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Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication

hal.structure.identifierDepartment of Mathematics [College Park]
dc.contributor.authorBALLENTINE, Sean
hal.structure.identifierUniversity of Calgary
hal.structure.identifierPacific Institute for the Mathematical Sciences [PIMS]
dc.contributor.authorGUILLEVIC, Aurore
hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorLORENZO GARCÍA, Elisa
hal.structure.identifierUniversiteit Leiden = Leiden University
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorMARTINDALE, Chloe
hal.structure.identifierUniversity of New South Wales [Sydney] [UNSW]
dc.contributor.authorMASSIERER, Maike
hal.structure.identifierLaboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
hal.structure.identifierGeometry, arithmetic, algorithms, codes and encryption [GRACE]
dc.contributor.authorSMITH, Benjamin
hal.structure.identifierBernoulli Institute for Mathematics and Computer Science and Artificial Intelligence
dc.contributor.authorTOP, Jaap
dc.contributor.editorE. W. Howe
dc.contributor.editorK. E. Lauter
dc.contributor.editorJ. L. Walker
dc.date.accessioned2024-04-04T03:08:09Z
dc.date.available2024-04-04T03:08:09Z
dc.date.created2016-12-16
dc.date.issued2017
dc.date.conference2016-02-22
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193505
dc.description.abstractEnSchoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit isogenies. Moving to Jacobians of genus-2 curves, the current state of the art for point counting is a generalization of Schoof's algorithm. While we are currently missing the tools we need to generalize Elkies' methods to genus 2, recently Martindale and Milio have computed analogues of modular polynomials for genus-2 curves whose Jacobians have real multiplication by maximal orders of small discriminant. In this article, we prove Atkin-style results for genus-2 Jacobians with real multiplication by maximal orders, with a view to using these new modular polynomials to improve the practicality of point-counting algorithms for these curves.
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherSpringer
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.source.titleAssociation for Women in Mathematics Series
dc.title.enIsogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
dc.typeCommunication dans un congrès
dc.identifier.doi10.1007/978-3-319-63931-4_3
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halInformatique [cs]/Cryptographie et sécurité [cs.CR]
dc.identifier.arxiv1701.01927
bordeaux.page63-94
bordeaux.volume9
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleAlgebraic Geometry for Coding Theory and Cryptography
bordeaux.countryUS
bordeaux.title.proceedingAssociation for Women in Mathematics Series
bordeaux.conference.cityLos Angeles
bordeaux.peerReviewedoui
hal.identifierhal-01421031
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2016-02-26
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01421031v1
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