Paper 2016/941

A New Class of Differentially 4-uniform Permutations from the Inverse Function

Jian Bai and Dingkang Wang

Abstract

Differentially 4-uniform permutations on $\mathbb{F}_{2^{2k}}$ with high nonlinearity and algebraic degree are often used in block ciphers and some stream ciphers as Substitution boxes. Recently,Chen et al.(An equivalent condition on the switching construction of differentially 4-uniform permutations on from the inverse function, International Journal of Computer Mathematics, DOI:10.1080/00207160.2016.1167884) presented a n equivalent condition on the switching construction. More precisely,they presented a sufficient and necessary condition on differentially 4-uniform permutations on $\mathbb{F}_{2^{2k}}$ of the form $G(x)=x^{-1}+f(x^{-1})$, where $f$ is a Boolean function. However, the number of the satisfied functions is so enormous that it is difficult to find all the functions. In this paper,a new class of such functions are constructed. These functions may provide more options for the design of Substitute boxes.