| Project/Area Number |
21540025
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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 |
Algebra
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | DHO (高次元超卵形) / APN 関数 / S-box / CCZ-同値 / EA-同値 / 二重可移群 / split DHO / bilinear DHO / semibiplane / DHO / 部分DHOの直和 / APN関数 / 高次元双対超卵形 / Buratti-Del Fra DHO / Huybrechts DHO / Veronesean DHO / Taniguchi DHO / Coulter-Matthews function / Ding-Yuan function / 高次元双対弧 / 双対超卵形 / quadratic関数 / CCZ同値 / 拡大アフィン同値 / 多重可移群 / 有限単純群 |
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| Research Abstract |
It is shown that the concepts of DHO(dimensional dual hyperovals) and semibiplanes are useful in studying nonlinear functions (specifically, analyzing equivalence problem) such as APN functions, which are remarkable in symmetric cryptography. With this geometric approach, a conjecture by Y. Edel was established, which states that two quadratic APN functions are CCZ-equivalent if and only if they are EA-equivalent. DHOs with doubly transitive automorphism groups are classified. We obtain a unified description of four classes of simply connected DHOs.
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