Second-level NIST Randomness Tests for Improving Test Reliability
Open accessAbstract
Testing random number generators (RNGs) is as important as designing them. The paper considers the NIST test suite SP 800-22 and shows that, as suggested by NIST itself, to reveal non-perfect generators a more in-depth analysis should be performed using the outcomes of the suite over many generated sequences. Testing these second-level statistics is not trivial and, relying on a proper model that takes into account the errors due to the approximations in the first level tests, a tuning of the parameters in the simplest cases was propose. The validity of this consideration is widely supported by experimental results on several RNG currently employed by major IT players, as well as a chaos-based RNG designed by authors.
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The failure of two-level tests for extremely large N is due to approximation errors in the computation of basic test p-values, causing deviation of p distribution from uniform.
“According to [12], this problem is due to approximation errors in the computation of the p -value of basic tests, which result in a deviation of the distribution of p from the expected uniform one.”
From On Statistical Tests for Randomness Included in the NIST SP800-22 Test Suite and Based on the Binomial Distribution (2012) · cites this paper as [12]
An upper bound for the error between the approximated p-value p and the actual p0 in the Frequency Test can be computed using the Berry-Esséen inequality.
“Thanks to Berry and Ess´ een inequality [22], in [12] we were able to compute an upper bound in the Frequency Test for the error between the approximated p -value p and the actual one p 0 :”
From On Statistical Tests for Randomness Included in the NIST SP800-22 Test Suite and Based on the Binomial Distribution (2012) · cites this paper as [12]
The value N < 5975 is coherent with the value found in Section II-C and coming from [12].
“Note that this value is coherent with the value found in Section II-C and coming from [12].”
From On Statistical Tests for Randomness Included in the NIST SP800-22 Test Suite and Based on the Binomial Distribution (2012) · cites this paper as [12]
Cites
Bassham, L. E., Rukhin, A. L., Soto, J., Nechvatal, J. R., Smid, M. E., Barker, E. B., Leigh, S. D., Levenson, M., Vangel, M., Banks, D. L., et al. (2010) · NIST Special Publication 800-22 Revision 1a · doi:10.6028/nist.sp.800-22r1a · Cited by 3,617 · see citing works
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Pareschi, F., Rovatti, R., & Setti, G. (2012) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2012.2185227 · Cited by 189 · see citing works
Self-citationError Analysis of NIST SP 800-22 Test Suite
Chen, D., Chen, H., Fan, L., & Luo, K. (2023) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2023.3287391 · Cited by 14 · see citing works
Study on upper limit of sample size for a two-level test in NIST SP800-22
Haramoto, H. (2021) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/s13160-020-00434-y · Cited by 5 · see citing works
“d level makes the two-level test makes reliable: we can maximize the power and avoid erroneous rejections of the two-level test. You can nd further descriptions and explanations of two-level tests in [6, 7, 8, 9, 14, 15]. However, NIST recommends that the sample size at the second level should be on the order of the i…”
Background
- Authors
- Pareschi, F., Rovatti, R., & Setti, G.
- Affiliations
- University of Ferrara (IT)
- University of Bologna (IT)
- Venue
- 2007 IEEE International Symposium on Circuits and Systems (ISCAS)
- Publisher
- IEEE
- Published
- 2007-05
- Pages
- 1437-1440
- ISSN
- 0271-4302 (ISSN-L)
- OpenAlex
- W2116948326
- Cited by
- 45
- References
- 1
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 1 · 2023: 1 · 2022: 1 · 2021: 5 · 2020: 2 · 2019: 4 · 2018: 4 · 2017: 4 · 2016: 1 · 2014: 2 · 2013: 3 · 2012: 1
- FWCI
- 1.73
- Type
- conference paper
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- IEEE International Symposium on Circuits and Systems proceedings (publishedVersion)
- PORTO@Iris (submittedVersion, other-oa)
- Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
- PORTO Publications Open Repository TOrino (Politecnico di Torino) (submittedVersion)
- Institutional Research Information System University of Ferrara (University of Ferrara) (submittedVersion)
- Funders
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- random number generators, NIST SP 800-22, randomness testing, test reliability
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