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Point Multiplication on Ordinary Elliptic Curves over Fields of Characteristic Three
Authors: N. P. Smart, J. WestwoodAbstract:
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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