On the diffusion of the Improved Generalized Feistel
| Autor: | Tsonka Baicheva, Svetlana Topalova |
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| Rok vydání: | 2022 |
| Předmět: |
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Algebra and Number Theory Computer Networks and Communications Generalization Applied Mathematics Structure (category theory) Feistel cipher 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Microbiology Transformation (music) Combinatorics Permutation Cipher 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Diffusion (business) Mathematics |
| Zdroj: | Advances in Mathematics of Communications. 16:95 |
| ISSN: | 1930-5338 1930-5346 |
| DOI: | 10.3934/amc.2020102 |
| Popis: | 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_a< k $\end{document} and \begin{document}$ k_b< k $\end{document} subblocks respectively. Using computer, we apply these constructions to obtain permutation sequences with good diffusion for each even \begin{document}$ k\le 2048 $\end{document}. Finally we obtain infinite families of permutation sequences for \begin{document}$ k>2048 $\end{document}. |
| Databáze: | OpenAIRE |
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