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Several classes of polynomials with low differential uniformity over finite fields of odd characteristic

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Abstract

In this paper, two infinite classes of quadratic differentially p-uniform binomials over \(\mathbb {F}_{p^n}\) (n is divisible by 4 or 3) are constructed from known perfect nonlinear binomials. In particular, for \(p=3\), such functions are ternary differentially 3-uniform functions which are not CCZ-equivalent to known ones. In addition, two classes of permutation monomials with low differential uniformity over finite fields of odd characteristic are also provided.

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Acknowledgments

The authors are grateful to the anonymous referees for their helpful comments and suggestions. This research is supported by NNSF Grant of China (11371011, 61403157) and Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (No. KJ2015A256).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Guangkui Xu, Xiwang Cao & Shanding Xu

  2. Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China

    Guangkui Xu

  3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xiwang Cao

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  1. Guangkui Xu
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  2. Xiwang Cao
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  3. Shanding Xu
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Correspondence to Guangkui Xu.

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Xu, G., Cao, X. & Xu, S. Several classes of polynomials with low differential uniformity over finite fields of odd characteristic. AAECC 27, 91–103 (2016). https://doi.org/10.1007/s00200-015-0272-5

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  • DOI: https://doi.org/10.1007/s00200-015-0272-5

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