An exploration of affine group laws for elliptic curves

Hisil, Huseyin, Wong, Kenneth Koon-Ho, Carter, Gary, & Dawson, Ed (2011) An exploration of affine group laws for elliptic curves. Journal of Mathematical Cryptology, 5(1), pp. 1-50.

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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.

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ID Code: 52451
Item Type: Journal Article
Refereed: Yes
Keywords: Elliptic Curve, Group Law, Point Addition, Point Doubling, Projective Coordinates
DOI: 10.1515/jmc.2011.005
ISSN: 1862-2976
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > DATA FORMAT (080400) > Data Encryption (080402)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2011 Walter de Gruyter
Copyright Statement: The final publication is available at
Deposited On: 19 Jul 2012 06:30
Last Modified: 30 Jul 2013 00:15

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