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Mat. Vopr. Kriptogr., 2018, Volume 9, Issue 2, Pages 47–58 (Mi mvk252)  

The permutation group insight on the diffusion property of linear mappings

D. A. Burova, B. A. Pogorelovb

a TVP Laboratories, Moscow
b Academy of Cryptography of the Russian Federation, Moscow

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.

Key words: block cipher, linear mapping, wreath product, exponentiation, structures of permutation groups, metrics.

DOI: https://doi.org/10.4213/mvk252

Full text: PDF file (197 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.719.2
Received 05.II.2017
Language: English

Citation: D. A. Burov, B. A. Pogorelov, “The permutation group insight on the diffusion property of linear mappings”, Mat. Vopr. Kriptogr., 9:2 (2018), 47–58

Citation in format AMSBIB
\Bibitem{BurPog18}
\by D.~A.~Burov, B.~A.~Pogorelov
\paper The permutation group insight on the diffusion property of linear mappings
\jour Mat. Vopr. Kriptogr.
\yr 2018
\vol 9
\issue 2
\pages 47--58
\mathnet{http://mi.mathnet.ru/mvk252}
\crossref{https://doi.org/10.4213/mvk252}
\elib{http://elibrary.ru/item.asp?id=35276437}


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