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Fast computation of elliptic curve isogenies in characteristic two

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.
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https://hal.archives-ouvertes.fr/hal-02508825
Contributor : Xavier Caruso Connect in order to contact the contributor
Submitted on : Monday, March 16, 2020 - 8:56:19 AM
Last modification on : Monday, November 29, 2021 - 10:48:40 PM

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

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