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BY-NC-ND 3.0 license Open Access Published by De Gruyter April 10, 2011

An exploration of affine group laws for elliptic curves

  • Huseyin Hisil EMAIL logo , Kenneth Koon-Ho Wong , Gary Carter and Ed Dawson


Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.

Received: 2010-09-04
Revised: 2011-03-03
Published Online: 2011-04-10
Published in Print: 2011-June

© Walter de Gruyter 2011

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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