Finding suitable curves for the elliptic curve method of factorization-Reference-Cited by-同舟云学术

Finding suitable curves for the elliptic curve method of factorization

Published:1993 Issue:201 Volume:60 Page:399-405
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Atkin A. O. L.,Morain F.

Abstract

Using the parametrizations of Kubert, we show how to produce infinite families of elliptic curves which have prescribed nontrivial torsion over Q and rank at least one. These curves can be used to speed up the ECM factorization algorithm of Lenstra. We also briefly discuss curves with complex multiplication in this context.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1993-60-201/S0025-5718-1993-1140645-1/S0025-5718-1993-1140645-1.pdf

Reference11 articles.

1. Elliptic curves and primality proving;Atkin, A. O. L.;Math. Comp.,1993

2. Contemporary Mathematics;Brillhart, John,1988

3. The University Series in Mathematics;Chahal, J. S.,1988

4. Universal bounds on the torsion of elliptic curves;Kubert, Daniel Sion;Proc. London Math. Soc. (3),1976

5. Factoring integers with elliptic curves;Lenstra, H. W., Jr.;Ann. of Math. (2),1987

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