A Method to Compute an Appropriate Sample Size of a Two-Level Test for the NIST Test Suite

Haramoto, Hiroshi; Matsumoto, Makoto

doi:10.1007/978-3-319-91436-7_15

Cited by 2 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we study practical upper limits of the sample sizes of the twolevel test. With our previous work [4], we derive upper limits of the two-level MT 2,000,000 3.54e-02 2.50e-01 9.63e-01 4.46e-01 7.60e-01 SHA-1 2,000,000 1.68e-01 3.68e-01 9.02e-01 7.97e-01 6.90e-01 DFT WELL 100,000 8.97e-01 1.03e-01 9.99e-01 1.87e-01 8.71e-01 SHA-1 100,000 8.01e-01 9.51e-01 8.82e-01 9.75e-01 5.92e-01 test for nine one-level tests in NIST SP800-22. The upper limits proposed in this paper reveals that NIST's recommendation of the second sample size, the order of the inverse of the significance level, might be misleading: appropriate order of the second sample size strongly depends on the one-level test and the first sample size.…”

Section: Discussionmentioning

confidence: 70%

“…The aim of this paper is to extend the previous work [4], in particular, we propose a practical upper limit of the sample size at the second level for each of the following six tests in NIST SP800-22: the Longest-Run-of-Ones in a Block, the Overlapping Template Matching test, the Linear Complexity test, the Random Excursions test, the Frequency test within a Block, and the Discrete Fourier Transform test. The results indicate that appropriate upper limits heavily depend on the one-level tests and sample sizes at the first level.…”

Section: Introductionmentioning

confidence: 96%

“…Their research is based on Berry-Esséen inequality [16], but it seems difficult to derive upper limits of the other one-level tests. By contrast, we propose a practical upper limit of the sample size at the second level for each of the Frequency test, the Binary Matrix Rank test and the Runs test [4]. Those upper limits are derived by the chi-squared discrepancy between the distribution of approximated p-values and the uniform distribution.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Study on upper limit of sample sizes for a two-level test in NIST SP800-22

Haramoto¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

NIST SP800-22 is one of the most widely used statistical testing tools for pseudorandom number generators (PRNGs). This tool consists of 15 tests (onelevel tests) and two additional tests (two-level tests). Each one-level test provides one or more p-values. The two-level tests measure the uniformity of the obtained p-values for a fixed one-level test. One of the two-level tests categorizes the p-values into ten intervals of equal length, and apply a chi-squared goodness-of-fit test. This two-level test is often more powerful than one-level tests, but sometimes it rejects even good PRNGs when the sample size at the second level is too large, since it detects approximation errors in the computation of p-values.In this paper, we propose a practical upper limit of the sample size in this two-level test, for each of six tests appeared in SP800-22. These upper limits are derived by the chi-squared discrepancy between the distribution of the approximated p-values and the uniform distribution U (0, 1). We also computed a "risky" sample size at the second level for each one-level test. Our experiments show that the twolevel test with the proposed upper limit gives appropriate results, while using the risky size often rejects even good PRNGs.We also propose another improvement: to use the exact probability for the ten categories in the computation of goodness-of-fit at the two-level test. This allows us to increase the sample size at the second level, and would make the test more sensitive than the NIST's recommending usage.

show abstract

Section: Discussionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation