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An L(1/3) algorithm for ideal class group and regulator computation in certain number fields

hal.structure.identifierLaboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorBIASSE, Jean-François
dc.date.accessioned2024-04-04T02:31:12Z
dc.date.available2024-04-04T02:31:12Z
dc.date.issued2014
dc.identifier.issn0025-5718
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190288
dc.description.abstractEnWe analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3,O(1))) when both the discriminant and the degree of the extension tend to infinity by using techniques due to Enge and Gaudry in the context of algebraic curves over finite fields.
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.title.enAn L(1/3) algorithm for ideal class group and regulator computation in certain number fields
dc.typeArticle de revue
dc.subject.halInformatique [cs]/Cryptographie et sécurité [cs.CR]
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv0912.1927
bordeaux.journalMathematics of Computation
bordeaux.page2005-2031
bordeaux.volume83
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue288
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierinria-00440223
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//inria-00440223v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematics%20of%20Computation&rft.date=2014&rft.volume=83&rft.issue=288&rft.spage=2005-2031&rft.epage=2005-2031&rft.eissn=0025-5718&rft.issn=0025-5718&rft.au=BIASSE,%20Jean-Fran%C3%A7ois&rft.genre=article


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