In this paper, we study the differential \(\delta \)-uniform property of two position swapped Exponential Welch Costas (EWC) permutations on \({\mathbb {Z}}_{p-1}\) and construct permutations with \(\delta = 4, 6\) for different values of p. We calculate the number of swapped EWC permutations with differential uniformity 6 for primes of the form \(4d+3\). For primes of the form \(4d+1\), we obtain a lower bound on the number of swapped EWC permutations with differential uniformity 4.

中文翻译：

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来自指数排列的一类新的微分 4-均匀排列

在本文中，我们研究了\({\mathbb {Z}}_{p-1}\)上两个位置交换的指数 Welch Costas (EWC) 排列的微分\(\delta \) -均匀性质，并构造了排列\(\delta = 4, 6\)对于不同的p值。我们计算\(4d+3\)形式的素数的具有微分均匀性 6 的交换 EWC 排列的数量。对于\(4d+1\)形式的素数，我们获得了具有微分均匀性 4 的交换 EWC 排列数量的下限。