The results of studies of the properties of random substitutions are summarized. It is shown that random substitutions have overwhelmingly good cryptographic and, in particular, algebraic properties. It is shown that the deterioration of the differential and linear indices of the known block cipher designs (SPN ciphers will be discussed here) when using random substitutions can be offset by the use of a cycle function design with controlled substitutions. An advanced design for constructing such a cycle function is proposed, which allows to increase the minimum number of activated S-blocks on the first cycles of ciphers in comparison with the known structures that implement the wide-trace strategy. The prospect of using random S-blocks for the construction of block symmetric ciphers with improved dynamic parameters of arrival to random substitution is substantiated. A refined random substitution model and the corresponding criteria are proposed; by which it is possible to check the suitability of substitutions generated randomly for use in modern cipher designs. It is a test, since it is very likely that the tested substitutions will be suitable.