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More permutation polynomials with differential uniformity six

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References

  1. Biham E, Shamir A. Differential cryptanalysis of DESlike cryptosystems. J Cryptol, 1991, 4: 3–72

    Article  MATH  Google Scholar 

  2. Browning K, Dillon J, Kibler R, et al. APN polynomials and related codes. J Combin Inf Syst Sci, 2009, 34: 135–159

    MATH  Google Scholar 

  3. Browning K, Dillon J, McQuistan M, et al. An APN permutation in dimension six. In: Proceedings of the 9th Conference on Finite Fields and Applications FQ9, Dublin, 2010. 33–42

    MATH  Google Scholar 

  4. Bracken C, Leander G. A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree. Finite Fields Their Appl, 2010, 16: 231–242

    Article  MathSciNet  MATH  Google Scholar 

  5. Daemen J, Rijmen V. The design of rijndael. In: AES-The Advanced Encryption Standard. Berlin: Springer-Verlag, 2002. 221–227

    Google Scholar 

  6. Blondeau C, Canteaut A, Charpin P. Differential properties of \(x \mapsto {x^{{2^t} - 1}}\). IEEE Trans Inf Theory, 2011, 57: 8127–8137

    Article  MATH  Google Scholar 

  7. Blondeau C, Perrin L. More differentially 6-uniform power functions. Designs Codes Cryptogr, 2014, 73: 487–505

    Article  MathSciNet  MATH  Google Scholar 

  8. Cao X, Hu L, Zha Z. Constructing permutation polynomials from piecewise permutations. Finite Fields Their Appl, 2014, 26: 162–174

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11401172, 61672212, 61370220).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471003, China

    Ziran Tu

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Xiangyong Zeng

  3. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471003, China

    Zhiyong Zhang

Authors
  1. Ziran Tu
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  2. Xiangyong Zeng
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  3. Zhiyong Zhang
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Corresponding author

Correspondence to Xiangyong Zeng.

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The authors declare that they have no conflict of interest.

Supporting information Appendix A. The supporting information is available online at info.scichina. com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

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Tu, Z., Zeng, X. & Zhang, Z. More permutation polynomials with differential uniformity six. Sci. China Inf. Sci. 61, 038104 (2018). https://doi.org/10.1007/s11432-017-9118-5

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