Paper 2007/253 Original: eprint.iacr.org/2007/253 ↗
Choosing the correct elliptic curve in the CM method
Abstract
We give an elementary way to distinguish between the twists of an ordinary elliptic curve $E$ over $\Fp$ in order to identify the one with $p+1-2U$ points, when $p=U^2+\d V^2$ with $2U, 2V\in \Z$ and $E$ is constructed using the CM method for finding elliptic curves with a prescribed number of points. Our algorithms consist in most cases of reading off simple congruence conditions on $U$ and $V$ modulo $4$.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2009-01-21: last updated
- 2007-06-27: published
- Short URL
- https://ia.cr/2007/253
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2007/253,
author = {K. Rubin and A. Silverberg},
title = {Choosing the correct elliptic curve in the CM method},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/253},
year = {2007},
url = {https://eprint.iacr.org/2007/253}
}