08. Ivanov A.I., Bannykh A.G. Rapid Estimation of the Entropy of Long Codes with Dependent Bits on Low-Power, Low-Bit Microcontrollers (Review of Literature on Reducing the Dimension of a Problem)

UDK 621.865.8:004.032.26

DOI: 10.15507/2658-4123.030.202002.300-312

Rapid Estimation of the Entropy of Long Codes with Dependent Bits on Low-Power, Low-Bit Microcontrollers (Review of Literature on Reducing the Dimension of a Problem)

Aleksandr I. Ivanov
Head of Laboratory of Biometric and Neural Network Technologies, Penza Research Electrotechnical Institute (9 Sovetskaya St., Penza 440000, Russia), D.Sc. (Engineering), Associate Professor, Researcher ID: R-4514-2019, ORCID: https://orcid.org/0000-0003-3475-2182, This email address is being protected from spambots. You need JavaScript enabled to view it.

Andrey G. Bannykh
Postgraduate Student of Chair of Information Security of Systems and Technologies, Penza State University (40 Krasnaya St., Penza 440026, Russia), ORCID: https://orcid.org/0000-0003-4776-5273, This email address is being protected from spambots. You need JavaScript enabled to view it.

Introduction. The aim of the work is to reduce the requirements for bit depth and processor performance of a trusted computing environment when estimating the entropy of long codes with dependent bits.
Materials and Methods. Testing procedures recommended by the Russia national standards are used. The transition from the analysis of ordinary long codes to Hamming distances between random Alien codes and the Own image code is used.
Results. It is shown that the transition to the presentation of data by the normal distribution law in the space of Hamming distances makes the relationship between mathematical expectation and entropy almost linear. Low-bit tables are constructed that relate the first statistical moments of the distribution of Hamming distances to the entropy of long codes. In calculations, the correlation index of the digits of the studied codes can vary widely.
Discussion and Conclusion. The calculation of the mathematical expectation and standard deviation is easily feasible on low-discharge low-power microcontrollers. The use of the synthesized tables makes it possible to pass easily from the lower statistical moments of the Hamming distances to the entropy of long codes. The task of calculating entropy is accelerated many times in comparison with Shannon’s procedures and becomes feasible on cheap low-bit processors.

Keywords: low-power microcontrollers, testing of neural networks, the entropy of long codes, dependent bits, code

For citation: Ivanov A.I., Bannykh A.G. Rapid Estimation of the Entropy of Long Codes with Dependent Bits on Low-Power, Low-Bit Microcontrollers (Review of Literature on Reducing the Dimension of a Problem). Inzhenerernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2020; 30(2):300-312. DOI: https://doi.org/10.15507/2658-4123.030.202002.300-312

Contribution of the authors: A. I. Ivanov – articulating the basic concept, goals and objectives of the study, performing the calculations, preparing the text, drawing the conclusions; A. G. Bannykh – conducting a numerical experiment, synthesis of the tables for rapid calculation of the entropy of long codes on low-bit processors.

All authors have read and approved the final manuscript.

Received 15.01.2020; revised 20.02.2020; published online 30.06.2020

REFERENCES

1. Juels A., Wattenberg M. A Fuzzy Commitment Scheme. In: CCS’99: Proceedings of the 6^th ACM Conference on Computer and Communications Security; 1999. Pp 28-36. (In Eng.) DOI: https://doi.org/10.1145/319709.319714

2. Ramírez-Ruiz J.A., Pfeiffer C.F., Nolazco-Flores J. Cryptographic Keys Generation Using Finger Codes. Advances in Artificial Intelligence – IBERAMIA-SBIA. 2006; Pp. 178–187. (In Eng.) DOI: https://doi.org/10.1007/11874850_22

3. Ushmaev O.S., Kuznetsov V.V. Secured Biometric Verification Based on Fingerprint Topology Binary Representation. Informatika i eyo primeneniya = Informatics and Applications. 2012; 6(1):132-140. Available at: http://www.ipiran.ru/journal/issues/2012_01_eng/ (accessed 29.04.2020). (In Russ.)

4. Ivanov A.I., Chernov P.A. Protocols of Biometric Cryptological Handshaking: Protecting Artificial Intelligence of the Internet of Things by Neural Network Methods. Sistemy bezopasnosti = Safety Systems. 2018; (6):50-59. Available at: http://cs.groteck.ru/SS_6_2018/index.html?pn=&pageNumber= (accessed 29.04.2020). (In Russ.)

5. Ivanov A., Akhmetov B., Funtikov V., et al. Statistical Description of Output States of the Neural Network “Biometrics-code” Transformers. In: Progress in Electromagnetics Research Symposium: PIERS Proceedings. Moscow; 2012. Pp. 62-65. Available at: https://piers.org/pierspublications/PIERS2012MoscowFinalProgram.pdf (accessed 29.04.2020). (In Eng.)

6. Akhmetov B.S., Kachalin S.V., Ivanov A.I. Supplement Fuzzy Biometric Morphing Reproduction Examples of Parents in Several Generations of Descendants Examples. Vestnik KazNTU = Vestnik KazNTU. 2014; (4):194-199. Available at: https://official.satbayev.university/download/document/7138/ВЕСТНИК-2014 №4.pdf (accessed 29.04.2020). (In Russ.)

7. Malygin A.Yu, Fedulaev V.V., Nadeev D.N., et al. Requirements for Synthetic Bases of Biometric Images and Generators for Their Formation. Neyrokompyutery: razrabotka, primenenie = Neurocomputers. 2007; (12):60-64. Available at: http://www.radiotec.ru/article/3747 (accessed 29.04.2020). (In Russ.)

8. Akhmetov B., Ivanov A., Malyghin A., et al. Morph-Reproduction Examples of Parents in Several Generations of Examples Descen. In: International Conference on Global Trends in Academic Research. Lumpur; 2014. Pp. 188-190. Available at: https://globalilluminators.org/conferences/icmrp-2014-kualalumpur-malaysia/icmrp-full-paper-proceeding-2014/ (accessed 29.04.2020). (In Eng.)

9. Volchikhin V.I., Ivanov A.I., Bannykh A.G. Regularizing Calculations of the Output Entropy of a Neural Network “Biometrics-Code” Converter though Multiplication of a Small Sample of Original Data. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University Proceedings. Volga Region. Engineering Sciences. 2017; (4):14-23. (In Russ.) DOI: https://doi.org/10.21685/2072-3059-2017-4-2

10. Akhmetov B., Kachalin S., Ivanov A., et al. Solving the Inverse Task of Neural Network Biometrics without Mutations and Jenkins “Nightmare” in the Implementation of Genetic Algorithms. In: International Conference “Computational and Informational Technologies in Science, Engineering and Education”. 2015. Available at: http://conf.ict.nsc.ru/citech-2015/en/reportview/261166 (accessed 29.04.2020). (In Eng.)

11. Kachalin S.V. Algorithm of Genetic Circulation of Neural Network Functional Matrices without Jenkins’ Nightmare Defects. Yevraziyskiy Soyuz Uchenykh = Eurasian Union of Scientists. 2015; (4):59-62. Available at: https://euroasia-science.ru/tehnicheskie-nauki/лгоритм-генетического-обращения-ма/ (accessed 29.04.2020). (In Russ.)

12. Kachalin S.V., Ivanov A.I. Direction of the Morph-Reproduction Biometric Images, the Exclusuve Degeneracy Effects of Their Populations. Voprosy radioelektroniki = Questions of Radio Electronics. 2015; (1):76-85. (In Russ.)

13. Nadeev D.N., Funtikov V.A., Ivanov A.I. Connection Between the Entropy of Neural Network Converters “Biometrics-Code” Output States and the Pair Correlation Coefficients. Neyrokompyutery: razrabotka, primenenie = Neurocomputers. 2012; (3):74-77. Available at: http://www.radiotec.ru/article/10426 (accessed 29.04.2020). (In Russ.)

14. Akhmetov B.S., Volchikhin V.I., Kulikov S.V., et al. Modeling of Long Biometric Codes, Reproducing Correlation of Neural Network Converter Output Data. Neyrokompyutery: razrabotka, primenenie = Neurocomputers. 2012; (3):40-43. Available at: http://www.radiotec.ru/article/10418 (accessed 29.04.2020). (In Russ.)

15. Bezyaev V., Serikov I., Kruchinin A., et al. On the Issue of Modeling Long Biometric Codes with Dependent Bit States. In: Progress in Electromagnetics Research Symposium: PIERS Proceedings. Moscow; 2012. Pp. 62-65. Available at: https://piers.org/pierspublications/PIERS2012MoscowAbstracts.pdf (accessed 29.04.2020). (In Eng.)

16. Ivanov A.I., Lozhnikov P.S., Serikova Yu.I. Reducing the Size of a Sample Sufficient for Learning Due to the Symmetrization of Correlation Relationships Between Biometric Data. Cybernetics and Systems Analysis. 2016; (52):379-385. (In Eng.) DOI: https://doi.org/10.1007/s10559-016-9838-x

17. Volchikhin V.I., Akhmetov B.B., Ivanov A.I. A Fast Symmetrization Algorithm for Correlations of Biometric Data of High Dimension. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University Proceedings. Volga Region. Engineering Sciences. 2016; (1):3-7. Available at: https://izvuz_tn.pnzgu.ru/tn1116 (accessed 29.04.2020). (In Russ.)

18. Ivanov A.I., Bezyaev A.V., Gazin A.I. Simplification of Statistical Description of Quantum Entanglement of Multidimensional Biometric Data Using Simmetrization of Paired Correlation Matrices. Journal of Computational and Engineering Mathematics. 2017; 4(2):3-13. Available at: https://jcem.susu.ru/jcem/article/view/110 (accessed 29.04.2020). (In Eng.)

19. Kachalin S.V. Assessment of Stability Learning Algorithms Large Artificial Neural Networks of Biometric Application. Vestnik SibGAU = Vestnik SibGAU. 2014; (3):68-72. Available at: https://vestnik.sibsau.ru/vestnik/897/ (accessed 29.04.2020). (In Russ.)

20. Ivanov A.I., Serikova Yu.I. Nomograms Error Estimates of Correlation Rates, Calculated for Small Samples of Biometric Data. Voprosy radioelektroniki = Questions of Radio Electronics. 2015; (12):123-130. (In Russ.)

21. Volchikhin V.I., Ivanov A.I., Serikova Yu.I. Compensation of Methodological Errors in Calculations of Standard Deviations and Correlation Coefficients Caused by Small Sample Sizes. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University Proceedings. Volga Region. Engineering Sciences. 2016; (1):45-49. Available at: https://izvuz_tn.pnzgu.ru/tn9116 (accessed 29.04.2020). (In Russ.)

22. Ivanov A.I., Serikova Yu.I., Bannykh A.G. Adjustment of Methodological Error Calculating the Statistical Moments of the Fourth Order for Small Samples of Biometric Data. Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve = Models, Systems, Networks in Economics, Engineering, Nature and Society. 2016; (4):108-114. Available at: https://mss.pnzgu.ru/mss416 (accessed 29.04.2020). (In Russ.)

23. Akhmetov B., Ivanov A., Funtikov V. Evaluation of Multidimensional Entropy on Short Strings of Biometric Codes with Dependent Bits. In: Progress in Electromagnetics Research Symposium: PIERS Proceedings. Moscow; 2012. Pp. 66-69. Available at: https://piers.org/pierspublications/PIERS2012MoscowFinalProgram.pdf (accessed 29.04.2020). (In Eng.)

24. Ivanov A.I., Malygina Ye.A. Biometric Identity Vertification: Inversion of Matrices of Neural Network Functionals in the Hamming Space. Voprosy zashchity informatsii = Information Security Questions. 2015; (1):23-29. Available at: http://izdat.ntckompas.ru/editions/magazine_news/detail.php?ELEMENT_ID=20164&SECTION_ID=155&ID=184 (accessed 29.04.2020). (In Russ.)

25. Volchikhin V.I., Ivanov A.I., Bezyaev A.V., et al. Evaluation of the Calculation Acceleration Effect, Caused by the Support of Quantum Superposition States during Adjustment of Output Conditions of a “Biometrics-Code” Neural Network Converter. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University Proceedings. Volga Region. Engineering Sciences. 2017; (1):43-55. (In Russ.) DOI: https://doi.org/10.21685/2072-3059-2017-1-4

26. Volchikhin V.I., Ivanov A.I. Neural Network Molecule: a Solution of the Inverse Biometry Problem through Software Support of Quantum Superposition on Outputs of the Network of Artificial Neurons. Vestnik Mordovskogo universiteta = Mordovia University Bulletin. 2017; 27(4):518-529. (In Russ.) DOI: https://doi.org/10.15507/0236-2910.027.201704.518-529

27. Gulov V.P., Ivanov A.I., Yazov Yu.K., et al. Perspective of Neuro Network Protection of Cloud Services through Biometric Deployment of Personal Information on the Example of Medical Electronic History of Disease (Brief Review of the Literature). Vestnik novykh meditsinskikh tekhnologiy = Journal of New Medical Technologies. 2017; 24(2):220-225 (In Russ.) DOI: https://doi.org/10.12737/article_5947d5509f0411.58967456

28. Ivanov A.I., Bezyaev A.V., Yelfimov A.V., et al. Estimating the Probability of Biometric Authentication Errors on Small Samples using the Hypothesis of Beta Distribution Hamming Distances. Spetsialnaya tekhnika = Special equipment. 2017; (1):48-51. (In Russ.)

29. Ivanov A.I., Lozhnikov P.S., Bannykh A.G. A Simple Nomogram for Fast Computing the Code Entropy for 256-Bit Codes That Artificial Neural Networks Output. Journal of Physics: Conference Series. 2019; 1260(2). Available at: https://iopscience.iop.org/article/10.1088/1742-6596/1260/2/022003/meta (accessed 29.04.2020). (In Eng.)

This work is licensed under a Creative Commons Attribution 4.0 License.