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Diskr. Mat., 2016, Volume 28, Issue 4, Pages 100–121 (Mi dm1396)  

On groups containing the additive group of the residue ring or the vector space

B. A. Pogorelova, M. A. Pudovkinab

a Academy of Cryptography of Russian Federation
b Bauman Moscow State Technical University

Abstract: Groups which are most frequently used as key addition groups in iterative block ciphers include the regular permutation representation $V_n^ + $ of the group of vector key addition, the regular permutation representation $\mathbb{Z}_{{2^n}}^ + $ of the additive group of the residue ring, and the regular permutation representation $\mathbb{Z}_{{2^n} + 1}^ \odot $ of the multiplicative group of a prime field (in the case where ${2^n} + 1$ is a prime number). In this work we consider the extension of the group ${G_n}$ generated by $V_n^ + $ and $\mathbb{Z}_{{2^n}}^ + $ by means of transformations and groups which naturally arise in cryptographic applications. Examples of such transformations and groups are the groups $\mathbb{Z}_{{2^d}}^ + \times V_{n - d}^ + $ and $V_{n - d}^ + \times \mathbb{Z}_{{2^d}}^ + $ and pseudoinversion over the field $GF({2^n})$ or over the Galois ring $GR({2^{md}}{,2^m})$.

Keywords: key addition group, additive regular group, wreath product of permutation groups, multiplicative group of the residue ring, Galois ring.

DOI: https://doi.org/10.4213/dm1396

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English version:
Discrete Mathematics and Applications, 2018, 28:4, 231–247

Bibliographic databases:

UDC: 512.541.4
Received: 28.10.2016

Citation: B. A. Pogorelov, M. A. Pudovkina, “On groups containing the additive group of the residue ring or the vector space”, Diskr. Mat., 28:4 (2016), 100–121; Discrete Math. Appl., 28:4 (2018), 231–247

Citation in format AMSBIB
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\paper On groups containing the additive group of the residue ring or the vector space
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\issue 4
\pages 100--121
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\jour Discrete Math. Appl.
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\vol 28
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