Name
Abstract | ||
|---|---|---|
In this paper we describe an algorithm that outputs the order and the structure, including generators, of the 2-Sylow subgroup of an elliptic curve over a finite field. To do this, we do not assume any knowledge of the group order. The results that lead to the design of this algorithm are of inductive type. Then a right choice of points allows us to reach the end within a linear number of successive halvings. The algorithm works with abscissas, so that halving of rational points in the elliptic curve becomes computing of square roots in the finite field. Efficient methods for this computation determine the efficiency of our algorithm. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1090/S0025-5718-04-01640-0 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
rational point,finite field,elliptic curve | Discrete mathematics,Applied mathematics,Modular elliptic curve,Mathematical analysis,Schoof–Elkies–Atkin algorithm,Elliptic curve point multiplication,Jacobian curve,Hessian form of an elliptic curve,Mathematics,Schoof's algorithm,Elliptic curve,Tripling-oriented Doche–Icart–Kohel curve | Journal |
Volume | Issue | ISSN |
74 | 249 | 0025-5718 |
Citations | PageRank | References |
6 | 1.20 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Josep M. Miret | 1 | 81 | 14.88 |
| R. Moreno | 2 | 6 | 1.20 |
| A. Rio | 3 | 12 | 2.56 |
| Magda Valls | 4 | 67 | 8.68 |