Combinatorial properties of block symmetric ciphers key schedule

We investigate combinatorial properties of the block symmetric ciphers key schedule in the assumption that the cyclic (round) keys are generated randomly, with equal probability and independently of each other. The model of random homogeneous substitution is used for an abstract description of this formation. Analytical expressions allow us to estimate the power of implemented encryption-decryption maps set, obtain estimates of the probability properties of round keys sequences and ratios of the average number of different key sequences to power of different master keys set. The simulation results confirm the accuracy and validity of these analytical expressions.