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JOURNALS // Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography] // Archive

Mat. Vopr. Kriptogr., 2025 Volume 16, Issue 1, Pages 5–28 (Mi mvk487)

Random equiprobable substitutions with labeled cycles. I

V. E. Viktorenkov

Academy of Cryptography of the Russian Federation, Moscow

Abstract: Random uniformly distributed substitution is considered. Its cycles are independently labeled with probabilities depending only on cycle length and the degree of substitution. The exact and limit distribution of the characteristics of the cyclic structure of labeled cycles are studied.

Key words: random substitution, probabilistic cycle labeling scheme, parametric model of substitutions of random degree, total variation distance, convergence to Poisson and normal distributions.

UDC: 519.212.2+519.12

Received 11.II.2025

DOI: 10.4213/mvk487



© Steklov Math. Inst. of RAS, 2025