logo

SCIENCE CHINA Information Sciences, Volume 63 , Issue 10 : 209101(2020) https://doi.org/10.1007/s11432-018-9741-6

Permutation polynomials $x^{2^{k+1}+3}+ax^{2^k+2}+bx$ over $F_{2^{2k}}$ and their differential uniformity

More info
  • ReceivedSep 23, 2018
  • AcceptedJan 11, 2019
  • PublishedAug 25, 2020

Abstract

There is no abstract available for this article.


Acknowledgment

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).


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 CrossRef 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 CrossRef Google Scholar

[3] Peng J, Tan C H, Wang Q C. A new family of differentially 4-uniform permutations over $\mathbb{F}_{2^{2k}~}$ for odd k. Sci China Math, 2016, 59: 1221-1234 CrossRef ADS 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 CrossRef Google Scholar

[5] Qu L J, Tan Y, Tan C H. Constructing Differentially 4-Uniform Permutations Over ${F}_{2^{2k}}$ via the Switching Method. IEEE Trans Inform Theor, 2013, 59: 4675-4686 CrossRef 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 CrossRef Google Scholar

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

[8] Zha Z B, Hu L, Sun S W. Further results on differentially 4-uniform permutations over $\mathbb{F}_{2^{2m}~}~$. Sci China Math, 2015, 58: 1577-1588 CrossRef ADS arXiv 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 CrossRef Google Scholar

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号