2007 Fiscal Year Final Research Report Summary
Fast implementation and security analysis of hyperelliptic curve cryptosystems
| Project/Area Number |
17500010
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Chuo University |
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Principal Investigator |
CHAO Jinhui Chuo University, Faculty of Science and Engineering, Professor (60227345)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJII Shigeo Institute of Information Security, Graduate School of Information Security, Professor (50020350)
MOMOSE Fumiyuki Chuo University, Faculty of Science and Engineering, Professor (80182187)
MATSUO Kazuto Institute of Information Security, Graduate School of Information Security, Professor
SHIMURA Mahoro Tokai University, Department of Science, Lecturer (30308209)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Elliptic Curve Crwtosystems / Hverelliptic Curve Cryptosystems / Fast Addition Algorithms / Weil Restriction Attack / GHS Attack / Security Analysis |
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| Research Abstract |
1. It is known that among the algebraic curve based cryptosystems, only hyperelliptic curves of gene ra less or equal to three are secure. In this research, we first developed fast algorithms for hyper elliptic curves of genus three. Cryptosystems based on these curves are implemented on cheap processors of 64 bits with single decision, thus more efficient cryptosystems than elliptic curve crypt osystems are possible. In particular, fast addition algorithms with the least computational cost are obtained. These algorithms are implemented to achieve a new record of fast scalar multiplication with173 microseconds.
2. As to security analysis, we show for the first time the existence of a huge number of elliptic curves which are believed to be secure but can be broken by GHS attack. In particular, we show explicitly classes of elliptic and hyperelliptic curves of low genera defined over extension fields, which have weak coverings, i.e. their Well restrictions can be attacked by either index calculus attacks to hyperelliptic curves or Diem's recent attack to non-hyperelliptic curves. A complete classification of such weak curves is obtained. Besides, we show how to construct such coverings from these curves and analyze density of these weak curves.
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Research Products
(34 results)
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[Journal Article] Improvements of addition algorithm on genus 3 hyperelliptic curves and their implementation2005
Author(s)
Masaki, Gonda, Kazuto, Matsuo, Kazumaro, Aoki, Jinhui, Chao, Shigeo, Tsujii
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Journal Title
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E88-A(1)
Pages: 89-96
Description
「研究成果報告書概要(欧文)」より
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[Book] 暗号理論と楕円曲線2008
Author(s)
辻井, 笠原, 趙, 松尾, 境, 有田
Total Pages
340
Publisher
森北出版
Description
「研究成果報告書概要(和文)」より
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[Book] Theory of cryptography and elliptic curvees2008
Author(s)
S., Tsujii, M., Kasahara, J., Chao, K., Matsuo, R., Sakai, G., Arita
Publisher
Morikita Publication
Description
「研究成果報告書概要(欧文)」より
