{
  "id": "0809.2774",
  "version": "v1",
  "published": "2008-09-16T19:07:19.000Z",
  "updated": "2008-09-16T19:07:19.000Z",
  "title": "On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field",
  "authors": [
    "Reynald Lercier",
    "Thomas Sirvent"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-16T19:07:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T99",
      "14H52",
      "14G50",
      "11T71"
    ],
    "keywords": [
      "elliptic curves",
      "finite field",
      "l-torsion points",
      "elkies subgroups",
      "count points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2774L"
    }
  }
}