An exploration of affine group laws for elliptic curves

Journal of mathematical cryptology

article

Huseyin Hisil¹  Kenneth Koon-Ho Wong¹  Gary Carter¹  Ed Dawson¹ 

[1] Information Security Institute

关键词: Elliptic curve;    group law;    point addition;    point doubling;    projective coordinates;    rational maps;    birational equivalence;    Riemann–Roch theorem;    rational simplification;    scalar multiplication;    elliptic curve cryptography;   

DOI  :  10.1515/jmc.2011.005

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY|CC BY-NC-ND