A MULTIDIMENSIONAL PICTURE OF NUMERICAL SEQUENCES OF THE IDEAL “WHITE NOISE”
IN HAMMING CONVOLUTIONS 

Volchikhin Vladimir Ivanovich, Doctor of engineering sciences, professor, President of Penza State University (40 Krasnaya street, Penza, Russia), president@pnzgu.ru
Ivanov Aleksandr Ivanovich,  Doctor of engineering sciences, associate professor, head of the laboratory of biometric and neural network technologies, Penza Research Institute of Electrical Engineering (9 Sovetskaya street, Penza, Russia), ivan@pniei.penza.ru
Yunin Aleksey Petrovich, Lead expert, Penza Research Institute of Electrical Engineering (9 Sovetskaya street, Penza, Russia), mal890@yandex.ru
Malygina Elena Aleksandrovna, Candidate of engineering sciences, research worker, the interindustrial testing laboratory of biometric devices and technologies, Penza State University (40 Krasnaya street, Penza, Russia), mal890@yandex.ru

519.24; 53; 57.017

10.21685/2072-3059-2017-4-1

Background. The aim of the work is to describe the ideal picture of “white noise” that enables to control its quality on small testing samples.
Materials and methods. Shannon entropy calculation for numerical sequences of 256 bits is a complicated problem. In this regard, the problem’s computation complexity is decreased by transition into the Hammings distances’ space, when testing neural network “biometrics-code” converters according to state standard GOST R 52633.3. In this case there occurs convolution of the problem’s dimensions. However such a computting solution may end up incorrect for small testing samples.
Results. It is suggested to use several Hamming convolutions taking place in field modulo 2, 4, 8 or higher. At the same time the volume of data on proximity of the analyzed numerical sequence’s picture to the picture of the ideal “white noise” increases. The work gives a list of defects featuring the real “white noise” observed in Hamming convolutions’ spaces and adduces the error estimates regarding features of the examined picture of “white noise” occurring due to the finite size of testing sample.
Conclusions. The procedures recommended by GOST R 52633.3 are insufficient at “deep” control of hashing properties of neural network “biometrics-code” convertersр. It is necessary to supplement the “white noise” quality control in a regular Hamming distances’ space, calculated by a code convolution modulo 2, Hamming convolutions in field with high modulo values.

neural network “biometrics-code” converter, biometric data, large dimensionality of data, Hamming convolutions, “white noise”

1. GOST R 52633.3–2011. Zashchita informatsii. Tekhnika zashchity informatsii. Testirovanie stoykosti sredstv vysokonadezhnoy biometricheskoy zashchity k atakam podbora [GOST R 52633.3–2011. Data protection. Data protecting technology. Testing of highly reliable biometric protective means’ resistance to breaking attacks]. Moscow, 2011.
2. Kobzar' A. I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov [Applied mathematical statistics. For engineers and researchers]. Moscow: Fizmatlit, 2006, 816 p.
3. GOST R 52633.0–2006. Zashchita informatsii. Tekhnika zashchity informatsii. Trebovaniya k sredstvam vysokonadezhnoy biometricheskoy autentifikatsii [Data protection. Data protecting technology. Requirements to highly reliable means of biometric authentication]. Moscow, 2006.
4. GOST R 52633.5–2011. Zashchita informatsii. Tekhnika zashchity informatsii. Avtomaticheskoe obuchenie neyrosetevykh preobrazovateley biometriya–kod dostupa [Data protection. Data protecting technology. Automatic learning of neural network “biometricsaccess code” converters]. Moscow, 2011.
5. Ivanov A. I., Bezyaev A. V., Elfimov A. V., Vyatchanin S. E. Spetsial'naya tekhnika [Special devices]. 2017, no. 1, pp. 48–51.
6. Ivanov A. I., Perfilov K. A., Malygina E. A. Izmerenie. Monitoring. Upravlenie. Kontrol' [Measurement. Monitoring. Management. Control]. 2016, no. 2 (16), pp. 58–66.
7. Akhmetov B. B., Ivanov A. I., Bezyaev A. V., Funtikova Yu. V. Vestnik Natsional'noy akademii nauk Respubliki Kazakhstan [Bulletin of the National Academy of Sciences of the Republic of Kazakhstan]. Almaty, 2015, no. 1, pp. 5–11.
8. Volchikhin V. I., Ivanov A. I., Serikova N. I., Funtikova Yu. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2015, no. 1 (33), pp. 50–59.
9. Yunin A. P., Korneev O. V. Trudy nauchno-tekhnicheskoy konferentsii klastera penzenskikh predpriyatiy, obespechivayushchikh bezopasnost' informatsionnykh tekhnologiy [Proceedings of a scientific and technical conference of Penza’s enterprises in the field of IT security]. Penza, 2016, vol. 10, pp. 40–42. Available at: http://pniei.rf/ activity/science/BIT/T10-p40.pdf
10. Bezyaev A. V., Ivanov A. I., Korneev O. V. Trudy nauchno-tekhnicheskoy konferentsii klastera penzenskikh predpriyatiy, obespechivayushchikh bezopasnost' informatsionnykh tekhnologiy [Proceedings of a scientific and technical conference of Penza’s enterprises in the field of IT security]. Penza, 2016, vol. 10, pp. 15–20. Available at: http://pniei.rf/activity/science/BIT/T10-p15.pdf