Fast computation of elliptic curve isogenies in characteristic two
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | CARUSO, Xavier | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | EID, Elie | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LERCIER, Reynald | |
| dc.date.accessioned | 2024-04-04T02:55:14Z | |
| dc.date.available | 2024-04-04T02:55:14Z | |
| dc.date.issued | 2021-11 | |
| dc.identifier.issn | 0024-6107 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192344 | |
| dc.description.abstractEn | We propose an algorithm that calculates isogenies between elliptic curves defined over an extension $K$ of $\mathbb{Q}_2$. It consists in efficiently solving with a logarithmic loss of $2$-adic precision the first order differential equation satisfied by the isogeny. We give some applications, especially computing over finite fields of characteristic 2 isogenies of elliptic curves and irreducible polynomials, both in quasi-linear time in the degree. | |
| dc.description.sponsorship | Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026 | |
| dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | London Mathematical Society ; Wiley | |
| dc.title.en | Fast computation of elliptic curve isogenies in characteristic two | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/jlms.12487 | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.identifier.arxiv | 2003.06367 | |
| bordeaux.journal | Journal of the London Mathematical Society | |
| bordeaux.page | 1901-1929 | |
| bordeaux.volume | 104 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02508825 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02508825v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20the%20London%20Mathematical%20Society&rft.date=2021-11&rft.volume=104&rft.issue=4&rft.spage=1901-1929&rft.epage=1901-1929&rft.eissn=0024-6107&rft.issn=0024-6107&rft.au=CARUSO,%20Xavier&EID,%20Elie&LERCIER,%20Reynald&rft.genre=article |
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