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arXiv · 2003.06367

Fast computation of elliptic curve isogenies in characteristic two

Xavier Caruso·Elie Eid·Reynald Lercier
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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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Xavier Caruso, Elie Eid, Reynald Lercier. 2020-03-13. Fast computation of elliptic curve isogenies in characteristic two. https://arxiv.org/abs/2003.06367

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