Intelligent system for analysing and classifying pseudorandom number generators

Aim. This paper examines the construction of an intelligent system for analysing and classifying pseudorandom number generators (PRNGs) that combines the capabilities of machine learning and directed search for determining the type of the source of a random sequence of numbers. The focus is on identifying weaknesses in non-cryptographic PRNGs that may be predictable, which entails risks for their use in information security. Methods. The research used machine learning methods, including neural networks, correlation analysis, and NIST statistical tests. The developed models were trained on large samples of PRNG output strings, which allowed estimating the predictability of the PRNG and internal state restorability. Neural network structures were chosen taking into account the results of optimisation of the neural network hyperparameter values. The paper shows the effect of the sample size on the obtained results. Results. The analysis and classification of a PRNG involves a number of steps: calculating the autocorrelation function of the output strings and their spectrum; execution of statistical tests developed by the NIST laboratory; classification of PRNGs based on the output strings analysis; identifying the specificity of the PRNG’s internal structure or its internal states; prediction of the output values. For the Xorshift128 algorithm, the neural network showed a high accuracy of output value restoration, which confirms its vulnerability. An analysis of the Mersenne Twister algorithm revealed certain patterns, but required more complex architectures to completely reconstruct the strings. Using machine learning algorithms, the authors managed to identify the structure building patterns for the “stop-and-go” algorithm, but failed to highly accurately predict the PRNG output value based only on the prior output string values with no knowledge of the internal states. Directed search algorithms allow classifying and predicting a linear congruentional generator and a Geffe generator. The models combined into a system classify PRNGs according to their characteristics and predict their eventual output values. An analysis of the obtained results confirms the significance of not only the selected PRNG structure, but also the numerical parameters and the bits within numbers involved in the computation. Conclusion. The conducted study confirms the efficiency of the combination of machine learning and directed search as part of the analysis and classification of PRNGs. The findings allow recommending the developed system for use in practical PRNG safety assessment. Further research will focus on expanding the set of analysed PRNGs and examining other types of neural networks for improving the quality and performance of models.

1. Schneier B., Ferguson N. Fortuna. (accessed 15.12.2024). Available at: https://www.schneier.com/academic/fortuna.

2. Kuminov V.P., Sidorenko V.G. [Analysing cryptographic strength of pseudorandom number generators using machine learning]. In: Proceedings of the XXXII International Conference Complex System Security Management (in memory of V.V. Kulba). Moscow: IPU RAS; 2024. (accessed 20.01.2025). (in Russ.) Available at: https://iccss2024.ipu.ru/proceedings/%D0%9A%D1%83%D0%B C%D0%B8%D0%BD%D0%BE%D0%B2.pdf.

3. Kuminov V.P., Sidorenko V.G. [Methods for evaluating the quality of pseudorandom number generators]. In: Intelligent Transportation Systems: Proceedings of the III International Research and Practice Conference. Moscow; May 30, 2024. Moscow: Russian University of Transport (MIIT); 2024. Pp. 631-636. (in Russ.) DOI: 10.30932/9785002446094-2024-631-636.

4. Hassan M. Cracking Random Number Generators using Machine Learning – Part 1: xorshift128. (accessed 26.06.2025). Available at: https://www.nccgroup.com/us/research-blog/cracking-random-number-generators-usingmachine-learning-part-1-xorshift128.

5. Common Weakness Enumeration. (accessed 20.01.2025). Available at: https://cwe.mitre.org/data/definitions/330.html.

6. Mersenne twister (reference). (accessed 20.01.2025). Available at: https://dic.academic.ru/dic.nsf/ruwiki/88739.

7. Hassan M. Cracking Random Number Generators using Machine Learning – Part 1: Xorshift128. (accessed 20.01.2025). Available at: https://research.nccgroup.com/2021/10/15/cracking-random-number-generatorsusing-machine-learning-part-1-Xorshift128.

8. Voronina E.G., Sidorenko V.G. [Random number generators: A textbook]. Moscow: Russian University of Transport; 2018. (in Russ.)