Computing the 2-adic Canonical Lift of Genus 2 Curves
| hal.structure.identifier | Université Cheikh Anta Diop de Dakar [Sénégal] [UCAD] | |
| dc.contributor.author | MAIGA, Abdoulaye | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:47:35Z | |
| dc.date.available | 2024-04-04T02:47:35Z | |
| dc.date.conference | 2021-03-02 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191657 | |
| dc.description.abstractEn | Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined over k. We first compute modular polynomials in function of invariants with good reduction modulo two. We then use these modular polynomials to compute the canonical lift of genus 2 curves in even characteristic. The lifted Frobenius is characterized by the reduction behaviors of the Weierstrass points over k. This allows us to compute the cardinality of the Jacobian variety. We give a detailed description with the necessary optimizations for an efficient implementation. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.language.iso | en | |
| dc.subject.en | Arithmetic invariants of genus 2 curves | |
| dc.subject.en | Modular polynomials | |
| dc.subject.en | Canonical lift | |
| dc.subject.en | Point counting | |
| dc.title.en | Computing the 2-adic Canonical Lift of Genus 2 Curves | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| 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 | ICMC 2021 - 7th International Conference on Mathematics and Computing | |
| bordeaux.country | IN | |
| bordeaux.conference.city | Shibpur / Virtual | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03119147 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.organizer | Indian Institute of Engineering Science and Technology | |
| hal.conference.end | 2021-03-05 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03119147v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=MAIGA,%20Abdoulaye&ROBERT,%20Damien&rft.genre=unknown |
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