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

  • Boris A. Pogorelov and Marina A. Pudovkina EMAIL logo
Published/Copyright: August 16, 2018

Abstract

Groups which are most frequently used as key addition groups in iterative block ciphers include the regular permutation representation Vn+ of the group of vector key addition, the regular permutation representation Z2n+ of the additive group of the residue ring, and the regular permutation representation Z2n+1 of the multiplicative group of a prime field (in the case where 2n + 1 is a prime number). In this work we consider the extension of the group Gn generated by Vn+ and Z2n+ by means of transformations and groups which naturally arise in cryptographic applications. Examples of such transformations and groups are the groups Z2d+×Vnd+andVnd+×Z2d+ and pseudoinversion over the field GF(2n) or over the Galois ring GR(2md, 2m).


Originally published in Diskretnaya Matematika (2016) 28, №4, 100–121 (in Russian).


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Received: 2016-10-28
Published Online: 2018-08-16
Published in Print: 2018-08-28

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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