2012 Fiscal Year Final Research Report
Dimensional Dual Arcs and Nonlinear Functions
| 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
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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 |
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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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