Choosing the correct elliptic curve in the CM method

K.  Rubin; A.  Silverberg

Paper 2007/253

Choosing the correct elliptic curve in the CM method

K. Rubin and A. Silverberg

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 $4$.

Note: Minor changes from last version.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curves CM method point-counting
Contact author(s): asilverb @ math uci edu
History: 2009-01-21: last of 4 revisions; 2007-06-27: received; See all versions
Short URL: https://ia.cr/2007/253
License: CC BY

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},
      note = {\url{https://eprint.iacr.org/2007/253}},
      url = {https://eprint.iacr.org/2007/253}
}