Conference material: "Academician O.B. Lupanov XIV International Scientific Seminar "Discrete Mathematics and Its Applications" (20-25 June 2022, Moscow)"
On cardinality of image of correct families of Boolean functions
Abstract:
Finite quasigroups are a promising structure for realizing various cryptographic primitives. Table job quasigroup operation requires quadratic on the order of the quasigroup the amount of memory; as a consequence, when using quasigroups of large order, the problem of minimizing spatial complexity. One possible solution is to move from tabular assignment of an operation to a functional one. V.A. The bow was a construction based on proper families of functions and allowing one to define large parametric families of quasigroups big order. We have previously announced results on the power sets of quasigroups generated by a given regular family. It turned out that this power is completely determined by the power of the image correct family. In our work, we present a number of results on cardinalities of the image of regular families of Boolean functions.
