A new family of differentially 4-uniform permutations over F_（2~（2k）） for odd k

We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values x~（-1） are modified to be（γx）~（-1） on some cosets of a fixed subgroup γ of F_（2n）~＊. We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent（CCZ-equivalent） classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.