# Fast computation of elliptic curve isogenies in characteristic two

2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02508825
Contributor : Xavier Caruso <>
Submitted on : Monday, March 16, 2020 - 8:56:19 AM
Last modification on : Friday, July 10, 2020 - 4:05:08 PM

### Identifiers

• HAL Id : hal-02508825, version 1
• ARXIV : 2003.06367

### Citation

Xavier Caruso, Elie Eid, Reynald Lercier. Fast computation of elliptic curve isogenies in characteristic two. 2020. ⟨hal-02508825⟩

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