Name
Abstract | ||
|---|---|---|
The algorithm we develop outputs the order and the structure, including generators, of the l-Sylow subgroup of the group of rational points of an elliptic curve defined over a finite field. To do this, we do not assume any knowledge of the group order. We are able to choose points in such a way that a linear number of successive l-divisions leads to generators of the subgroup under consideration. After the computation of a couple of polynomials, each division step relies on finding rational roots of polynomials of degree l. We specify in complete detail the case l = 3, when the complexity of each trisection is given by the computation of cubic roots in finite fields. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1090/S0025-5718-08-02201-1 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
rational point,elliptic curve,finite field | Elliptic rational functions,Finite field,Combinatorics,Torsion (mechanics),Polynomial,Mathematical analysis,Pure mathematics,Numerical analysis,Schoof's algorithm,Elliptic curve,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
78 | 267 | 0025-5718 |
Citations | PageRank | References |
3 | 0.43 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Josep M. Miret | 1 | 81 | 14.88 |
| R. Moreno | 2 | 3 | 0.43 |
| A. Rio | 3 | 12 | 2.56 |
| Magda Valls | 4 | 67 | 8.68 |