In this paper, we study the differential uniformity of the composition of two functions with the help of Boolean matrix theory. Based on the result of our research, we can construct new differentially 4-uniform permutations from known ones. In addition, we find some clues about the existence of APN permutations of \(\mathbb {F}_{2^{n}}\) for even n ≥ 8.

中文翻译：

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两个函数组成的差分均匀性

在本文中，我们借助布尔矩阵理论研究了两个函数的微分均匀性。根据我们的研究结果，我们可以从已知的序列构造新的差分4均匀置换。此外，我们找到的APN排列存在一些线索\（\ mathbb {F} _ {2 ^ {N}} \）甚至ñ ≥8。