TY - CHAP

T1 - Application of Time Series Forecasting Methods to Test Random Number Generators

AU - Osipova, Ulyana

AU - Rakitsky, Anton

AU - Agalakov, Anton

N1 - U. Osipova, A. Rakitsky and A. Agalakov, "Application of Time Series Forecasting Methods to Test Random Number Generators," 2025 IEEE XVII International Scientific and Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE), Novosibirsk, Russian Federation, 2025, pp. 1-4, doi: 10.1109/APEIE66761.2025.11289286.

PY - 2025/12/18

Y1 - 2025/12/18

N2 - The core hypothesis of our research is that a truly random sequence is inherently unpredictable. Therefore, the accuracy of a forecast model applied to a sequence's output can serve as a direct indicator of its quality: a higher prediction accuracy suggests a higher degree of determinism and, consequently, weaker cryptographic properties. For the experiment, we generated multiple datasets using both cryptographically secure (e.g., based on hardware entropy sources) and weak generators (like the linear congruential method). Each generated sequence was treated as a time series. We then applied a suite of forecasting models, ranging from classical statistical methods like ARIMA to more complex machine learning models, including LSTMs and Gradient Boosting. The choice of a diverse set of models was crucial to ensure that the results were not biased towards a specific forecasting technique. Each model was trained on a segment of the sequence and tasked with predicting subsequent values. The proposed χ2-based metric was then used to compare the forecasted values against the actual subsequent values in the sequence. The key finding was a strong correlation: the outputs of weak generators showed a statistically significant deviation from the expected random distribution under the χ2 test when analyzed through the lens of forecasting errors. In contrast, cryptographically strong generators demonstrated no predictable patterns, resulting in forecast errors that were indistinguishable from random noise. This approach provides a novel, data-driven methodology for evaluating RNGs, complementing traditional statistical test suites like NIST SP 800-22 by introducing the concept of predictability as a core measure of weakness.

AB - The core hypothesis of our research is that a truly random sequence is inherently unpredictable. Therefore, the accuracy of a forecast model applied to a sequence's output can serve as a direct indicator of its quality: a higher prediction accuracy suggests a higher degree of determinism and, consequently, weaker cryptographic properties. For the experiment, we generated multiple datasets using both cryptographically secure (e.g., based on hardware entropy sources) and weak generators (like the linear congruential method). Each generated sequence was treated as a time series. We then applied a suite of forecasting models, ranging from classical statistical methods like ARIMA to more complex machine learning models, including LSTMs and Gradient Boosting. The choice of a diverse set of models was crucial to ensure that the results were not biased towards a specific forecasting technique. Each model was trained on a segment of the sequence and tasked with predicting subsequent values. The proposed χ2-based metric was then used to compare the forecasted values against the actual subsequent values in the sequence. The key finding was a strong correlation: the outputs of weak generators showed a statistically significant deviation from the expected random distribution under the χ2 test when analyzed through the lens of forecasting errors. In contrast, cryptographically strong generators demonstrated no predictable patterns, resulting in forecast errors that were indistinguishable from random noise. This approach provides a novel, data-driven methodology for evaluating RNGs, complementing traditional statistical test suites like NIST SP 800-22 by introducing the concept of predictability as a core measure of weakness.

KW - Machine learning algorithms

KW - Accuracy

KW - Time series analysis

KW - Stability criteria

KW - Predictive models

KW - NIST

KW - Generators

KW - Cryptography

KW - Forecasting

KW - Testing

KW - forecasting

KW - random number generators

KW - cryptographic stability

KW - r-measure

KW - automaton

UR - https://www.scopus.com/pages/publications/105031766628

UR - https://www.mendeley.com/catalogue/9f8b0108-760e-33b0-8b8a-a56d731e657c/

U2 - 10.1109/apeie66761.2025.11289286

DO - 10.1109/apeie66761.2025.11289286

M3 - Chapter

SN - 979-8-3315-5917-5

SP - 1

EP - 4

BT - 2025 IEEE XVII International Scientific and Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE)

PB - Institute of Electrical and Electronics Engineers Inc.

ER -