Geodesic
Criteria for testing the hypothesis on a noisy functional dependency between random binary vectors and bits
Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 55-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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A sequence of random independent and uniformly distributed binary vectors $\vec x(t)$ and a sequence of random independent bits $y(t)$ are observed. Hypothesis $H_1\colon \{\vec x(t),y(t)$ are independent$\}$ is tested against $H_2\colon\{y(t)$ is corrupted value of $f(\vec x(t))\}$, the function $f$ essentially depends on an unknown part of the variables. We construct criteria based on sets of spectral statistics in situations of unknown $f$ or known $f$, and give asymptotic estimates of the volume of the size of the sample. 
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O. V. Denisov. Criteria for testing the hypothesis on a noisy functional dependency between random binary vectors and bits. Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 55-76. http://geodesic.mathdoc.fr/item/MVK_2022_13_3_a3/

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