Fast Genus Three Hyperelliptic Curve Cryptosystems

This paper presents a fast addition algorithm for the divisor class groups of genus three hyperelliptic curves. This algorithm improves the most recently proposed Harley algorithm for genus three hyperelliptic curves, which have brought up a noticeable progress since the well known Cantor algorithm. In this paper, we extend the Harley algorithm to genus three curves. The computational cost of the proposed algorithm is I +8 1M for an addition and I +7 4M for a doubling. (Here I and M denote the cost of an inversion and a multiplication on the definition fields.) We also show the implementation of the algorithm on Alpha 21264 / 667MHz, which takes 932 µs for a 160bit scalar multiplication on a divisor class group.

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