**Elliptic curves in Huff's model**

*Hongfeng Wu and Rongquan Feng*

**Abstract: **This paper introduce generalizes the Huff curves $x(ay^2-1)=y(bx^2-1)$ which contains Huff's model $ax(y^2-1)=by(x^2-1)$ as a
special case. It is shown that every elliptic curve over the finite
field with three points of order $2$ is isomorphic to a general Huff curve.
Some fast explicit formulae for general Huff curves in projective coordinates are presented. These explicit formulae for addition and doubling are almost as fast in the general case as they are for the Huff curves in \cite{Joye}. Finally, the number of isomorphism classes of general Huff curves
defined over the finite field $\mathbb{F}_q$ is enumerated.

**Category / Keywords: **elliptic curve, Huff curve, isomorphism classes, scalar multiplication, cryptography

**Date: **received 9 Jul 2010, last revised 12 May 2011

**Contact author: **whfmath at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20110512:111047 (All versions of this report)

**Short URL: **ia.cr/2010/390

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