Cryptology ePrint Archive: Report 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 $4$.
Category / Keywords: implementation / elliptic curves, CM method, point-counting
Date: received 26 Jun 2007, last revised 20 Jan 2009
Contact author: asilverb at math uci edu
Available format(s): PDF | BibTeX Citation
Note: Minor changes from last version.
Version: 20090121:013955 (All versions of this report)
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