On the Diffusion Property of Iterated Functions

For vectorial Boolean functions, the behavior of iteration has consequence in the diffusion property of the system. We present a study on the diffusion property of iterated vectorial Boolean functions. The measure that will be of main interest here is the notion of the degree of completeness, which has been suggested by the NESSIE project. We provide the first (to the best of our knowledge) two constructions of (n, n)-functions having perfect diffusion property and optimal algebraic degree. We also obtain the complete enumeration results for the constructed functions.