Checking the quality of approximation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml84" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi>p</mml:mi></mml:math>-values in statistical tests for random number generators by using a three-level test

Haramoto, Hiroshi; Matsumoto, Makoto

doi:10.1016/j.matcom.2018.08.005

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…The p-value uniformity test requires at least 55 samples. As mentioned before, it is remarked that passing the NIST SP 800-22 does not ensure a sequence to be truly random (Kim et al 2020;Fan et al 2014;Haramoto and Matsumoto 2019).…”

Section: Test Descriptionmentioning

confidence: 99%

Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

Tamura

Shikano

2020

Mathematics for Industry

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A cloud quantum computer is similar to a random number generator in that its physical mechanism is inaccessible to its users. In this respect, a cloud quantum computer is a black box. In both devices, its users decide the device condition from the output. A framework to achieve this exists in the field of random number generation in the form of statistical tests for random number generators. In the present study, we generated random numbers on a 20-qubit cloud quantum computer and evaluated the condition and stability of its qubits using statistical tests for random number generators. As a result, we observed that some qubits were more biased than others. Statistical tests for random number generators may provide a simple indicator of qubit condition and stability, enabling users to decide for themselves which qubits inside a cloud quantum computer to use.

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Section: Test Descriptionmentioning

confidence: 99%

Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

Tamura

Shikano

2020

Mathematics for Industry

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“…The p-value uniformity test requires at least 55 samples. As mentioned before, it is remarked that passing the NIST SP 800-22 does not ensure a sequence to be truly random [21,22,23].…”

Section: Cumulative Sums Testmentioning

confidence: 99%

Quantum Random Numbers generated by the Cloud Superconducting Quantum Computer

Tamura,

Shikano

2019

Preprint

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A cloud quantum computer is similar to a random number generator in that its physical mechanism is inaccessible to the users. In this respect, a cloud quantum computer is a black box. In both devices, the users decide the device condition from the output. A framework to achieve this exists in the field of random number generation in the form of statistical tests for random number generators. In the present study, we generated random numbers on the 20-qubit cloud quantum computer and evaluated the condition and stability of its qubits using statistical tests for random number generators. As a result, we observed that the qubits varied in bias and stability. Statistical tests for random number generators may provide a simple indicator of qubit condition and stability, enabling users to decide for themselves which qubits inside a cloud quantum computer to use.

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“…First, we consider the twolevel test for the following three one-level tests: the test for the Longest-Runof-Ones in a Block, the Overlapping Template Matching test, and the Linear Complexity test. Note that we apply a modification to the test for the Longest-Run-of-Ones in a Block to improve the approximation of p-values [3].…”

Section: Computing the Distributions Of P-values Of Some Statistical ...mentioning

confidence: 99%

“…Later, Pareschi et al [15] found a further good approximation value σ 2 2 = 0.05 • 0.95n/3.8. According to [3], we use σ 2 2 for variance in the following experiments.…”

Section: Monte Carlo Computation Of the Distributions Of P-valuesmentioning

confidence: 99%

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

Haramoto¹

2019

Preprint

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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.

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Checking the quality of approximation of p-values in statistical tests for random number generators by using a three-level test

Cited by 7 publications

References 12 publications

Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

Quantum Random Numbers Generated by a Cloud Superconducting Quantum Computer

Quantum Random Numbers generated by the Cloud Superconducting Quantum Computer

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

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