On groups generated by mixed type permutations and key addition groups

Three groups are often used as key addition groups in iterated block ciphers: V+, Z+ and Zfn₊₁. They are the regular permutation representations, respectively, of the group of vector key addition, of the additive group of the residue ring Z₂n, and of the multiplicative group of the residue ring Z₂n₊₁, where 2 +1 is a prime number. In this paper, we describe some properties of the extensions of the group G_n = (V+, Z+) by transformations and groups related to cryptographic applications. The groups Z+_d x V+__d, V+__d x Z+_d and a pseudoinverse permutation of the field GF(2) or the Galois ring GR(2, 2) are examples of such groups and transformations.

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