Difference equations, stationary and non-stationary discrete systems in block ciphers

In this article, for Markov ciphers, we prove that they are resistant to differential cryptanalysis and some statements made for MS are obtained. The upper estimates of the probabilities of integer differentials are significantly improved when compared to previously known results. Our differential cryptanalytic algorithm finds weak subkeys that have more than 80 bits and 128 bits for 128-bit keys.