The permutation group insight on the diffusion property of linear mappings

Abstract

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.

Implementation of a nonlinear transformation of a substitution in the form of elements of a numbering system of a number of factorial sets

“…Алгоритмы блочного шифрования могут строиться при помощи различных структур, таких как SP-сети, сети Фейстеля, схемы Лая-Мэсси и др., однако все данные подходы состоят из различных преобразований, часто схожих друг с другом [1][2][3]. Все данные преобразования можно рассматривать как линейные и нелинейные преобразования.…”

Construction of orthomorphic $\mathrm{MDS}$ matrices with primitive characteristic polynomial

“…Although, several articles published by D. A. Burov, B. A. Pogorelov and M. A. Pudovkina are devoted to the question on the influence of the linear mapping reducibility on the security of block ciphers [7,8,[13][14][15], in this work we continued the research started in [16], considering the problem of constructing a special kind of linear mappings with primitive characteristic polynomial and acceptable implementation cost having the additional advantages such as no non-zero fixed points and better resistance against the so-called invariant subspaces attacks.…”