The permutation group insight on the diffusion property of linear mappings

We investigate the properties of linear mappings related to the structures of the group generated by S-box layer and the group of key addition layer, i. e. the translation group of a vector space. We propose new parameters characterizing the diffusion properties of linear mapping. A new characterization of MDS linear mappings is given. MDS linear mappings that have arisen to provide the security with respect to the differential and linear methods, as well as other components of the round transformation, may be synthesized on the base of the permutation groups theory.