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Title:
Constructing differential 4-uniform permutations from know ones
Authors: Yuyin Yu, Mingsheng Wang, Yongqiang Li
Abstract:It is observed that exchanging two values of a function over {\mathbb F}_{2^n}, its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential 4-uniform over {\mathbb F}_{2^6} whose number of the pairs of input and output differences with differential 4-uniform is 54, less than 63, which provides a solution for an open problem proposed by Berger et al. \cite{ber}. Moreover, for the inverse function over \mathbb{F}_{2^n} (n even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity 4 which are CCZ-inequivalent to the inverse function on \mathbb{F}_{2^n}.
ePrint: https://eprint.iacr.org/2011/047
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