Paper 2016/941

A New Class of Differentially 4-uniform Permutations from the Inverse Function

Jian Bai and Dingkang Wang


Differentially 4-uniform permutations on $\mathbb{F}_{2^{2k}}$ with high nonlinearity and algebraic degree are often used in block ciphers and some stream ciphers as Substitution boxes. Recently,Chen et al.(An equivalent condition on the switching construction of differentially 4-uniform permutations on from the inverse function, International Journal of Computer Mathematics, DOI:10.1080/00207160.2016.1167884) presented a n equivalent condition on the switching construction. More precisely,they presented a sufficient and necessary condition on differentially 4-uniform permutations on $\mathbb{F}_{2^{2k}}$ of the form $G(x)=x^{-1}+f(x^{-1})$, where $f$ is a Boolean function. However, the number of the satisfied functions is so enormous that it is difficult to find all the functions. In this paper,a new class of such functions are constructed. These functions may provide more options for the design of Substitute boxes.

Available format(s)
Publication info
Differentially 4-uniform permutationSubstitute box4-Uniform BFIPreferred Boolean function
Contact author(s)
baijian @ amss ac cn
2016-10-01: received
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Creative Commons Attribution


      author = {Jian Bai and Dingkang Wang},
      title = {A New Class of Differentially 4-uniform Permutations from the Inverse Function},
      howpublished = {Cryptology ePrint Archive, Paper 2016/941},
      year = {2016},
      note = {\url{}},
      url = {}
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