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This article is cited in 9 scientific papers (total in 10 papers)
On the matrices of transitions of differences for some modular groups
M. M. Glukhov Academy of Cryptography of the Russian Federation, Moscow
Abstract:
Let $G_t$ be a translation group in a direct sum of groups $(Z/2^t,+)$. For the system of substitutions $G_rhG_s$ of order $2^n$ the matrices of digram transitions are investigated. A well-known hypothesis on the nonexistence of APN-substitutions of the field $GF(2^n)$ for even $n$ is partly verified. Some methods of construction of differentially $4$-uniform substitutions are suggested.
Key words:
modular group, difference characteristics, systems of substitutions, APN-functions.
Received 22.IV.2013
Citation:
M. M. Glukhov, “On the matrices of transitions of differences for some modular groups”, Mat. Vopr. Kriptogr., 4:4 (2013), 27–47
Linking options:
https://www.mathnet.ru/eng/mvk98https://doi.org/10.4213/mvk98 https://www.mathnet.ru/eng/mvk/v4/i4/p27
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Abstract page: | 577 | Full-text PDF : | 311 | References: | 78 | First page: | 3 |
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