Abstract
We introduce a search algorithm to find permutation S-boxes with low differential uniformity, high nonlinearity and high algebraic degree, which play important roles in block ciphers. Inspired by the results of our search algorithm, we propose a method to calculate differential uniformity for permutations. We establish a sufficient condition for differentially 4-uniform permutations based on our method and construct some example classes of differentially 4-uniform permutations.
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Acknowledgements
We gratefully acknowledge the anonymous reviewers who read drafts and made many helpful suggestions. This work is supported by the National Natural Science Foundation of China under Grant No.U1603116.
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Communicated by C. Carlet.
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Shuai, L., Li, M. A method to calculate differential uniformity for permutations. Des. Codes Cryptogr. 86, 1553–1563 (2018). https://doi.org/10.1007/s10623-017-0412-y
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DOI: https://doi.org/10.1007/s10623-017-0412-y