Properties of the group generated by translation groups of the vector space and the residue ring
In this paper, we consider the additive group Z+n of the residue ring Z 2n, the additive group V+ of the vector space V n over the field GF(2), and subgroups of the group G n generated by Z+, V+. These groups are subgroups of the Sylow 2-subgroup of the symmetrical group S(Z 2n) and have common systems of imprimitivity. In cryptography, Z+, V+ are connected with groups generated by all key additions. We describe a permutation structure of subgroups of G n. We prove that the group of lower triangular (n x n)-matrices over GF(2) and the full affine group over Z 2n are subgroups of G n. We also describe properties of imprimitive subgroups of G n.
Keywords
ARX block cipher, additive group of the vector space, additive group of the residue ring, Sylow 2-subgroup, imprimitive group, wreath product, ARX-шифрсистема, аддитивная группа векторного пространства, аддитивная группа кольца вычетов, си-ловская 2-подгруппа, импримитивная группа, сплетение групп подстановокAuthors
| Name | Organization | |
| Pogorelov B.A. | Academy of Cryptography of the Russian Federation (Moscow) | |
| Pudovkina M. A. | National Research Nuclear University "Moscow Engineering Physics Institute" (Moscow) | maricap@rambler.ru |
References
Properties of the group generated by translation groups of the vector space and the residue ring | Applied Discrete Mathematics. Supplement. 2015. № 8.