… inverse function on \(\mathbb {F}_{2^{8}}\), which has been proved to be a differentially 4-uniform
permutation … Recently, Zha et al. proposed two constructions of differentially 4-uniform …

… f is a Boolean function. They proved that G is a differentially 4uniform permutation over F22k
if … Carlet and XH Tang, Differentially 4-Uniform Bijections by Permuting the Inverse Function. …

… involutions constructed by composing the inverse function and cycles with length 3 are also
… cipher uses a differentially 4-uniform permutation, the multiplicative inverse function over \(\…

… We define the compositional inverse function G of an (n, n)-permutation F as G ◦ F = F ◦ G
= id, where id is the identity mapping on F2n . It has been shown that G and F are CCZ-…

… from differentially 4-uniform permutation. In this paper, we examine all (to the best of our
knowledge) the differentially 4-uniform … to the Inverse function. In the following, we list the known …

… functions are called almost perfect nonlinear (APN) functions. … permutation in even dimension,
constructions of differentially \(… Note that for the multiplicative inverse function \(x^{-1}\), we …

… block cipher uses a differentially 4-uniform permutation, namely the inverse function over F28
as S-… permutations with optimal algebraic degree from the inverse function by applying the …

… by permuting the inverse function, which could produce a large number of differentially 4-uniform …
In Sect.3 we give the new method to construct differentially 4-uniform permutations. We …

… when used in block ciphers of the Substitution-Permutation-Network (SPN) structure such as
the … ) are EA-equivalent Inverse functions, we give explicitly differentially 4-uniform (n, n − 1)-…

… 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 F 2 2 …