Mostrar el registro sencillo del ítem

hal.structure.identifierCryptography group
dc.contributor.authorLAUTER, Kristin
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorROBERT, Damien
dc.contributor.editorEverett W. Howe
dc.contributor.editorKiran S. Kedlaya
dc.date.accessioned2024-04-04T02:22:15Z
dc.date.available2024-04-04T02:22:15Z
dc.date.created2012-05
dc.date.issued2013-11-14
dc.date.conference2012-07-09
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189638
dc.description.abstractEnWe present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Br{ö}ker-Gruenewald-Lauter algorithm for the genus~2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for ''going up'' to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right isogeny class. Then we use the structure of the Shimura class group and the computation of $(\ell,\ell)$-isogenies to compute all isogenous maximal curves from an initial one. This is an extended version of the article published at ANTS~X.
dc.description.sponsorshipEspaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes - ANR-12-BS01-0010
dc.language.isoen
dc.publisherMathematical Sciences Publisher
dc.subject.enClass polynomials
dc.title.enImproved CRT Algorithm for Class Polynomials in Genus $2$
dc.typeCommunication dans un congrès
dc.identifier.doi10.2140/obs.2013.1.437
dc.subject.halInformatique [cs]/Calcul formel [cs.SC]
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.page437-461
bordeaux.volume1
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleANTS X - Algorithmic Number Theory 2012
bordeaux.countryUS
bordeaux.conference.citySan Diego
bordeaux.peerReviewedoui
hal.identifierhal-00734450
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2012-07-13
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00734450v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2013-11-14&rft.volume=1&rft.spage=437-461&rft.epage=437-461&rft.au=LAUTER,%20Kristin&ROBERT,%20Damien&rft.genre=unknown


Archivos en el ítem

ArchivosTamañoFormatoVer

No hay archivos asociados a este ítem.

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem