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— 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… (More)

- Masaki Gonda, Kazuto Matsuo, Kazumaro Aoki, Jinhui Chao, Shigeo Tsujii
- IEICE Transactions
- 2005

SUMMARY Genus 3 hyperelliptic curve cryptosystems are capable of fast-encryption on a 64-bit CPU, because a 56-bit field is enough for their definition fields. Recently, Kuroki et al. proposed an extension of the Harley algorithm, which had been known as the fastest addition algorithm of divisor classes on genus 2 hyperelliptic curves, on genus 3… (More)

— Genus 3 hyperelliptic curve cryptosystems are able to carry out fast-encryption on a 64-bit CPU because a 56-bit field is enough for their definition fields. Recently, Kuroki et al. proposed an extension of the Harley algorithm, which had been known as the fastest addition algorithm of divisor classes on genus 2 hyperelliptic curves, on genus 3… (More)

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