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A distinguisher for high-rate McEliece cryptosystems

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dc.creatorFaugère, Jean-Charlesspa
dc.creatorGauthier-Umaña, Valériespa
dc.creatorOtmani, Ayoubspa
dc.creatorPerret, Ludovicspa
dc.creatorTillich, Jean-Pierrespa
dc.date.accessioned2020-08-19T14:42:02Z
dc.date.available2020-08-19T14:42:02Z
dc.date.created2013-07-03spa
dc.description.abstractThe Goppa Code Distinguishing (GD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. The hardness of this problem is an assumption to prove the security of code-based cryptographic primitives such as McEliece's cryptosystem. Up to now, it is widely believed that the GD problem is a hard decision problem. We present the first method allowing to distinguish alternant and Goppa codes over any field. Our technique can solve the GD problem in polynomial time provided that the codes have sufficiently large rates. The key ingredient is an algebraic characterization of the key-recovery problem. The idea is to consider the rank of a linear system which is obtained by linearizing a particular polynomial system describing a key-recovery attack. It appears that this dimension depends on the type of code considered. Explicit formulas derived from extensive experimentations for the rank are provided for “generic” random, alternant, and Goppa codes over any field. Finally, we give theoretical explanations of these formulas in the case of random codes, alternant codes over any field of characteristic two and binary Goppa codes.eng
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1109/TIT.2013.2272036
dc.identifier.issnISSN: 0096-1000
dc.identifier.issnEISSN: 2168-2712
dc.identifier.urihttps://repository.urosario.edu.co/handle/10336/27398
dc.language.isoengspa
dc.publisherIEEEspa
dc.relation.citationEndPage6844
dc.relation.citationIssueNo. 10
dc.relation.citationStartPage6830
dc.relation.citationTitleIEEE Transactions on Information Theory
dc.relation.citationVolumeVol. 59
dc.relation.ispartofIEEE Transactions on Information Theory, ISSN: 0096-1000;EISSN: 2168-2712, Vol.59, No.10 (Oct 2013); pp. 6830-6844spa
dc.relation.urihttps://ieeexplore.ieee.org/document/6553164spa
dc.rights.accesRightsinfo:eu-repo/semantics/restrictedAccess
dc.rights.accesoRestringido (Acceso a grupos específicos)spa
dc.sourceIEEE Transactions on Information Theoryspa
dc.source.instnameinstname:Universidad del Rosario
dc.source.reponamereponame:Repositorio Institucional EdocUR
dc.subject.keywordCryptographyspa
dc.subject.keywordDecodingspa
dc.subject.keywordPolynomialsspa
dc.subject.keywordLinear systemsspa
dc.subject.keywordGeneratorsspa
dc.subject.keywordLinear codesspa
dc.titleA distinguisher for high-rate McEliece cryptosystemsspa
dc.title.TranslatedTitleUn distintivo para los criptosistemas McEliece de alta velocidadspa
dc.typearticleeng
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersion
dc.type.spaArtículospa
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