Improvements of Addition Algorithm on Genus 3 Hyperelliptic Curves and Their Implementation
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- GONDA Masaki
- Dept. of Information and System Engineering, Chuo University
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- MATSUO Kazuto
- Graduate School of Information Security, Institute of Information Security
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- AOKI Kazumaro
- NTT Information Sharing Platform Laboratories, NTT Corporation
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- CHAO Jinhui
- Dept. of Information and System Engineering, Chuo University
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- TSUJII Shigeo
- Graduate School of Information Security, Institute of Information Security
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説明
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 hyperelliptic curves and Pelzl et al. improved the algorithm. This paper shows an improvement of the Harley algorithm on genus 3 hyperelliptic curves using Toom's multiplication. The proposed algorithm takes only I+70M for an addition and I+71M for a doubling instead of I+76M and I+74M respectively, which are the best possible of the previous works, where I and M denote the required time for an inversion and a multiplication over the definition field respectively. This paper also shows 2 variations of the proposed algorithm in order to adapt the algorithm to various platforms. Moreover this paper discusses finite field arithmetic suitable for genus 3 hyperelliptic curve cryptosystems and shows implementation results of the proposed algorithms on a 64-bit CPU. The implementation results show a 160-bit scalar multiplication can be done within 172μS on a 64-bit CPU Alpha EV68 1.25 GHz.
収録刊行物
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- IEICE transactions on fundamentals of electronics, communications and computer sciences
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IEICE transactions on fundamentals of electronics, communications and computer sciences 88 (1), 89-96, 2005-01-01
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詳細情報 詳細情報について
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- CRID
- 1570009752557477632
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- NII論文ID
- 110003213214
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- NII書誌ID
- AA10826239
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- ISSN
- 09168508
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- 本文言語コード
- en
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- データソース種別
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- CiNii Articles
