Boolean Function Representation of S-Boxes and Boolean Permutations

Abstract

S-boxes are often the core nonlinear component in many encryption algorithms. By using vector Boolean functions to represent S-boxes, cryptographic properties as well as constructions can be made possible. This chapter studies the S-boxes by the view of vector Boolean functions, with focus being on Boolean permutations, which are a special class of vector Boolean functions. Properties and constructions of Boolean permutations are studied; computation of inverses of Boolean functions is also studied. The concept of one-way trapdoor Boolean permutation is proposed. Construction of Boolean permutations using function composition is studied which enables the construction of one-way trapdoor Boolean permutations.