On security of pairing based elliptic curve cryptosystems in view of number theory
| Project/Area Number |
18340005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SATOH Takakazu Tokyo Institute of Technology, 大学院・理工学研究科, 准教授 (70215797)
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| Co-Investigator(Kenkyū-buntansha) |
黒川 信重 東京工業大学, 大学院・理工学研究科, 教授 (70114866)
川内 毅 東京工業大学, 大学院・理工学研究科, 助教 (30323778)
田口 雄一郎 九州大学, 大学院・数理学研究院, 准教授 (90231399)
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| Co-Investigator(Renkei-kenkyūsha) |
KUROKAWA Nobushige 東京工業大学, 大学院・理工学研究科, 教授 (70114866)
KAWACHI Takeshi 東京工業大学, 大学院・理工学研究科, 助教 (30323778)
TAGUCHI Yuichiro 九州大学, 数理学研究院, 准教授 (90231399)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥7,950,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | ペアリング / 楕円曲線暗号 / 離散対数問題 / 楕円曲線 / ρ値 / 公開鍵暗号 / 有限体 / 明示公式 / ペアリング反転 / アルゴリズム帰着 / シャンクス予想 |
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| Research Abstract |
A pairing inversion formula is considered to be a possible pairing based elliptic curve cryptography specific cryptanalysis. In this research, we gave explicit formulae for the Weil pairing inversion. The result is a dense rational formula and therefore pairing based cryptosystems are not vulnerable to evaluation of the explicit formula. We also constructed pairing friendly hyperelliptic curves from certain pairing non-friendly elliptic curves.
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Report
(6 results)
Research Products
(45 results)
