Abstract
A set-theoretic approach to the analysis of statistically equivalent mappings of a finite set is elaborated. Some model problems are resolved, namely, the investigation of collisions of mappings, analysis of the computational security of a sequence of mappings provided that the number of arguments increases without bound and computation of the asymptotic computational security for this sequence of mappings, analysis of the structure of classes of statistically equivalent mappings, and analysis of conditions under which a mapping is statistically equivalent to its superposition with a given set of mappings.
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