Constructing Differentially 4-Uniform Permutations over GF (22k) from the Inverse Function Revisited

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Provided by: International Association for Cryptologic Research
Topic: Security
Format: PDF
Constructing the S-boxes with low differential uniformity and high non-linearity is of cardinal significance in cryptography. In this paper, the authors show that numerous differentially 4-uniform permutations over F22k can be constructed by composing the inverse function and cycles over F22k. Two sufficient conditions are given, which ensure that the differential uniformity of the corresponding compositions equals 4. A lower bound on non-linearity is also given for permutations constructed with the method in this paper.
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