L.V. Kovalchuk, O.Yu. Bespalov, T.M. Klymenko
Èlektron. model. 2025, 47(5):03-22
https://doi.org/10.15407/emodel.47.05.003
ABSTRACT
The issue of verifying the correct functioning of random/pseudorandom sequence generators designed for cryptographic applications is considered. Three different methods for checking the quality of the generator are proposed: a first-level method designed to check the cryptographic qualities of the generator when it is approved for operation or after major repairs; a second-level method designed for periodic checking of the generator’s operation (for example, every month); and a third-level method designed for continuous checking of the generator throughout its entire operation. Each method has its own tasks: the first-level method conducts the most detailed study and determines whether the developed generator can actually be used to generate key data; the second-level method verifies that there has been no deterioration in the quality of the generator’s operation during its operation; the third-level methodology operates in real time and is aimed at instantly detecting significant malfunctions in the generator. All these methodologies are developed and described step by step in the paper. A full justification of the conclusions drawn from the application of the methods is also provided. The results obtained are the basis for the development of a National Standard for Testing the Cryptographic Qualities of Generators, which is still absent in Ukraine.
KEYWORDS
random/pseudorandom number generators, statistical tests, cryptographic qualities of the number generator.
REFERENCES
- Bikos, Anastasios, Panagiotis, E. Nastou, Georgios, Petroudis, Yannis, C. Stamatiou. (2023). Random Number Generators: Principles and Applications. Cryptography 7(4), 54. https://doi.org/10.3390/cryptography7040054
- Blum, L., Blum, M., Shub, M.A. (1986). Simple Unpredictable Pseudo-random Number Generator. SIAM Journal on Computing, 15(2), 364-383.
- Bassham, III L.E., Rukhin, A.L., Soto, J., Nechvatal, J.R., Smid, M.E., Barker, E.B. and others. (2010). A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22, Revision 1a. https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf
- Maurer, U.M. A Universal Statistical Test for Random Bit Generators. (1992). Journal of Cryptolojy. 5, 89-105.
- Ziv, J., Lempel, A.A. (2023). Universal Algorithm for Sequential Data Compression. IEEE Transactions on Information Theory. 22, 337-3432.
- Crocetti, L., Nannipieri, P., Di Matteo, S., Fanucci, L., Saponara, S. (2023). Review of Methodologies and Metrics for Assessing the Quality of Random Number Generators. Electronics. 12(3), 723. https://doi.org/10.3390/electronics12030723, https://www.mdpi.com/2079-9292/12/3/723
- Marsaglia, G. (2008). The Marsaglia random number CDROM including the diehard battery of tests of randomness. URL: http://www.stat. fsu. edu/pub/diehard/
- Verbytskyi, O.V. (1998). Introduction to Cryptology. Lviv: Publishing House of Scientific and Technical Literature. 247. (ukr).
- Foreman, C., Yeung, R., Curchod, F.J. (2024). Statistical Testing of Random Number Generators and Their Improvement Using Randomness Extraction. Entropy. 26(12), 1053. https://doi.org/10.3390/e26121053, https://www.mdpi.com/1099-4300/26/12/1053
- Pseudorandom Number Generation Using a Block Cipher. https://www.brainkart.com/article/ Pseudorandom-Number-Generation-Using-a-Block-Cipher_8424/
- Yu Long Chen1, Eran Lambooij2, and Bart Mennink. How to Build Pseudorandom Functions from Public Random Permutations. https://eprint.iacr.org/2019/554.pdf
- Administration of the State Service for Special Communications and Information Protection of Ukraine. Order. 20.07.2007. No 141. On approval of the Regulation on the procedure for the development, production and operation of cryptographic information security means. (ukr) https://zakon.rada.gov.ua/laws/show/z0862-07#Text
- Kovalchuk, L., Bezditny, V. (2006). Verification of the independence of statistical tests intended for assessing the cryptographic qualities of GPV. Information Security. 8, 2(29), 18-23. (ukr) https://doi.org/10.18372/2410-7840.8.4944
- Kovalchuk, L., Kuchynska, N. (2017). Methods for checking the independence of statistical tests. Information Technology and Security. July-December. 5, 2 (9), 20-32. (ukr) https:// ela.kpi.ua/server/api/core/bitstreams/9bdb5292-8ff8-4932-95e0-a6ba40d62969/content
- Kochana, R., Kovalchuk, L., Korchenko O., Kuchynska N. (2021). Statistical Tests Independence Verification Methods. Procedia Computer Science. 192, 2678-2688. https://doi.org/10.1016/j.procs.2021.09.038, https://www.sciencedirect.com/science/article/ pii/S1877050921017750
- Der Kiureghian, Armen Liu, Pei-Ling. (1985). Structural reliability under incomplete probability information. https://escholarship.org/uc/item/3739w8d3
- Kovalchuk, L., Nelasa, H., Rodinko, M., Bespalov, O. (2024). A new extended strategy of processing of statistical testing results. 11th International Research Conference Information Technology and Implementation 2024 - Workshop: Intelligent Systems and Security, IT and I-WS, CEUR Workshop Proceedings, 3933, 158-167. ISSN 16130073 Publisher CEUR-WS. https://ceur-ws.org/Vol-3933/Paper_12.pdf
- Kovalchuk, L.V., Koryakov, I.V., Bespalov, O.Yu. (2024). Statistical tests for checking the independence of random variables describing the generation of sequences in cryptoalgorithms. Electronic modeling. 46(3), 22-38. (ukr). https://doi.org/10.15407/emodel. 46.03.022
- DSTU 9041:2020 Information technologies. Cryptographic information security. Short message encryption algorithm based on twisted elliptic Edwards curves. Effective from 2020-11-01. Kyiv: UkrNDNTS, 2020. IV, 36p. (ukr)
- A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, NIST Special Publication 800-22 Revision 1a, April 2010. https://nvlpubs.nist.gov/nistpubs/legacy/sp/nistspecialpublication800-22r1a.pdf