New Differentially 4-Uniform Piecewise Permutations over F22k from the Inverse Function
Shuai Li, Li Miao · Symmetry · 2023
Permutations with low differential uniformity, high nonlinearity and high algebraic degree over F22k are preferred substitution boxes in modern block ciphers. In this paper, we study the bijectivity and the difference uniformity of piecewise function with the help of permutation group theory. Based on our results, We found many at least differentially 6-uniform and differentially 4-uniform permutations over F22k, which can be chosen as the substitution boxes.