CARUSO, Xavier; LEUDIÈRE, Antoine

doi:10.48550/arXiv.2307.02879

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CARUSO, Xavier
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

LEUDIÈRE, Antoine
Cryptology, arithmetic : algebraic methods for better algorithms [CARAMBA]

Langue

Document de travail - Pré-publication

Ce document a été publié dans

2023-12-11

Résumé en anglais

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.< Réduire

Mots clés en anglais

Drinfeld modules

Anderson motives

algorithms

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190262

DOI

http://dx.doi.org/10.48550/arXiv.2307.02879

Project ANR

Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Fonctions L : aspects p-adiques, analytiques et effectifs - ANR-22-CE40-0013
Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications - ANR-21-CE39-0009
Post-quantum padlock for web browser - ANR-22-PETQ-0008

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251