A. K. Vishnevsky, O. A. Finko

Substitution is a unique reflection of a finite set on itself. At corresponding numbering (or ordering) of elements of a finite set on which substitution is possible certain, it can be reduced to substitution on some finite subset of natural numbers. The Function of substitution is used in the majority of modern block codes, therefore it is meaningful to consider features of its numerical realization. It is shown that the system of substitutions can be presented by the system Boolean functions. The algorithm of construction of a modular numerical polynomial of systems of substitutions is offered. For presentation the example of values of substitutions, factors and the module of numerical substitutions in a hexadecimal notation are is resulted. Features of realization of systems of substitutions by modular numerical polynomials on an example of substitutions of the cipher GOST 28.147-89 are considered. It is shown that the top border of complexity of realization by modular numerical polynomials of systems of substitutions is much less than for systems of any Boollean functions for the same number of variables.