Computing the Canonical Lift of Genus 2 Curves in Odd Characteristics
| 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 | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAIGA, Abdoulaye | |
| dc.date.accessioned | 2024-04-04T02:40:51Z | |
| dc.date.available | 2024-04-04T02:40:51Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191096 | |
| dc.description.abstractEn | Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and if available the Hilbert modular polynomials to compute the canonical lift of A. As an application, if q = p n , we show how to use the canonical lift to count the number of points on A in quasi-quadratic time Õ(n 2), this is a direct extension of Satoh's original algorithm for elliptic curves. 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 | Abelian variety | |
| 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 Canonical Lift of Genus 2 Curves in Odd Characteristics | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| 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-03738314 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03738314v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ROBERT,%20Damien&MAIGA,%20Abdoulaye&rft.genre=preprint |
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