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Permutation polynomials \({x^{{2^{k + 1}} + 3}} + a{x^{{2^k} + 2}} + bx\) over \({F_{{2^{2k}}}}\) and their differential uniformity

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References

  1. Peng J, Tan C H. New explicit constructions of differentially 4-uniform permutations via special partitions of \({F_{{2^{2k}}}}\). Finite Fields Their Appl, 2016, 40: 73–89

    Article  MathSciNet  Google Scholar 

  2. Peng J, Tan C H. New differentially 4-uniform permutations by modifying the inverse function on subfields. Cryptogr Commun, 2017, 9: 363–378

    Article  MathSciNet  Google Scholar 

  3. Peng J, Tan C H, Wang Q C. A new family of differentially 4-uniform permutations over \(\mathbb{_{{2^{2k}}}}\) for odd k. Sci China Math, 2016, 59: 1221–1234

    Article  MathSciNet  Google Scholar 

  4. Peng J, Tan C H, Wang Q C. New secondary constructions of differentially 4-uniform permutations over. Int J Comput Math, 2017, 94: 1670–1693

    Article  MathSciNet  Google Scholar 

  5. Qu L J, Tan Y, Tan C H, et al. Constructing differentially 4-uniform permutations over \({F_{{2^{2k}}}}\) via the switching method. IEEE Trans Inform Theor, 2013, 59: 4675–4686

    Article  Google Scholar 

  6. Tang D, Carlet C, Tang X. Differentially 4-uniform bijections by permuting the inverse function. Des Codes Cryptogr, 2015, 77: 117–141

    Article  MathSciNet  Google Scholar 

  7. Tu Z, Zeng X, Zhang Z. More permutation polynomials with differential uniformity six. Sci China Inf Sci, 2018, 61: 038104

    Article  Google Scholar 

  8. Zha Z B, Hu L, Sun S W, et al. Further results on differentially 4-uniform permutations over \(\mathbb{_{{2^{2m}}}}\). Sci China Math, 2015, 58: 1577–1588

    Article  MathSciNet  Google Scholar 

  9. Xiong M, Yan H, Yuan P. On a conjecture of differentially 8-uniform power functions. Des Codes Cryptogr, 2018, 86: 1601–1621

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61672166, 11701488), Shanghai Excellent Academic Leader (Grant No. 16XD1400200), Shanghai Innovation Plan of Science & Technology (Grant No. 16JC1402700), and Scientific Research Fund of Hunan Provincial Education Department (Grant No. 17B040).

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China

    Jie Peng

  2. School of Mathematics and Physics, University of South China, Hengyang, 421001, China

    Lijing Zheng

  3. Department of Mathematics, Lianyungang Normal University, Lianyungang, 222006, China

    Chunsheng Wu

  4. Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, 200433, China

    Haibin Kan

  5. Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Shanghai Blockchain Engineering Research Center, Shanghai, 200433, China

    Haibin Kan

  6. Shanghai Institute for Advanced Communication and Data Science, Shanghai, 200433, China

    Haibin Kan

  7. Shanghai Institute of Intelligent Electronics & Systems, Shanghai, 200433, China

    Haibin Kan

Authors
  1. Jie Peng
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  2. Lijing Zheng
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  3. Chunsheng Wu
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  4. Haibin Kan
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Correspondence to Haibin Kan.

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Peng, J., Zheng, L., Wu, C. et al. Permutation polynomials \({x^{{2^{k + 1}} + 3}} + a{x^{{2^k} + 2}} + bx\) over \({F_{{2^{2k}}}}\) and their differential uniformity. Sci. China Inf. Sci. 63, 209101 (2020). https://doi.org/10.1007/s11432-018-9741-6

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  • DOI: https://doi.org/10.1007/s11432-018-9741-6

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