Computing isogenies from modular equations in genus two
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KIEFFER, Jean | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | PAGE, Aurel | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:49:01Z | |
| dc.date.available | 2024-04-04T02:49:01Z | |
| dc.date.created | 2020-01-12 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191788 | |
| dc.description.abstractEn | We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.language.iso | en | |
| dc.subject.en | Abelian surfaces | |
| dc.subject.en | Algorithm | |
| dc.subject.en | Modular equations | |
| dc.subject.en | Isogenies | |
| dc.title.en | Computing isogenies from modular equations in genus two | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 2001.04137 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02436133 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02436133v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=KIEFFER,%20Jean&PAGE,%20Aurel&ROBERT,%20Damien&rft.genre=preprint |
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