Fast algorithms for computing isogenies between elliptic curves

Alin Bostan; Bruno Salvy; Francois Morain; Eric Schost

doi:10.1090/s0025-5718-08-02066-8

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Fast algorithms for computing isogenies between elliptic curves

Alin Bostan·Bruno Salvy·Francois Morain·Eric Schost

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Abstract

We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\ell$ ($\ell$ different from the characteristic) in time quasi-linear with respect to $\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\wp$-function and related functions.

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Alin Bostan, Bruno Salvy, Francois Morain, Eric Schost. 2006-09-06. Fast algorithms for computing isogenies between elliptic curves. https://doi.org/10.1090/s0025-5718-08-02066-8

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