Algorithms for computing norms and characteristic polynomials on general Drinfeld modules
CARUSO, Xavier
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
CARUSO, Xavier
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
This item was published in
2023-12-11
English Abstract
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. ...Read more >
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.Read less <
English Keywords
Drinfeld modules
Anderson motives
algorithms
ANR Project
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
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
Origin
Hal imported