An exploration of affine group laws for elliptic curves

Autor:	Hisil Huseyin, Wong Kenneth Koon-Ho, Carter Gary, Dawson Ed
Jazyk:	angličtina
Rok vydání:	2011
Předmět:	elliptic curve group law point addition point doubling projective coordinates rational maps birational equivalence riemann–roch theorem rational simplification scalar multiplication elliptic curve cryptography Mathematics QA1-939
Zdroj:	Journal of Mathematical Cryptology, Vol 5, Iss 1, Pp 1-50 (2011)
Druh dokumentu:	article
ISSN:	1862-2976 1862-2984
DOI:	10.1515/jmc.2011.005
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/e624ac981af4422782d0bbf8ada0ed67 Zobrazit plný text záznamu View record in DOAJ