On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field
| dc.creator | Lercier, Reynald | |
| dc.creator | Sirvent, Thomas | |
| dc.date | 2008-09-16 | |
| dc.date.accessioned | 2026-07-07T10:03:19Z | |
| dc.date.available | 2026-07-07T10:03:19Z | |
| dc.description | 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. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0809.2774 | |
| dc.identifier | http://arxiv.org/abs/0809.2774 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169246 | |
| dc.subject | Number Theory | |
| dc.subject | 11T99; 14H52; 14G50; 11T71 | |
| dc.title | On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field | |
| dc.type | text |