Abstract:
This paper is concerned with images of cosets in the direct product of groups by bijective mappings from factors to groups. We prove necessary and sufficient conditions on bijective mappings for existence a coset in the direct product of two groups whose image is a coset. Under some constraints on bijective mappings, we describe the cosets in the direct product of groups, whose images by bijective mappings from factors to groups are cosets, We described the cosets in the direct product of elementary abelian 2-groups whose images by the inversion permutation of nonzero elements of a finite field on factors are cosets. We also describe the similar cosets for the permutation used an an $s$-box of Kuznyechik algorithm, Under some constraints on bijective mappings, we describe the automorphisms of the direct product groups which commute with bijective mappings from factors to groups.
Keywords:
invariant coset attack, self-similiarity attack, $s$-box layer, inversion permutation of nonzero elements of a finite field, Kuznyechik algorithm.
Citation:
D. A. Burov, “On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets”, Diskr. Mat., 35:4 (2023), 18–45; Discrete Math. Appl., 35:2 (2025), 63–83
\Bibitem{Bur23}
\by D.~A.~Burov
\paper On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
\jour Diskr. Mat.
\yr 2023
\vol 35
\issue 4
\pages 18--45
\mathnet{http://mi.mathnet.ru/dm1772}
\crossref{https://doi.org/10.4213/dm1772}
\transl
\jour Discrete Math. Appl.
\yr 2025
\vol 35
\issue 2
\pages 63--83
\crossref{https://doi.org/10.1515/dma-2025-0004}
Linking options:
https://www.mathnet.ru/eng/dm1772
https://doi.org/10.4213/dm1772
https://www.mathnet.ru/eng/dm/v35/i4/p18
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