REGULARIZING CALCULATIONS OF THE OUTPUT ENTROPY OF A NEURAL NETWORK “BIOMETRICS-CODE”  CONVERTER THOUGH MULTIPLICATION OF A SMALL SAMPLE OF ORIGINAL DATA

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
Bannykh Andrey Grigor'evich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), ibst@pgzgu.ru

519.24; 53; 57.017

10.21685/2072-3059-2017-4-2

Background. The aim of the paper is to regularize calculations of the entropy of long codes with dependent bits on a small testing sample.
Materials and methods. The algorithm is based on predicting the probability of occurrence of rare events using the hypothesis of normal distribution of Hamming distances. It is suggested to abandon calculations of mathematical expectation and standard deviation in small samples, and proposed to multiply the original data by adding mutations obtained from a pseudorandom noise generator to them. Limitations to the mutation noise generator’s amplitude are given.
Results. It is shown that the transition to the Hamming distances’ space leads to a logarithmic compression of the initial alphabet’s size of the output states spectrum of a “biometrics-code” converter’s molecule. This ultimately allows rapid testing of converters through calculation of their entropy.
Conclusions. The procedure of regularization of calculations proposed in the article makes it possible to obtain the same accuracy of evaluating the entropy of a neural network converter on a sample of 21 experiments as the accuracy of calculations provided by standard computational procedures in accordance with GOST R 52633.3 on a sample of 2100 experiments. There is a 100-fold increase in the stability of computations.

statistical analysis of small samples, prediction of the probability of rare events occurrence, artificial neural networks, entropy

1. Yaglom A. M., Yaglom I. M. Veroyatnost' i informatsiya [Probability and information]. Moscow: Dom Knigi, 2007, 512 p.
2. Juels A. A, Wattenberg M. Proc. ACM Conf. Computer and Communications Security (1–4 November, 1999). Singapore, 1999, pp. 28–36.
3. Monrose F., Reiter M., Li Q., Wetzel S. In Proc. IEEE Symp. on Security and Privacy (14–16 May, 2001). Okland, California USA, 2001, pp. 202–213.
4. Dodis Y., Reyzin L., Smith A. EUROCRYPT. 2004, April 13, pp. 523–540.
5. Hao F., Anderson R, Daugman J. IEEE Transactions on computers. 2006, vol. 55, no. 9. 
6. Ivanov A. I., Zakharov O. S. Sreda modelirovaniya «BioNeyroAvtograf». Programmnyy produkt sozdan laboratoriey biometricheskikh i neyrosetevykh tekhnologiy, razmeshchen s 2009 g. na sayte AO «PNIEI» [“BioNeyroAvtograph” simulation environment. The product was established by the laboratory of biometric and neural network technologies and announced in 2009 on the PNIEI website]. Available at: http://pniei.rf/activity/science/noc.htm (dlya svobodnogo ispol'zovaniya universi-tetami Rossii, Belorussii, Kazakhstana).
7. Volchikhin V. I., Ivanov A. I., Funtikov V. A. Bystrye algoritmy obucheniya neyrosetevykh mekhanizmov biometriko-kriptograficheskoy zashchity informatsii: monografiya [Fast learning algorithms for neural network mechanisms of biometric cryptographic data protection: monograph]. Penza: Izd-vo PGU, 2005, 273 p.
8. Akhmetov B. S., Ivanov A. I., Funtikov V. A., Bezyaev A. V., Malygina E. A. Tekhnologiya ispol'zovaniya bol'shikh neyronnykh setey dlya preobrazovaniya nechetkikh biometricheskikh dannykh v kod klyucha dostupa: monografiya [The technology of large neural networks’ implementation for fuzzy biometric data transformation into access code: monograph]. Almaty, Kazakhstan: LEM, 2014, 144 p. Available at: http://portal.kazntu.kz/files/publicate/2014-06-27-11940.pdf
9. Malygin A. Yu., Volchikhin V. I., Ivanov A. I., Funtikov V. A. Bystrye algoritmy testirovaniya neyrosetevykh mekhanizmov biometriko-kriptograficheskoy zashchity informatsii [Fast testing algorithms for newural network mechanisms of biometric cryptographic data protection]. Penza: Izd-vo PGU, 2006, 161 p.
10. GOST R 52633.3–2011. Zashchita informatsii. Tekhnika zashchity informatsii. Testirovanie stoykosti sredstv vysokonadezhnoy biometricheskoy zashchity k atakam podbora [Data protection. Data protecting technology. Testing of highly reliable biometric protective means’ resistance to breaking attacks]. Moscow, 2011.
11. Serikova N. I., Ivanov A. I., Serikova Yu. I. Voprosy radioelektroniki. Ser.: SOIU [Problems of radioelectronics. Series: SOIU]. 2015, iss. 1, pp. 85–94.
12. Ivanov A. I., Gazin A. I., Vyatchanin S. E., Perfilov K. A. Nadezhnost' i kachestvo slozhnykh system [Reliability and quality of complex systems]. 2016, no. 2 (14), pp. 67–72.
13. Ivanov A. I., Perfilov K. A., Malygina E. A. Izmerenie. Monitoring. Upravlenie. Kontrol' [Measurement. Monitoring. Management. Control]. 2016, no. 2 (16), pp. 58–66.
14. GOST R 52633.2–2010. Zashchita informatsii. Tekhnika zashchity informatsii. Trebovaniya k formirovaniyu sinteticheskikh biometricheskikh obrazov, prednaznachennykh dlya testirovaniya sredstv vysokonadezhnoy biometricheskoy autentifikatsii [Data protection. Data protecting technology. Requirements to creation of synthetic biometric images intended for highly reliable biometric authentication means testing]. Moscow,
15. Akhmetov B., Kachalin S., Ivanov A., Bezyaev A., Mukapil K. Computational and Informational Technologies in Science, Engineering and Education (CITech-2015): International Conference. Almaty, Kazakhstan, 2015, pp. 89–92.