In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a point cannot remain APN. In the second part of the paper, we find conditions for some transformations not to be partially APN, and in the process, we find classes of functions that are never APN for infinitely many extensions of the prime field \(\mathbb {F}_{2}\), extending some earlier results of Leander and Rodier.

中文翻译：

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APN布尔函数的一部分以及不是APN无限频繁的函数的类

在本文中，我们定义了部分APN的概念，并找到了满足此条件的函数类别的各种表征和构造。我们将此概念与已知的猜想联系在一起，即在某个点修改的APN函数不能保持APN。在本文的第二部分中，我们找到了一些不完全为APN的转换的条件，并且在此过程中，我们发现了素数域\（\ mathbb {F} _ {2} \），扩展了Leander和Rodier的一些早期结果。