On the diffusion of the Improved Generalized Feistel
Tsonka Stefanova Baicheva, Svetlana Topalova · Advances in Mathematics of Communications · 2020
We consider the Improved Generalized Feistel Structure (IGFS) suggested by Suzaki and Minematsu (LNCS, 2010). It is a generalization of the classical Feistel cipher. The message is divided into \begin{document}$ k $\end{document} subblocks, a Feistel transformation is applied to each pair of successive subblocks, and then a permutation of the subblocks follows. This permutation affects the diffusion property of the cipher. IGFS with relatively big \begin{document}$ k $\end{document} and good diffusion are of particular interest for light weight applications. Suzaki and Minematsu (LNCS, 2010) study the case when one and the same permutation is applied at each round, while we consider IGFS with possibly different permutations at the different rounds. In this case we present permutation sequences yielding IGFS with the best known by now diffusion for all even \begin{document}$ k\le 2048 $\end{document} . For \begin{document}$ k\le 16 $\end{document} they are found by a computer-aided search, while for \begin{document}$ 18\le k\le 2048 $\end{document} we first consider several recursive constructions of a permutation sequence for \begin{document}$ k $\end{document} subblocks from two permutation sequences for \begin{document}$ k_a2048 $\end{document} .