Adapted spectral-differential method for construction of differentially 4-uniform piecewise-linear permutations, orthomorphisms, and involutions of the field F2n $\mathbb{F}_{2^{n}}$
Andrey V. Menyachikhin · Discrete Mathematics and Applications · 2025
Abstract We propose a method to construct permutations of the field F 2 n $\mathbb{F}_{2^{n}}$ with low value of the Δ -uniformity such that their restrictions to the cosets of the group F 2 n × $\mathbb{F}^{\times}_{2^{n}}$ by some of its subgroup H are linear. Using the proposed method, we construct a large number of new CCZ-nonequivalent differentially 4-uniform permutations, orthomorphisms, and involutions over the field F 2 n $\mathbb{F}_{2^{n}}$ with n = 6, 8.