On the power of tests of multidimensional discrete uniformity used for statistical analysis of random number generators

Authors

  • Valeriy A. Voloshko Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-9693-0688
  • Anton I. Trubey Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

power of a test, serial test, test of multidimensional discrete uniformity, contiguous alternatives, non-central chi-squared distribution, random number generator, Markov chain

Abstract

In this paper, we obtained the asymptotic power values for the statistical tests of multidimensional discrete uniformity under conditions of contiguous convergence of alternatives. Two versions of the test are considered, namely, with overlapping blocks (included in the NIST SP 800-22 test suit) and with non-overlapping blocks. The null hypothesis H0 is related to the so-called pure randomness of the observed sequence, i. e. independence and the same uniform distribution of its elements. An alternative H1 is assumed to be a Markov chain of some arbitrary fixed finite order.

Author Biographies

  • Valeriy A. Voloshko, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); head of the sector of computer data analysis

  • Anton I. Trubey, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    head of the laboratory of applied informatics

References

  1. Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, et al. A statistical test suite for random and pseudorandom number generators for cryptographic applications: NIST SP 800-22. Revision 1a [Internet]. Gaithersburg: National Institute of Standards and Technology; 2010 [cited 2021 September 20]. 131 p. Available from: https://csrc.nist.gov/publications/detail/sp/800-22/rev-1a/final.
  2. Trubey AI, Palukha VYu, Pirshtuk IK, Mal’tsev MV, Rashcheny NA. [A technique for testing random sequences based on statistical distance and the law of the iterated logarithm]. In: Problemy zashchity informatsii (s grifom «Sekretno»). Nomer 16 [Problems of information security (with the heading «Secret»). Number 16]. Minsk: Belarusian State University; 2020. p. 64–94. Russian.
  3. Amari S, Nagaoka H. Methods of information geometry. Harada D, translator. Providence: American Mathematical Society; 2000. 206 p. (Translations of mathematical monographs; volume 191). Co-published by the Oxford University Press.
  4. Billingsley P. Statistical methods in Markov chains. The Annals of Mathematical Statistics. 1961;32(1):12–40. DOI: 10.1214/aoms/1177705136.
  5. Hayashi M, Watanabe S. Information geometry approach to parameter estimation in Markov chains. The Annals of Statistics. 2016;44(4):1495–1535. DOI: 10.1214/15-AOS1420.
  6. Kharin YS, Petlitskii AI. [A Markov chain of order s with r partial connections and statistical inference on its parameters]. Diskretnaya matematika. 2007;19(2):109–130. Russian. DOI: 10.4213/dm26.
  7. Voloshko VA, Vecherko EV. New upper bounds for noncentral chi-square cdf. Journal of the Belarusian State University. Mathematics and Informatics. 2020;1:70–74. DOI: 10.33581/2520-6508-2020-1-70-74.

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Published

2022-03-30

Issue

No. 1 (2022): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Voloshko, .V.A. and Trubey, A.I. 2022. On the power of tests of multidimensional discrete uniformity used for statistical analysis of random number generators. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Mar. 2022), 26–37. DOI:https://doi.org/10.33581/2520-6508-2022-1-26-37.