Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»

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, ed. L. E. Bassham III, NIST, 27 April 2010.Suche in Google Scholar

[2] Serov A. A., “Formulas for the numbers of sequences containing a given pattern given number of times”, Discrete Math. Appl., 32:4 (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”, Matematicheskie Voprosy Kriptografii, 12:1 (2021), 131–142 (in Russian).10.4213/mvk352Suche in Google Scholar

[4] Zubkov A. M., Serov A. A., “Testing the NIST Statistical Test Suite on artificial pseudorandom sequences”, Matematicheskie Voprosy Kriptografii, 10:2 (2019), 89–96 (in Russian).10.4213/mvk286Suche in Google Scholar

[5] 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

[6] Sulak F., Doǧanaksoy A., Uǧuz 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

[7] Soto J., Bassham L., “Randomness Testing of the Advanced Encryption Standard Finalist Candidates”, NIST IR 6483, Nat. Inst. Stand. and Technol., 1999.10.6028/NIST.IR.6483Suche in Google Scholar

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

[9] 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

[10] 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

[11] Ryabko B. Ya., Pestunov A. I., ““Book stack” as a new statistical test for random numbers”, Problems Inform. Transmission, 40:1 (2004), 66–71.10.1023/B:PRIT.0000024881.86267.b5Suche in Google Scholar

[12] Maltsev M. V., Kharin Yu. S., “On testing of cryptographyc generators output sequences using Markov chains of conditional order”, Informatics, 4 (2013), 104–111 (in Russian).Suche in Google Scholar

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

[14] Savelov M. P., “The limit joint distributions of statistics of four tests of the NIST package”, Discrete Math. Appl., 33:1 (2023), 55–64.10.1515/dma-2023-0006Suche in Google Scholar

[15] Savelov M. P., “The limit joint distributions of statistics of three tests of the NIST package”, Discrete Math. Appl., 33:4 (2023), 247–257.10.1515/dma-2023-0022Suche in Google Scholar

[16] Savelov M. P., “Limit theorem for a smoothed version of the spectral test for testing the equiprobability ofa binary sequence”, Discrete Math. Appl., 33:5 (2023), 317–323.Suche in Google Scholar

[17] Balakrishnan N., Koutras M. V., Runs and Scans with Applications, John Wiley & Sons, New York, 460 pp.Suche in Google Scholar

[18] Serfling R., Approximation Theorems of Mathematical Statistics, John Wiley & Sons, New York, 1980, 398 pp.10.1002/9780470316481Suche in Google Scholar

[19] Tumanyan S. H., “Asymptotic distribution of χ² criterion when the size of observations and the number of groups simultaneously increase.”, Theory Probab. Appl., 1:1 (1956), 117–131.10.1137/1101010Suche in Google Scholar