LUBICZ, David; ROBERT, Damien

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LUBICZ, David
Institut de Recherche Mathématique de Rennes [IRMAR]

ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

Langue

Document de travail - Pré-publication

Résumé en anglais

Let K A be a Kummer variety defined as the quotient of an Abelian variety A by the automorphism (−1) of A. Let T * 0 (A) be the co-tangent space at the point 0 of A. Let End(A) be the additive group of endomorphisms of A. There is a well defined map ρ : End(A) → Aut(T * 0 (A)), f → (df) * 0 , where (df) * 0 is the differential of f in 0 acting on T * 0 (A). The data of f ∈ End(K A) which comes from f ∈ End(A), determines ρ(f) up to a sign. The aim of this paper is to describe an efficient algorithm to recover ρ(f) up to a sign from the knowledge of f. Our algorithm is based on a study of the tangent cone of a Kummer variety in its singular 0 point. We give an application to Mestre's point counting algorithm.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191574

Project ANR

Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251