Two classes of differentially 4-uniform permutations over $ \mathbb{F}_{2^{n}} $ with $ n $ even
Guangkui Xu, Longjiang Qu · Advances in Mathematics of Communications · 2019
A construction of differentially 4-uniform permutations by modifying the values of the inverse function on a union of some cosets of a multiplication subgroup of $ \mathbb{F}_{2^n}^* $ was given by Peng et al. in [15]. In this paper, we extend their results to differentially 4-uniform permutations whose values are different from the values of the inverse function on some subsets of the unit circle of $ \mathbb{F}_{2^n} $ or on the multiplication group of some subfield of $ \mathbb{F}_{2^n} $. Moreover, it has been checked by the Magma software that some permutations in the resulted differentially 4-uniform permutations are CCZ-inequivalent to the known functions for small $ n $.