Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
| hal.structure.identifier | Department of Mathematics [College Park] | |
| dc.contributor.author | BALLENTINE, Sean | |
| hal.structure.identifier | University of Calgary | |
| hal.structure.identifier | Pacific Institute for the Mathematical Sciences [PIMS] | |
| dc.contributor.author | GUILLEVIC, Aurore | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LORENZO GARCÍA, Elisa | |
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | MARTINDALE, Chloe | |
| hal.structure.identifier | University of New South Wales [Sydney] [UNSW] | |
| dc.contributor.author | MASSIERER, Maike | |
| hal.structure.identifier | Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX] | |
| hal.structure.identifier | Geometry, arithmetic, algorithms, codes and encryption [GRACE] | |
| dc.contributor.author | SMITH, Benjamin | |
| hal.structure.identifier | Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence | |
| dc.contributor.author | TOP, Jaap | |
| dc.contributor.editor | E. W. Howe | |
| dc.contributor.editor | K. E. Lauter | |
| dc.contributor.editor | J. L. Walker | |
| dc.date.accessioned | 2024-04-04T03:08:09Z | |
| dc.date.available | 2024-04-04T03:08:09Z | |
| dc.date.created | 2016-12-16 | |
| dc.date.issued | 2017 | |
| dc.date.conference | 2016-02-22 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193505 | |
| dc.description.abstractEn | Schoof'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.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.source.title | Association for Women in Mathematics Series | |
| dc.title.en | Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.1007/978-3-319-63931-4_3 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.identifier.arxiv | 1701.01927 | |
| bordeaux.page | 63-94 | |
| bordeaux.volume | 9 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | Algebraic Geometry for Coding Theory and Cryptography | |
| bordeaux.country | US | |
| bordeaux.title.proceeding | Association for Women in Mathematics Series | |
| bordeaux.conference.city | Los Angeles | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01421031 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.end | 2016-02-26 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01421031v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Association%20for%20Women%20in%20Mathematics%20Series&rft.date=2017&rft.volume=9&rft.spage=63-94&rft.epage=63-94&rft.au=BALLENTINE,%20Sean&GUILLEVIC,%20Aurore&LORENZO%20GARC%C3%8DA,%20Elisa&MARTINDALE,%20Chloe&MASSIERER,%20Maike&rft.genre=unknown |
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