Algorithms for computing norms and characteristic polynomials on general Drinfeld modules
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | CARUSO, Xavier | |
| hal.structure.identifier | Cryptology, arithmetic : algebraic methods for better algorithms [CARAMBA] | |
| dc.contributor.author | LEUDIÈRE, Antoine | |
| dc.date.accessioned | 2024-04-04T02:30:38Z | |
| dc.date.available | 2024-04-04T02:30:38Z | |
| dc.date.created | 2023-07-04 | |
| dc.date.issued | 2023-12-11 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190262 | |
| dc.description.abstractEn | We provide two families of algorithms to compute characteristic polynomials of endomorphisms and norms of isogenies of Drinfeld modules. Our algorithms work for Drinfeld modules of any rank, defined over any base curve. When the base curve is $\mathbb P^1_{\mathbb F_q}$, we do a thorough study of the complexity, demonstrating that our algorithms are, in many cases, the most asymptotically performant. The first family of algorithms relies on the correspondence between Drinfeld modules and Anderson motives, reducing the computation to linear algebra over a polynomial ring. The second family, available only for the Frobenius endomorphism, is based on a formula expressing the characteristic polynomial of the Frobenius as a reduced norm in a central simple algebra. | |
| dc.description.sponsorship | Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026 | |
| dc.description.sponsorship | Fonctions L : aspects p-adiques, analytiques et effectifs - ANR-22-CE40-0013 | |
| dc.description.sponsorship | Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications - ANR-21-CE39-0009 | |
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| dc.language.iso | en | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.subject.en | Drinfeld modules | |
| dc.subject.en | Anderson motives | |
| dc.subject.en | algorithms | |
| dc.title.en | Algorithms for computing norms and characteristic polynomials on general Drinfeld modules | |
| dc.type | Document de travail - Pré-publication | |
| dc.identifier.doi | 10.48550/arXiv.2307.02879 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| dc.identifier.arxiv | 2307.02879 | |
| 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-04151171 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04151171v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-12-11&rft.au=CARUSO,%20Xavier&LEUDI%C3%88RE,%20Antoine&rft.genre=preprint |
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