUR - U. Rosarioinstname:Universidad del Rosarioinstacron:Universidad del Rosarioenghttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84905217777&doi=10.1007%2fs10623-014-9967-z&partnerID=40&md5=2d3741ccd9d58ebce49f8a5319179270info:eu-repo/semantics/openAccess2022-05-02T07:37:16Z
dc.title.none.fl_str_mv Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
title Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
spellingShingle Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
Couvreur, Alain
Matrix algebra
Public key cryptography
Recovery
Reed-Solomon codes
Code-based cryptography
Distinguishers
Generalized reed-solomon codes
Ho-momorphic encryptions
Key-recovery
Codes (symbols)
Code-based cryptography
Distinguisher
Generalized Reed-Solomon codes
Homomorphic encryption
Key-recovery
title_short Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
title_full Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
title_fullStr Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
title_full_unstemmed Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
title_sort Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
dc.creator.none.fl_str_mv Couvreur, Alain
Gaborit, Philippe
Gauthier-Umaña, Valérie
Otmani, Ayoub
Tillich, Jean-Pierre
author Couvreur, Alain
author_facet Couvreur, Alain
Gaborit, Philippe
Gauthier-Umaña, Valérie
Otmani, Ayoub
Tillich, Jean-Pierre
author_role author
author2 Gaborit, Philippe
Gauthier-Umaña, Valérie
Otmani, Ayoub
Tillich, Jean-Pierre
author2_role author
author
author
author
dc.subject.none.fl_str_mv Matrix algebra
Public key cryptography
Recovery
Reed-Solomon codes
Code-based cryptography
Distinguishers
Generalized reed-solomon codes
Ho-momorphic encryptions
Key-recovery
Codes (symbols)
Code-based cryptography
Distinguisher
Generalized Reed-Solomon codes
Homomorphic encryption
Key-recovery
topic Matrix algebra
Public key cryptography
Recovery
Reed-Solomon codes
Code-based cryptography
Distinguishers
Generalized reed-solomon codes
Ho-momorphic encryptions
Key-recovery
Codes (symbols)
Code-based cryptography
Distinguisher
Generalized Reed-Solomon codes
Homomorphic encryption
Key-recovery
description Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York.
publishDate 2014
dc.date.none.fl_str_mv 2014
2020-05-26T00:05:58Z
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s10623-014-9967-z
09251022
15737586
https://repository.urosario.edu.co/handle/10336/23845
url https://doi.org/10.1007/s10623-014-9967-z
https://repository.urosario.edu.co/handle/10336/23845
identifier_str_mv 09251022
15737586
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-84905217777&doi=10.1007%2fs10623-014-9967-z&partnerID=40&md5=2d3741ccd9d58ebce49f8a5319179270
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Kluwer Academic Publishers
publisher.none.fl_str_mv Kluwer Academic Publishers
dc.source.none.fl_str_mv reponame:Repositorio EdocUR - U. Rosario
instname:Universidad del Rosario
instacron:Universidad del Rosario
instname_str Universidad del Rosario
instacron_str Universidad del Rosario
institution Universidad del Rosario
reponame_str Repositorio EdocUR - U. Rosario
collection Repositorio EdocUR - U. Rosario
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score 15.812455

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