Planar functions and perfect nonlinear monomials over finite fields
Planar functions and perfect nonlinear monomials over finite fields
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DOI：
10.1007/s10623-013-9890-8
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发表时间：
2013-01
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影响因子：
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通讯作者：
Michael E. Zieve
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文献类型：
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作者：
Michael E. Zieve
有限射影平面的研究涉及到平面函数，即，函数使得，对于每一个，函数是一个双射。平面函数也用于DES类密码系统的构造，在那里它们被称为完美非线性函数。我们确定所有的平面函数的形式，在假设。这解决了埃尔南多，麦圭尔和蒙特塞拉特的两个问题。我们的论点也产生了一个新的证明的猜想塞格雷和Bartocci关于单项超椭圆在有限的Deskiesian投影平面。
The study of finite projective planes involves planar functions, namely, functionssuch that, for each, the functionis a bijection on. Planar functions are also used in the construction of DES-like cryptosystems, where they are called perfect nonlinear functions. We determine all planar functions onof the form, under the assumption that. This resolves two conjectures of Hernando, McGuire and Monserrat. Our arguments also yield a new proof of a conjecture of Segre and Bartocci about monomial hyperovals in finite Desarguesian projective planes.