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Point multiplication on ordinary elliptic curves over fields of characteristic three.

Nigel Smart, John Westwood, Point multiplication on ordinary elliptic curves over fields of characteristic three.. Applicable Algebra in Engineering, Communication and Computing, 13, pp. 485–497. July 2003. No electronic version available.

Abstract

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.

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