Two classes of differentially 4-uniform permutations over $ \mathbb{F}_{2^{n}} $ with $ n $ even

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 \begin{document}$ \mathbb{F}_{2^n}^* $\end{document} was given by Peng et al. in [ 15 ]. In this paper, we extend their results to differentially 4-uniform permutations whose values are different from the values of the inverse function on some subsets of the unit circle of \begin{document}$ \mathbb{F}_{2^n} $\end{document} or on the multiplication group of some subfield of \begin{document}$ \mathbb{F}_{2^n} $\end{document} . Moreover, it has been checked by the Magma software that some permutations in the resulted differentially 4-uniform permutations are CCZ-inequivalent to the known functions for small \begin{document}$ n $\end{document} .