Diffusion properties of XSLP-ciphers

We obtain an exact lower estimate for the number of local permutations in XSLP-cipher with an arbitrary number of rounds. The sum of linear probabilistic relations of these permutations forms the linear probabilistic relation connecting the bits of the plain text and that of the cipher text. In the considered ciphers the matrices $L$ of linear transformations are block-diagonal with maximally diffusive blocks and permutations $P$ are uniformly diffusive.