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On a relationship between linear and differential characteristics of binary vector spaces mappings and diffusion characteristics over blocks of imprimitivity systems of translation group of the binary vector space

  • Dmitry A. Burov
Published/Copyright: July 13, 2024

Abstract

We examine relationships between the nonlinearity parameters of mappings f : VnVm of binary vector spaces Vn = GF(2)n, Vm = GF(2)m, diffusion properties of imprimitivity systems of the translation group Vn+ of space Vn, and also (for m = n and fS(Vn)) transitivity and primitivity properties of the groups 〈W+, f〉, where W+ is the translation group of the subspace W < Vn. It is shown that, in some methods of cryptoanalysis of block cipher algorithms, in fact, insufficient diffusion of blocks of the imprimitivity system of the group Vn+ is used.


Originally published in Diskretnaya Matematika (2023) 35, №1, 3–34 (in Russian).


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Received: 2022-08-29
Published Online: 2024-07-13
Published in Print: 2024-06-25

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 3.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/dma-2024-0011/html
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