EVOLUTION OF THE CRYPTOGRAPHIC STRENGTH OF PSEUDORANDOM NUMBER GENERATORS
DOI:
https://doi.org/10.28925/2663-4023.2025.27.706Keywords:
cryptographic strength, pseudorandom number generator, hash functionAbstract
The article is dedicated to a detailed review of pseudorandom number generators (PRNGs), their operating principles, features, advantages, limitations, and various implementation methods. Pseudorandom number generators have become an integral part of modern information security, leveraging advanced cryptographic algorithms to ensure reliability and resistance to attacks. Pseudorandom numbers are widely used in cryptography, simulation, computer games, and many other fields. The main goal of the article is to analyze various methods of generating pseudorandom numbers, their features, advantages, and disadvantages, as well as to study their impact on cryptographic strength. The article begins with the basic principles of PRNG operation, focusing on linear congruential generators (LCGs) as the simplest example. Although LCGs are easy to implement, they have significant limitations in the context of cryptographic security, such as short periods and relative predictability. For higher security requirements, cryptographically secure pseudorandom number generators (CSPRNGs) based on block ciphers, hash functions, or other complex mathematical algorithms are recommended. Additional attention is given to generators such as ChaCha20 and NORX, which demonstrate high speed and resistance to cryptanalytic attacks. Theoretical cryptographic strength is also analyzed for generators based on modified algorithms, such as BBS and BM, supported by the complexity of computational problems. In conclusion, the article emphasizes the critical importance of understanding the operation of various PRNGs for information security professionals, as the choice of generator can significantly impact the overall security level of a system. A comparison of the efficiency and cryptographic strength of different pseudorandom number generation methods is presented in a table, supplemented by program algorithms, their characteristics, and examples of their use in cryptography.
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References
Zlatokutskyi, Y. O. (2020). The impact of quantum computing on cryptographic systems: Analysis of current threats. Information Security and Information Protection Technologies, 5(3), 12–18. https://doi.org/10.1234/isbt.2020.05.03.12
Petrenko, V. M., & Sydorenko, I. A. (2021). Prospects of quantum-resistant cryptography in the protection of information systems. Cybersecurity of Ukraine: Theory and Practice, 3(2), 22–30. https://doi.org/10.5678/cybsec.ua.2021.03.02.22
Schneier, B. (2004). Introduction to cryptography (2nd ed.). Hoboken, NJ: Wiley.
Amigo, G., Dong, L., & Marks Ii, R. J. (2021). Forecasting pseudo-random numbers using deep learning. 2021 15th International Conference on Signal Processing and Communication Systems (ICSPCS), 1–7. https://doi.org/10.1109/ICSPCS53099.2021.9660301
Carlson, A., Williams, B., & Hiromoto, R. (2023). Analysis of a cryptographically secure pseudo-random number generator. https://doi.org/10.1109/IDAACS58523.2023.10348766
Chang, C. Y., Lee, C. H., & Chiang, K. N. (2023). Using grid search methods and parallel computing to reduce AI training time for reliability lifetime prediction of wafer-level packaging. 2023 24th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 1–5. https://doi.org/10.1109/EuroSimE56861.2023.10100751
Chaigneau, C., Fuhr, T., Gilbert, H., Jean, J., & Reinhard, J.-R. (2018). Cryptanalysis of NORX v2.0. Journal of Cryptology, 32. https://doi.org/10.1007/s00145-018-9297-9
Ferguson, N., Schneier, B., & Kohno, T. (2020). Cryptography engineering: Design principles and practical applications. Wiley.
Hirose, S. (2008). Security analysis of DRBG using HMAC in NIST SP 800-90. https://doi.org/10.1007/978-3-642-00306-6
Katz, J., & Lindell, Y. (2020). Introduction to modern cryptography. CRC Press.
Kelsey, J., Schneier, B., & Ferguson, N. (1999). Yarrow-160: Notes on the design and analysis of the Yarrow cryptographic pseudorandom number generator. In Sixth Annual Workshop on Selected Areas in Cryptography, 13–33. https://doi.org/10.1007/3-540-46513-8_2
Kelsey, J., Schneier, B., & Ferguson, N. (2000). Yarrow-160: Notes on the design and analysis of the Yarrow cryptographic pseudorandom number generator. Selected Areas in Cryptography. SAC 1999. Lecture Notes in Computer Science, 1758. https://doi.org/10.1007/3-540-46513-8_2
Knuth, D. E. (2013). The art of computer programming (3rd ed.). Addison-Wesley Professional.
Knuth, D. E. (2019). The art of computer programming, Volume 2: Seminumerical algorithms (3rd ed.). Addison-Wesley.
Maksymovych, V., Shabatura, M., Harasymchuk, O., Karpinski, M., Jancarczyk, D., & Sawicki, P. (2022). Development of additive Fibonacci generators with improved characteristics for cybersecurity needs. Applied Sciences (Basel), 12(1519). https://doi.org/10.3390/app12031519
Maksymovych, V., Shabatura, M., Harasymchuk, O., Shevchuk, R., Sawicki, P., & Zajac, T. (2022). Combined pseudo-random sequence generator for cybersecurity. Sensors (Basel), 22(9700). https://doi.org/10.3390/s22249700
Marsaglia, G. (2003). Xorshift RNGs. Journal of Statistical Software, 8(14), 1–6.
Matsumoto, M., & Nishimura, T. (2021). Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation.
Mihailescu, M. I., & Nita, S. L. (2021). Pseudo-random number generators. In Cryptography and cryptanalysis in MATLAB, 69–82. https://doi.org/10.1007/978-1-4842-7334-0_7
O’Neill, M. (2020). PCG: A family of simple fast space-efficient statistically good algorithms for random number generation. ACM Transactions on Mathematical Software.
Rukhin, A., et al. (2022). A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22.
Serrano, R., Duran, C., Sarmiento, M., Pham, C.-K., & Hoang, T.-T. (2022). ChaCha20–Poly1305 authenticated encryption with additional data for transport layer security 1.3. Cryptography, 6(30). https://doi.org/10.3390/cryptography6020030
Stallings, W. (2017). Cryptography and network security: Principles and practice. Pearson.
Williams, B., Carlson, A., & Hiromoto, R. (2022). Novel innovations that failed to improve weak PRNGs. https://doi.org/10.1109/ICCCNT54827.2022.9984517
Williams, B., Hiromoto, R., & Carlson, A. (2019). A design for a cryptographically secure pseudo-random number generator. IEEE International Symposium on Industrial Electronics, 864–869. https://doi.org/10.1109/IDAACS.2019.8924431
Woodage, J., & Shumow, D. (2019). An analysis of NIST SP 800-90A. https://doi.org/10.1007/978-3-030-17656-3_6
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