Fast computation of elliptic curve isogenies in characteristic two - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of the London Mathematical Society Année : 2021

Fast computation of elliptic curve isogenies in characteristic two

Résumé

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.

Dates et versions

hal-02508825 , version 1 (16-03-2020)

Identifiants

Citer

Xavier Caruso, Elie Eid, Reynald Lercier. Fast computation of elliptic curve isogenies in characteristic two. Journal of the London Mathematical Society, 2021, 104 (4), pp.1901-1929. ⟨10.1112/jlms.12487⟩. ⟨hal-02508825⟩
130 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More