Constructing differentially 4-uniform involutions over [formula omitted] by using Carlitz form

Abstract

Differentially 4-uniform involutions on F22k play important roles in the design of substitution boxes (S-boxes). Despite the active researches on differentially 4-uniform permutation, there is not so much research on differentially 4-uniform involutions, especially over the field F2n with 4|n. In this paper, we introduce a new approach to construct differentially 4-uniform involutions by using Carlitz form. With this approach, we explicitly construct two new classes of differentially 4-uniform involutions over F2n with 4|n. We also show that our constructions have high nonlinearity and optimal algebraic degree. With the help of computer, we show that our constructions are CCZ-inequivalent to the known differentially 4-uniform involutions over F28.