Geodesic
Entropy as the quality characteristic of random sequences
Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 3, pp. 31-48 
A. M. Zubkov. Entropy as the quality characteristic of random sequences. Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 3, pp. 31-48. http://geodesic.mathdoc.fr/item/MVK_2021_12_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the meanings of the term “entropy” used in different fields (statistical physics, information theory, theory of dynamic systems) and application of this notion as characteristic of independence and uniformity of distributions of finite alphabet symbols. The main purpose is to use this example to show that the correct interpretation of results of statistical tests applications should include really used a priori hypotheses on probability models of analyzed sequences. An example of sequences having almost maximal possible entropy but unsatisfactory from the cryptographic viewpoint is given.

[1] Shennon K., “Matematicheskaya teoriya svyazi”, Raboty po teorii informatsii i kibernetike, IL, M., 1963, 243–332

[2] Faddeev D.K., “K ponyatiyu entropii konechnoi veroyatnostnoi skhemy”, Uspekhi matem. nauk, XI:1 (1956), 227–231 | Zbl

[3] 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, 2010

[4] Maurer U.M., “A universal statistical test for random bit generators”, J. Cryptology, 5:2 (1992), 89–105 | DOI | Zbl

[5] Dobrushin R. L., “Uproschennyi metod eksperimentalnoi otsenki entropii statsionarnoi posledovatelnosti”, Teoriya veroyatn. i ee primen., III:4 (1958), 462–464 | Zbl

[6] Vatutin V. A., Mikhailov V.G., “Statisticheskoe otsenivanie entropii diskretnykh sluchainykh velichin s bolshim chislom iskhodov”, Uspekhi matem. nauk, 50:5 (1995), 121–134 | Zbl

[7] Zubkov A. M., Serov A. A., “Testing the NIST Statistical Test Suite on artificial pseudorandom sequences”, Matematicheskie voprosy kriptografii, 10:2 (2019), 89–96 | Zbl

[8] 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 | Zbl