| Project/Area Number |
13440032
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
SUZUKI Joe Osaka University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50216397)
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Hiroyuki OGAWA,Hiroyuki, 大学院・理学研究科, 助手 (70243160)
IBUKIYAMA Tomoyoshi IBUKIYAMA,Tomoyoshi, 大学院・理学研究科, 教授 (60011722)
YAMAMOTO Yoshihiko YAMAMOTO,Yoshihiko, 大学院・理学研究科, 教授 (90028184)
HARASAWA Ryuichi Nagasaki Univ., Faculty of engineering, Assistant, 工学部, 助手 (10363467)
FUJIWARA Tohru FUJIWARA,Tohru, 大学院・情報科学研究科, 教授 (70190098)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥9,000,000 (Direct Cost: ¥9,000,000)
Fiscal Year 2003: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2002: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2001: ¥4,400,000 (Direct Cost: ¥4,400,000)
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| Keywords | Non Singular Curve / Discrete Logarithm / Information Security / Jacobian group / 代数曲線 / 情報セキュリティ / Index Calculus / 楕円曲線 / 整数論 |
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| Research Abstract |
K. Kedlaya proposed an method to count the number of IF_q-rational points in a hyper-elliptic curve, using the Leschetz fixed points formula in Monsky-Washinitzer Cohomology. The method has been extended to super-elliptic curves (Gaudry and. Gurel) immediately, to characteristic two hyper-elliptic curves, and to. C_<ab> curves (J. Denef, F. Vercauteren). Based on"Mi.ura theory, which is associated with how a curve is expressed as an affne variety, this paper applies Kedlaya's method to so-called strongly telescopic curves which are no longer plane curves and contain super-elliptic curves as special cages.
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