Paper 2013/731

Constructing Differentially 4-uniform Permutations over GF(2^{2k}) from the Inverse Function Revisited

Yongqiang Li, Mingsheng Wang, and Yuyin Yu


Constructing S-boxes with low differential uniformity and high nonlinearity is of cardinal significance in cryptography. In the present paper, we show that numerous differentially 4-uniform permutations over GF(2^{2k}) can be constructed by composing the inverse function and cycles over GF(2^{2k}). Two sufficient conditions are given, which ensure that the differential uniformity of the corresponding compositions equals 4. A lower bound on nonlinearity is also given for permutations constructed with the method in the present paper. Moreover, up to CCZ-equivalence, a new differentially 4-uniform permutation with the best known nonlinearity over GF(2^{2k}) with $k$ odd is constructed. For some special cycles, necessary and sufficient conditions are given such that the corresponding compositions are differentially 4-uniform.

Available format(s)
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Contact author(s)
yongq lee @ gmail com
2013-11-13: received
Short URL
Creative Commons Attribution


      author = {Yongqiang Li and Mingsheng Wang and Yuyin Yu},
      title = {Constructing Differentially 4-uniform Permutations over GF(2^{2k}) from the Inverse Function Revisited},
      howpublished = {Cryptology ePrint Archive, Paper 2013/731},
      year = {2013},
      note = {\url{}},
      url = {}
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