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- Title
An exploration of affine group laws for elliptic curves.
- Authors
Hisil, Huseyin; Wong, Kenneth Koon-Ho; Carter, Gary; Dawson, Ed
- Abstract
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.
- Subjects
AFFINE differential geometry; ELLIPTIC curves; DATA encryption; RIEMANN-Roch theorems; JACOBI forms; SCALAR field theory; WEIERSTRASS points; FOUNDATIONS of arithmetic; BERNSTEIN polynomials
- Publication
Journal of Mathematical Cryptology, 2011, Vol 5, Issue 1, p1
- ISSN
1862-2976
- Publication type
Article
- DOI
10.1515/JMC.2011.005