Finding permutations with good cryptographic parameters is a good research topic about constructing a secure S-box in substitution-permutation networks. In particular constructing differentially 4-uniform permutations has made considerable progress in recent years. In this paper, we present new differentially 4-uniform permutations from the inverse function composed by disjoint cycles. Our new differentially 4-uniform permutations have high nonlinearity and low differential-linear uniformity. We give the differential spectrum and the extended Walsh spectrum of some of our differentially 4-uniform permutations, and then we can see that they are CCZ-inequivalent to some permutations whose differential spectrum and extended Walsh spectrum are known.

寻找具有良好密码参数的排列是在替代排列网络中构建安全 S-box 的一个很好的研究课题。特别是构建差分 4-均匀排列近年来取得了相当大的进展。在本文中，我们从由不相交循环组成的反函数中提出了新的差分 4-均匀排列。我们新的差分 4-均匀排列具有高非线性和低差分线性均匀性。我们给出了一些微分 4-均匀排列的微分谱和扩展沃尔什谱，然后我们可以看到它们与一些已知微分谱和扩展沃尔什谱的排列是 CCZ 不等价的。