Abstract:
We give complete description of the set of n×n MDS-matrices, n>3, over GF(2t), t>1, with elements from the set {e,α,α2}, where e is an identity element, α≠0, e. It is proved that there are no such matrices if n⩾6. For n=4,5 the necessary and sufficient conditions of existence of MDS-matrices consisting of elements e,α,α2 are given.
Key words:
MDS-mapping, MDS-matrix.
Received 20.IV.2017
Bibliographic databases:
Document Type:
Article
UDC:519.719.2
Language: Russian
Citation:
A. V. Anashkin, “Complete description of a class of MDS-matrices over finite field of characteristic 2”, Mat. Vopr. Kriptogr., 8:4 (2017), 5–28
\Bibitem{Ana17}
\by A.~V.~Anashkin
\paper Complete description of a class of MDS-matrices over finite field of characteristic~2
\jour Mat. Vopr. Kriptogr.
\yr 2017
\vol 8
\issue 4
\pages 5--28
\mathnet{http://mi.mathnet.ru/mvk238}
\crossref{https://doi.org/10.4213/mvk238}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3770673}
\elib{https://elibrary.ru/item.asp?id=32641307}
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https://www.mathnet.ru/eng/mvk238
https://doi.org/10.4213/mvk238
https://www.mathnet.ru/eng/mvk/v8/i4/p5
This publication is cited in the following 4 articles:
Stanislav S. Malakhov, “On the circulant matrix MDS testing and the search for circulant MDS matrices”, Cryptogr. Commun., 2024
R. R. Aulet, R. A. de la Cruz Jiménes, “Construction of MDS matrices combining the Feistel, Misty and Lai-Massey schemes”, Matem. vopr. kriptogr., 12:2 (2021), 57–74
D. I. Trifonov, D. B. Fomin, “Ob invariantnykh podprostranstvakh v XSL-shifrakh”, PDM, 2021, no. 54, 58–76
M. I. Rozhkov, S. S. Malakhov, “Experimental methods for constructing MDS matrices of a special form”, J. Appl. Industr. Math., 13:2 (2019), 302–309
Citation in format AMSBIB
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