Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
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DOI：
10.1109/tit.2008.928275
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发表时间：
2008-09
影响因子：
2.5
通讯作者：
L. Budaghyan;C. Carlet;G. Leander
中科院分区：
文献类型：
--
作者：
L. Budaghyan;C. Carlet;G. Leander
本文介绍了第一个发现的无限类几乎完美非线性（APN）多项式，这是不Carlet-Charpin-Zinoviev（CCZ）-等价的幂函数（至少对于某些值的变量的数量）。这是从F2 n到F2 n的两类APN二项式（分别对于n可被3整除，4）。我们证明了这些功能的扩展仿射（EA）不等价于任何功率函数，他们是CCZ不等价的黄金，Kasami，逆，和Dobbertin功能时n ges 12。这意味着对于n，即使它们也是CCZ不等价于任何已知的APN函数。特别地，对于n = 12，20，24，它们因此与任何幂函数CCZ-不等价。
This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to power functions (at least for some values of the number of variables). These are two classes of APN binomials from F2n to F2n (for n divisible by 3, resp., 4). We prove that these functions are extended affine (EA)-inequivalent to any power function and that they are CCZ-inequivalent to the Gold, Kasami, inverse, and Dobbertin functions when n ges 12. This means that for n even they are CCZ-inequivalent to any known APN function. In particular, for n = 12,20,24, they are therefore CCZ-inequivalent to any power function.