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

dc.creatorLercier, Reynald
dc.creatorSirvent, Thomas
dc.date2008-09-16
dc.date.accessioned2026-07-07T10:03:19Z
dc.date.available2026-07-07T10:03:19Z
dc.descriptionAs 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.description13 pages
dc.identifierhttps://arxiv.org/abs/0809.2774
dc.identifierhttp://arxiv.org/abs/0809.2774
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169246
dc.subjectNumber Theory
dc.subject11T99; 14H52; 14G50; 11T71
dc.titleOn Elkies subgroups of l-torsion points in elliptic curves defined over a finite field
dc.typetext

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