Constructing Differentially 4 Uniform Permutations from Known Ones

Low differential uniformity functions provide good resistance to differential attacks. The AES (Advanced encryption standard) uses a differentially 4 uniform function (the inverse function) as its S-box. We give a further study of the inverse function in this paper. It is observed that after exchanging two values of a low differential uniformity function, its differential property still keeps good. Especially, for the inverse function over F₂ⁿ (n even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity 4 which are not CCZequivalent (Carlet Charpin-Zinoviev equivalent) to the inverse function on F₂ⁿ.