Startseite The limit joint distributions of statistics of four tests of the NIST package
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

The limit joint distributions of statistics of four tests of the NIST package

  • Maksim P. Savelov EMAIL logo
Veröffentlicht/Copyright: 24. Februar 2023
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

For sequences of independent random variables having a Bernoulli distribution with parameter p the limit joint distribution of statistics of four tests of the NIST statistical package (« Monobit Test », « Frequency Test within a Block », « Runs Test » and a generalization of « Non-overlapping Template Matching Test ») is obtained. Conditions of asymptotic uncorrelatedness and/or asymptotic independence of these statistics are given.


Note

Originally published in Diskretnaya Matematika (2021) 33, №4, 141–154 (in Russian).


Acknowledgment

The author is grateful to A. M. Zubkov for constant attention.

References

[1] Rukhin A., Soto J., Nechvatal J., Smid M., Barker E., Leigh S., Levenson M., Vangel M., Banks D., Heckert A., Dray J., Vo S., “A statistical test suite for the validation of random number generators and pseudo random number generators for cryptographic applications”, NIST Special Publication 800-22 Revision 1a, 27 April 2010.10.6028/NIST.SP.800-22r1aSuche in Google Scholar

[2] Serov A. A., “Formulas for the numbers of sequences containing a given pattern given number of times”, Discrete Math. Appl., 32:32 (2022), 233–245.10.1515/dma-2022-0020Suche in Google Scholar

[3] Zubkov A. M., Serov A. A., “A natural approach to the experimental study of dependence between statistical tests”, Matem-aticheskie voprosy kriptografii, 12:1 (2021), 131–142.10.4213/mvk352Suche in Google Scholar

[4] Zaman J. K. M. , Ghosh R., “Review on fifteen statistical tests proposed by NIST”, J. Theor. Phys. Cryptography, 1 (2012), 18–31.Suche in Google Scholar

[5] Sulak F., Doğanaksoy A., Uğuz M., Koçak O., “Periodic template tests: A family of statistical randomness tests for a collection of binary sequences”, Discrete Applied Mathematics, 271 (2019), 191–204.10.1016/j.dam.2019.07.022Suche in Google Scholar

[6] Soto J., Bassham L., “Randomness Testing of the Advanced Encryption Standard Finalist Candidates”, NIST IR 6483, 1999.10.6028/NIST.IR.6390Suche in Google Scholar

[7] Sulak F., Uğuz M., Koçak O., Doğanaksoy A., “On the independence of statistical randomness tests included in the NIST test suite”, Turkish J. Electr. Eng. & Comput. Sci., 25 (2017), 3673–3683.10.3906/elk-1605-212Suche in Google Scholar

[8] Georgescu C., Simion E., “New results concerning the power of NIST randomness tests”, Proc. Romanian acad., ser. A, 18 (2017), 381–388.Suche in Google Scholar

[9] Iwasaki A., Umeno K., “A new randomness test solving problems of Discrete Fourier Transform Test”, IEICE Trans. Fundam. Electronics, Commun. and Comput. Sci., E101.A:8 (2018), 1204–1214.10.1587/transfun.E101.A.1204Suche in Google Scholar

[10] Burciu P., Simion E., “Systematic approach of NIST statistical tests dependencies”, J. Electr. Eng., Electronics, Control and Comput. Sci., 5:15 (2019), 1–6.Suche in Google Scholar

[11] Billingsley P., Convergence of Probability Measures, New York: John Wiley & Sons, 1968, xii+253 pp.Suche in Google Scholar

[12] HoeffdingW., Robbins H., “The central limit theorem for dependent random variables”, Duke Math. J., 15:3 (1948), 773–780.10.1215/S0012-7094-48-01568-3Suche in Google Scholar

[13] Petrov V. V., “On the strong law of large numbers for nonnegative random variables”, Theory Probab. Appl., 53:2 (2009), 346–349.10.1137/S0040585X97983626Suche in Google Scholar

[14] Seber G. A. F., Wild C. J., Nonlinear regression, 2nd ed., John Wiley & Sons, New York, 2003, 582 pp.Suche in Google Scholar

Received: 2021-04-20
Published Online: 2023-02-24
Published in Print: 2023-02-23

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2023-0006/pdf?lang=de
Button zum nach oben scrollen