International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

J. Westwood

Publications

Year
Venue
Title
2002
EPRINT
Point Multiplication on Ordinary Elliptic Curves over Fields of Characteristic Three
Nigel P. Smart J. Westwood
In this paper we investigate the efficiency of cryptosystems based on ordinary elliptic curves over fields of characteristic three. We look at different representations for curves and consider some of the algorithms necessary to perform efficient point multiplication. We give example timings for our operations and compare them with timings for curves in characteristic two of a similar level of security. We show that using the Hessian form in characteristic three produces a point multiplication algorithm under $50$ percent slower than the equivalent system in characteristic two. Thus it is conceivable that curves in characteristic three, could offer greater performance than currently perceived by the community.

Coauthors

Nigel P. Smart (1)