An important problem on almost perfect nonlinear (APN) functions is the existence of APN permutations on even-degree extensions of ${\mathbb{F}}_2$ larger than 6. Browning et al. (2010) gave the first known example of an APN permutation on the degree-6 extension of ${\mathbb{F}}_2$. The APN permutation is CCZ-equivalent to the previously known quadratic Kim κ-function (Browning et al. (2009)). Aside from the computer based CCZ-inequivalence results on known APN functions on even-degree extensions of ${\mathbb{F}}_2$ with extension degrees less than 12, no theoretical CCZ-inequivalence result on infinite families is known. In this paper, we show that Gold and Kasami APN functions are not CCZ-equivalent to permutations on infinitely many even-degree extensions of ${\mathbb{F}}_2$. In the Gold case, we show that Gold APN functions are not equivalent to permutations on any even-degree extension of ${\mathbb{F}}_2$, whereas in the Kasami case we are able to prove inequivalence results for every doubly-even-degree extension of ${\mathbb{F}}_2$.

几乎完美的非线性（APN）函数的一个重要问题是在偶数次扩展的APN置换的存在 ${\mathbb{F}}_2$大于6。Browning等。（2010年）给出了关于APN的6级扩展的APN排列的第一个已知示例。${\mathbb{F}}_2$。该APN置换是CCZ-等同于先前已知的二次金κ -function（Browning等人（2009））。除了基于计算机的CCZ不等式以外，还对已知偶数扩展的APN函数进行了计算。${\mathbb{F}}_2$如果扩展度小于12，则无穷大的理论CCZ不等式结果是未知的。在本文中，我们证明Gold和Kasami APN函数不等于CCZ等效于无穷多个偶数次扩展的置换${\mathbb{F}}_2$。在Gold案例中，我们证明Gold APN函数不等于任何偶数阶扩展的置换${\mathbb{F}}_2$，而在Kasami案例中，我们能够证明每个双偶数度扩展的不等式结果 ${\mathbb{F}}_2$。