On properties of W-permutations over the residue ring

From the theory of Markov chains, it follows that the states of a Markov chain can be enlarged by a partition W of z_n if a number of conditions are satisfied for the blocks of this partition and the elements of the difference table of a permutation on z_n. However, using a modification of the differential attack, we require a condition for only one block W of the partition W. In this case, the permutations satisfying such a "softened" requirement for the block W are called W-permutations. Their properties are studied and described in this paper.

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