Permutations over 22kF with low differential uniformity, high algebraic degree and high nonlinearity are of great cryptographicimportance since they can be chosen as the S-boxes for many block ciphers with substitution permutation network structure. In this paper, new permutations with differential uniformity 4 are constructed by choosing two functions different from the inverse function defined on subfields of 2nF. Some other cryptographic properties, such as algebraic degree, walsh spectrum of the constructed functions are also studied. Inaddition, CCZ inequivalence relation with some known functions is discussed.
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