Fast algorithms for computing isogenies between elliptic curves
Alin Bostan, François Morain, Bruno Salvy, Éric Schost · Mathematics of Computation · 2008
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 ℓ \ell ( ℓ \ell different from the characteristic) in time quasi-linear with respect to ℓ \ell . This is based in particular on fast algorithms for power series expansion of the Weierstrass ℘ \wp -function and related functions.