Towards the Structure of a Class of Permutation Matrices Associated With Bent Functions

Bent functions, that are useful in cryptographic applications, can be characterized in different ways. A recently formulated characterization is in terms of the Gibbs dyadic derivative. This characterization can be interpreted through permutation matrices associated with bent functions by this differential operator. We point out that these permutation matrices express some characteristic block structure and discuss a possible determination of it as a set of rules that should be satisfied by the corresponding submatrices. We believe that a further study of this structure can bring interesting results providing a deeper insight into features of bent functions.