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Permutations with low differential uniformity, high algebraic degree, and high nonlinearity overF2    2  kcan be used as the substitution boxes for many block ciphers. In this paper, several classes of low differential uniformity permutations are constructed based on the method of choosing two permutations overF2    2  kto get the desired permutations. The resulted low differential uniformity permutations have high algebraic degrees and nonlinearities simultaneously, which provide more choices for the substitution boxes. Moreover, some numerical examples are provided to show the efficacy of the theoretical results.

mathematical problems in engineering

More Low Differential Uniformity Permutations over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>k</mml:mi></mml:math> Odd

More Low Differential Uniformity Permutations over F22k with k Odd