Implementation of a nonlinear transformation of a substitution in the form of elements of a numbering system of a number of factorial sets

Abstract

The paper investigates a nonlinear substitution transformation, presented as an element of the number system of factorial sets. This approach takes into account the characteristic features of substitutions and al-lows you to minimize the amount of memory for storing. Based on the unambiguous numbering approach for substitutions, three methods of storing in memory are considered: in the form of a vector, in the form of values of cyclic shifts of elements of an identical substitution, and in the form of a decimal substitution number. The results of the analysis of the amount of data required for storing the nonlinear substitution transformation for cryptographic primitives are presented. The complexity of translating the transformed substitutions into the standard form of storage by a vector is determined. The obtained results can be ap-plied in software solutions for ensuring information security using cryptographic primitives containing a nonlinear substitution transformation. The proposed approach to writing in the form of substitution trans-formations is recommended for implementation in complexes with a limited amount of memory.

Keywords

• cryptographic primitives, nonlinear substitution transformation, number system of a number of factorial sets.