
This article is cited in 2 scientific papers (total in 2 papers)
Methods of Signal Processing
Adaptive $\chi^2$ Criterion for Discrimination
of Near Hypotheses with a Large Number of Classes and Its Application to Some Cryptography
Problems
B. Ya. Ryabko^{}, V. S. Stognienko^{}, Yu. I. Shokin^{}
Abstract:
The main problem considered consists in testing the hypothesis $H_0$ that letters of an alphabet $A=\{a_1,a_2,…,a_k\}$ are generated with equal probabilities $\frac{1}{k}$ against the alternative complex hypothesis $H_1$, the negation of $H_0$. In many applications, in particular, those connected with cryptography, $k$ is large, but possible deviations from the uniform distribution are small. Therefore, application of Pearson's $\chi_2$ test, which is one of the most widespread and efficient tests, requires samples of a very large size, certainly exceeding $k$. We propose a socalled adaptive $\chi_2$ test, whose power can be considerably higher than that of the traditional method in the case described. This conclusion is based on the theoretical analysis of the proposed criterion for some classes of alternatives as well as on experimental results related to discriminating between enciphered Russian texts and random sequences.
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Problems of Information Transmission, 2003, 39:2, 207–215
Bibliographic databases:
UDC:
621.391.1:519.27 Received: 15.01.2002
Citation:
B. Ya. Ryabko, V. S. Stognienko, Yu. I. Shokin, “Adaptive $\chi^2$ Criterion for Discrimination
of Near Hypotheses with a Large Number of Classes and Its Application to Some Cryptography
Problems”, Probl. Peredachi Inf., 39:2 (2003), 53–62; Problems Inform. Transmission, 39:2 (2003), 207–215
Citation in format AMSBIB
\Bibitem{RyaStoSho03}
\by B.~Ya.~Ryabko, V.~S.~Stognienko, Yu.~I.~Shokin
\paper Adaptive $\chi^2$ Criterion for Discrimination
of Near Hypotheses with a Large Number of Classes and Its Application to Some Cryptography
Problems
\jour Probl. Peredachi Inf.
\yr 2003
\vol 39
\issue 2
\pages 5362
\mathnet{http://mi.mathnet.ru/ppi301}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=2105861}
\zmath{https://zbmath.org/?q=an:1130.62331}
\transl
\jour Problems Inform. Transmission
\yr 2003
\vol 39
\issue 2
\pages 207215
\crossref{https://doi.org/10.1023/A:1025104406075}
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http://mi.mathnet.ru/eng/ppi301 http://mi.mathnet.ru/eng/ppi/v39/i2/p53
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This publication is cited in the following articles:

B. Ya. Ryabko, A. I. Pestunov, ““Book Stack” as a New Statistical Test for Random Numbers”, Problems Inform. Transmission, 40:1 (2004), 66–71

B. Ya. Ryabko, V. A. Monarev, Yu. I. Shokin, “A New Type of Attacks on Block Ciphers”, Problems Inform. Transmission, 41:4 (2005), 385–394

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