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A new scalable evaluation method for random number generators: a permutation-based approach.

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Název: A new scalable evaluation method for random number generators: a permutation-based approach.
Autoři: Etem, Taha1 (AUTHOR) tahaetem@karatekin.edu.tr
Zdroj: Communications in Statistics: Simulation & Computation. Nov2025, p1-16. 16p. 12 Illustrations.
Témata: *STATISTICAL hypothesis testing, RANDOM number generators, EVALUATION methodology, VISUALIZATION, UNIFORM distribution (Probability theory)
Abstrakt: AbstractRandom number generators are generally evaluated by statistical test suites, but they have limitations in comparing and ranking the effective randomness of generators that pass all tests. This paper introduces a novel permutation-based evaluation method that quantifies an RNG’s ability to produce a comprehensive and uniform distribution of values across the number space. The proposed approach converts the high bit output of an RNG to lower bit numbers and examines how fully the RNG covers the range of possible values and in what proportions. This permutation analysis extracts new insights by visualizing number production patterns and calculating metrics like percentage coverage and quantity distribution across all outputs. Four RNG scenarios are evaluated using this method—a low-quality linear congruential generator (LCG), a modern LCG, a high-entropy TRNG based on ring oscillators, and an intentionally flawed counter-based generator. While all passed some statistical tests, permutation analysis reveals distinct quality differences. Low-ranking RNGs failed to generate many possible values, while the true RNG demonstrated superior comprehensive and uniform coverage. The permutation-based technique provides a complementary quality measure for RNGs that can discriminate effective randomness beyond passing statistical tests. The work introduces new visualization techniques and quantitative metrics valuable for comparing RNGs. [ABSTRACT FROM AUTHOR]
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Abstrakt:AbstractRandom number generators are generally evaluated by statistical test suites, but they have limitations in comparing and ranking the effective randomness of generators that pass all tests. This paper introduces a novel permutation-based evaluation method that quantifies an RNG’s ability to produce a comprehensive and uniform distribution of values across the number space. The proposed approach converts the high bit output of an RNG to lower bit numbers and examines how fully the RNG covers the range of possible values and in what proportions. This permutation analysis extracts new insights by visualizing number production patterns and calculating metrics like percentage coverage and quantity distribution across all outputs. Four RNG scenarios are evaluated using this method—a low-quality linear congruential generator (LCG), a modern LCG, a high-entropy TRNG based on ring oscillators, and an intentionally flawed counter-based generator. While all passed some statistical tests, permutation analysis reveals distinct quality differences. Low-ranking RNGs failed to generate many possible values, while the true RNG demonstrated superior comprehensive and uniform coverage. The permutation-based technique provides a complementary quality measure for RNGs that can discriminate effective randomness beyond passing statistical tests. The work introduces new visualization techniques and quantitative metrics valuable for comparing RNGs. [ABSTRACT FROM AUTHOR]
ISSN:03610918
DOI:10.1080/03610918.2025.2588690