from the inverse function
References
- W. Bosma, J. Cannon, and C. Playoust, The magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), pp. 235–265. doi: 10.1006/jsco.1996.0125
- C. Bracken and G. Leander, A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree, Finite Fields Appl. 16(4) (2010), pp. 231–242. doi: 10.1016/j.ffa.2010.03.001
- C. Bracken, C.H. Tan, and Y. Tan, Binomial differentially 4-uniform permutations with high nonlinearity, Finite Fields Appl. 18(3) (2012), pp. 537–546. doi: 10.1016/j.ffa.2011.11.006
- C. Carlet, On known and new differentially uniform functions, Information Security Privacy 6812 (2011), pp. 1–15.
- C. Carlet, More constructions of APN and differentially 4-uniform functions by concatenation, Sci. China 56(7) (2013), pp. 1373–1384. doi: 10.1007/s11425-013-4647-4
- P. Charpin and G.M. Kyureghyan, On a Class of Permutation Polynomials Over F2n, Sequences and Their Applications-SETA 5203 (2008), pp. 368–376.
- Y. Edel and A. Pott, A new almost perfect nonlinear function which is not quadratic, Adv. Math. Commun. 3(1) (2009), pp. 59–81. doi: 10.3934/amc.2009.3.59
- G. Lachaud and J. Wolfmann, The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. Inf. Theory 36(3) (1990), pp. 686–692. doi: 10.1109/18.54892
- Y.Q. Li, M.S. Wang, and Y.Y. Yu, Constructing differentially 4-uniform permutations over F22k from the inverse function revisited, https://eprint.iacr.org/2013/731.pdf.
- R. Lidl and H. Niederreiter, Finite fields, Encyclopedia Math. Appl. 20 (1997).
- L.J. Qu, Y. Tan, C. Tan, and C. Li, Constructing differentially 4-uniform permutations over F22k via the switching method, IEEE Trans. Inform. Theory 59(7) (2013), pp. 4675–4686. doi: 10.1109/TIT.2013.2252420
- L.J. Qu, Y. Tan, C. Li, and G. Gong, More constructions of differentially 4-uniform permutations on F22k, Des. Codes Cryptogr. Design Code Cryptogr. 78(2) (2016), pp. 391–408.
- D. Tang, C. Carlet, and X.H. Tang, Differentially 4-uniform bijections by permuting the inverse function, Des. Codes Cryptogr. Design Code Cryptogr. 77(1) (2015), pp. 117–141. doi: 10.1007/s10623-014-9992-y
- Y.Y. Yu, M.S. Wang, and Y.Q. Li, Constructing differential 4-uniform permutations from know ones, Chinese J. Electron. 22(3) (2013), pp. 495–499.
- Z. Zha, L. Hu, and S. Sun, Constructing new differentially 4-uniform permutations from the inverse function, Finite Fields Appl 25 (2014), pp. 64–78. doi: 10.1016/j.ffa.2013.08.003