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On Elkies subgroups of -torsion points in elliptic curves defined over a finite field

Reynald LercierThomas Sirvent — 2008

Journal de Théorie des Nombres de Bordeaux

As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic p , there exists an algorithm that computes, for an Elkies prime, -torsion points in an extension of degree - 1 at cost O ˜ ( max ( , log q ) 2 ) bit operations in the favorable case where p / 2 . We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the p -adic approach followed by Joux and Lercier to get an algorithm valid without...

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