掲載種別：研究論文（国際会議プロシーディングス）  

Pseudorandom number generators are essential for various stochastic simulations in physics, economics, engineering, etc. In this study, we propose a practical method for estimating appropriate sample sizes for lagged Fibonacci generators, one of the most traditional and widely used pseudorandom number generators. This estimation is based on an analogy with the theoretical one-dimensional random walk. The proposed method is formulated using a weight enumeration polynomial and the MacWilliams identity in coding theory. Generally, a weight enumeration polynomial requires an intractable exhaustive check of the seeds. However, under certain conditions, the MacWilliams identity allows for the direct derivation of the weight enumeration polynomial. To improve efficiency, we employ a heuristic technique to approximate the weight enumeration polynomial by truncating “non-essential” terms motivated by Fourier analysis in signal processing.

DOI： 10.3233/FAIA241398

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掲載種別：研究論文（学術雑誌）  

Xorshift128+ is a newly proposed pseudorandom number generator (PRNG), which is now the standard PRNG on a number of platforms. We demonstrate that three-dimensional plots of the random points generated by the generator have visible structures: they concentrate on particular planes in the cube. We provide a mathematical analysis of this phenomenon.

DOI： 10.1016/j.cam.2021.113791

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

NIST SP800-22 is one of the most widely used statistical testing tools for pseudorandom number generators (PRNGs). This tool consists of 15 tests (one-level 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 two-level 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.

DOI： 10.1007/s13160-020-00434-y

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記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：日本数学教育学会高専・大学部会  

CiNii Books

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/j.matcom.2018.08.005

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開催年月日： 2024年11月

記述言語：英語   会議種別：口頭発表（一般）  

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開催年月日： 2024年9月

記述言語：英語   会議種別：口頭発表（一般）  

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