Fast algorithms for computing isogenies between elliptic curves

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 ( different from the characteristic) in time quasi-linear with respect to . This is based in particular on fast algorithms for power series expansion of the Weierstrass -function and related functions.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Alin Bostan, Bruno Salvy, François Morain, Éric Schost
• Keywords: Algorithms, CORR 2006, Education, Elliptic Curves, Large Prime