Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Computing the $\ell$-power torsion of an elliptic curve over a finite field
HTML articles powered by AMS MathViewer

by J. Miret, R. Moreno, A. Rio and M. Valls PDF
Math. Comp. 78 (2009), 1767-1786 Request permission

Abstract:

The algorithm we develop outputs the order and the structure, including generators, of the $\ell$-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 $\ell$-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 $\ell$. We specify in complete detail the case $\ell =3$, when the complexity of each trisection is given by the computation of cubic roots in finite fields.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 11G20
  • Retrieve articles in all journals with MSC (2000): 11G20
Additional Information
  • J. Miret
  • Affiliation: Department de Matemàtica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain
  • Email: miret@eps.udl.es
  • R. Moreno
  • Affiliation: Department de Matemàtica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain
  • Email: ramiro@eps.udl.es
  • A. Rio
  • Affiliation: Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3. 08034-Barcelona, Spain
  • MR Author ID: 364632
  • Email: ana.rio@upc.edu
  • M. Valls
  • Affiliation: Department de Matemàtica, Universitat de Lleida, Jaume II 69, 25001-Lleida, Spain
  • Email: magda@eps.udl.es
  • Received by editor(s): March 30, 2005
  • Received by editor(s) in revised form: May 28, 2008
  • Published electronically: October 29, 2008
  • Additional Notes: The first, second and fourth authors were supported in part by grant MTM2007-66842-C02-02.
    The third author was supported in part by grants MTM2006-15038-C02-01 and 2005SGR 00443.
  • © Copyright 2008 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 1767-1786
  • MSC (2000): Primary 11G20
  • DOI: https://doi.org/10.1090/S0025-5718-08-02201-1
  • MathSciNet review: 2501074