| Project/Area Number |
15K00022
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | Chuo University |
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Principal Investigator |
Chao Jinhui 中央大学, 理工学部, 教授 (60227345)
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| Co-Investigator(Renkei-kenkyūsha) |
SHIMURA Mahoro 東海大学, 理学部, 准教授 (30308209)
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| Research Collaborator |
IIJIMA Tsutomu 光電株式会社, 特機部, 研究員
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | Cryptography / Elliptic Curve / Security Analysis / GHS attacks / Cover Attakcs / IoT Cryptosystems / Hardware Implementation / Extension Fields / 楕円暗号 / 超楕円暗号 / GHS攻撃 / 被覆攻撃 / 有限拡大体 / IoT暗号 / 安全性解析 / 楕円曲線暗号 / 超楕円曲線暗号 / 暗号理論 / 情報セキュリティ / 公開鍵暗号 / 楕円曲線 / 超楕円曲線 / ＧＨＳ攻撃 |
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| Outline of Final Research Achievements |
Elliptic curve and hyperelliptic curve based cryptosystems are the most secure systems available now comparing with those based on factorization and discrete logarithm. Moreover using the definition fields as finite extensions of finite fields, fast and compact implementation of these systems become possible, which are then expected to play an important role in IoT technology. On the other hand, aiming at curves over extension fields, the GHS attack was proposed by Frey first then generalized to cover attack. This research present the first and complete security analysis on cover attack and GHS attack. We show that these attacks are very powerful. By a systematic analysis of the mathematical structure, we proposed algorithms to mathematically classify all curves which are subjected to these attacks. Then we obtain a complete list of all weak curves which will be useful in system design. We also discuss variations of these attacks and methodology to build a secure cryptosystem.
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