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A new family of differentially 4-uniform permutations over \(\mathbb{F}_{2^{2k} }\) for odd k

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Abstract

We study the differential uniformity of a class of permutations over \(\mathbb{F}_{2^n } \) with n even. These permutations are different from the inverse function as the values x −1 are modified to be (γx)− on some cosets of a fixed subgroup 〈γ〉 of \(\mathbb{F}_{2^n }^* \). 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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Jie Peng

  2. Shanghai Key Laboratory of Intelligent Information Processing, Shanghai, 200433, China

    Jie Peng

  3. Temasek Laboratories, National University of Singapore, Singapore, 117411, Singapore

    Chik How Tan & QiChun Wang

Authors
  1. Jie Peng
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  2. Chik How Tan
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  3. QiChun Wang
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Correspondence to Jie Peng.

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Peng, J., Tan, C.H. & Wang, Q. A new family of differentially 4-uniform permutations over \(\mathbb{F}_{2^{2k} }\) for odd k . Sci. China Math. 59, 1221–1234 (2016). https://doi.org/10.1007/s11425-016-5122-9

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  • DOI: https://doi.org/10.1007/s11425-016-5122-9

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