Probabilistic properties of statistical dependencies between input and output of Markovian iterative cipher with round transformations on Abelian groups

We investigate the statistical dependencies between the input and output of an iterative cipher model, in which round keys are independent random variables, round transformations act on Abelian groups and depend on the round key and the round number. If the input and output of the cipher are uniformly distributed, then the statistical dependencies correspond the correlation coefficients between values of the characters. It is shown that for a cipher model with Markovian round mappings on Abelian groups the matrix of the second moments of the considered characteristics is equal to the product of the corresponding matrices constructed for round mappings. Upper and lower estimates for the expectations of absolute values of studied characteristics are obtained.