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

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

2008-09-16

arxiv.org/abs/0809.2774v1

Mathematics

Number Theory

13 pages

Scientific paper

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 l an Elkies prime, l-torsion points in an extension of degree l-1 at cost O(l max(l, \log q)^2) bit operations in the favorable case where l < 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 for the first time an algorithm valid without any limitation on l and p but of similar complexity.

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