Limit Joint Distribution of >, within a Block>>, and Rank Test>> Statistics

M. P. Savelov

Diskretnaya Matematika, Tome 34 (2022) no. 4, pp. 84-98.

Bibliographie

[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 random and pseudorandom number generators for cryptographic applications, NIST Special Publication 800-22 Revision 1a, ed. ed. L. E. Bassham III, NIST, April 2010

[2] Serov A. A., “Formuly dlya chisel posledovatelnostei, soderzhaschikh zadannyi shablon zadannoe chislo raz”, Diskretnaya matematika, 32:4 (2020), 120–136

[3] Zubkov A. M., Serov A. A., “A natural approach to the experimental study of dependence between statistical tests”, Matem. vopr. kriptogr., 12:1 (2021), 131–142 | DOI | MR | Zbl

[4] Zubkov A. M., Serov A. A., “Testing the NIST Statistical Test Suite on artificial pseudorandom sequences”, Matem. vopr. kriptogr., 10:2 (2019), 89–96 | DOI | MR | Zbl

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

[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 | DOI | MR | Zbl

[7] Soto J., Bassham L., “Randomness testing of the Advanced Encryption Standard finalist candidates”, NIST IR 6483, National Institute of Standards and Technology, 2000

[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., 25:5 (2017), 3673–3683 | DOI | MR

[9] Georgescu C., Simion E., “New results concerning the power of NIST randomness tests”, Proc. Romanian acad., ser. A., 18 (2017), 381–388 | MR

[10] Rukhin A. L., “Testing randomness: a suite of statistical procedures”, Teor. Veroyatnost. i Primenen., 45:1 (2000), 137—162 | DOI | MR | Zbl

[11] Ryabko B. Ya., Pestunov A. I., “«Stopka knig» kak novyi staticheskii test dlya sluchainykh chisel”, Probl. peredachi inform., 40:1 (2004), 73–78 | MR | Zbl

[12] Maltsev M. V., Kharin Yu. S., “O testirovanii vykhodnykh posledovatelnostei kriptograficheskikh generatorov na osnove tsepei Markova uslovnogo poryadka”, Informatika, 4 (2013), 104–111

[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

[14] Marsaglia G., Tsay L. H., “Matrices and the structure of random number sequences”, Linear Algebra Appl., 67 (1985), 147–156 | DOI | MR | Zbl

[15] Savelov M. P., “Predelnye sovmestnye raspredeleniya statistik chetyrekh kriteriev paketa NIST”, Diskretnaya matematika, 33:2 (2021), 141–154 | DOI

[16] Savelov M. P., “Predelnye sovmestnye raspredeleniya statistik trekh kriteriev paketa NIST”, Diskretnaya matematika, 33:3 (2021), 92–106

[17] Savelov M. P., “Predelnaya teorema dlya sglazhennogo varianta spektralnogo kriteriya ravnoveroyatnosti dvoichnoi posledovatelnosti”, Diskretnaya matematika, 33:4 (2021), 132–140

[18] Savelov M. P., “Predelnoe sovmestnoe raspredelenie kriteriev «Monobit test», «Frequency Test within a Block» i «Test for the Longest Run of Ones in a Block»”, Diskretnaya matematika, 34:3 (2022), 70–84

[19] Serfling R., Approximation Theorems of Mathematical Statistics, John Wiley Sons, New York, 1980, 398 pp. | MR | Zbl

[20] Tumanyan S. Kh., “Asimptoticheskoe raspredelenie kriteriya $\chi^2$ pri odnovremennom vozrastanii ob'ema nablyudenii i chisla grupp”, Teoriya veroyatn. i ee primen., 1:1 (1956), 131—145 | MR | Zbl

[21] Fulman J., Goldstein L., “Stein's method and the rank distribution of random matrices over finite fields”, Ann. Probab., 43:3 (2015), 1274–1314 | DOI | MR | Zbl

[22] Kolchin V. F., Sluchainye grafy, 2-e izd., FIZMATLIT, M., 2004, 256 pp.