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

Mat. Vopr. Kriptogr., 2020 Volume 11, Issue 4, Pages 77–96 (Mi mvk340)

This article is cited in 1 paper

Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions

V. A. Kopytcev

Academy of Cryptography of the Russian Federation, Moscow

Abstract: For a given subset $B$ of linear space $K^T$ over the field $K=GF(2)$ we study the distribution of the number $\xi$ of solutions of the system formed by inclusions $A_1x+A_2f(x)\in B$, $ x\in K^n\backslash \{0^n\}$, where $A_1$ and $A_2$ are random $T\times n$ and $T\times m$ matrices over $K$ with independend elements and $f(x)=$ $(f_1 (x),\ldots,f_m (x))\colon K^{n}\longrightarrow K^{m}$ is a given nonlinear mapping. Sufficient conditions for the convergence of distribution of $\xi$ to the standard normal distribution are obtained.

Key words: random inclusions, number of solutions, asymptotic normality.

UDC: 519.212.2+514.214

Received 12.II.2020

DOI: 10.4213/mvk340



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