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Probl. Peredachi Inf., 2003, Volume 39, Issue 2, Pages 53–62 (Mi ppi301)  

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 wide-spread and efficient tests, requires samples of a very large size, certainly exceeding $k$. We propose a so-called 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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English version:
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 53--62
\mathnet{http://mi.mathnet.ru/ppi301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2105861}
\zmath{https://zbmath.org/?q=an:1130.62331}
\transl
\jour Problems Inform. Transmission
\yr 2003
\vol 39
\issue 2
\pages 207--215
\crossref{https://doi.org/10.1023/A:1025104406075}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. Ya. Ryabko, A. I. Pestunov, ““Book Stack” as a New Statistical Test for Random Numbers”, Problems Inform. Transmission, 40:1 (2004), 66–71  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath
  • Проблемы передачи информации Problems of Information Transmission
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