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Sum-discrepancy test on pseudorandom number generators
https://hiroshima.repo.nii.ac.jp/records/2007686
https://hiroshima.repo.nii.ac.jp/records/20076860fd5e523-958a-4b46-85ac-c292d2d840c2
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
MathComSimu_62_431.pdf (149.0 KB)
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| Item type | デフォルトアイテムタイプ_（フル）(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2023-03-18 | |||||||||
| タイトル | ||||||||||
| タイトル | Sum-discrepancy test on pseudorandom number generators | |||||||||
| 言語 | en | |||||||||
| 作成者 |
Matsumoto, Makoto
× Matsumoto, Makoto
× Nishimura, Takuji
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| アクセス権 | ||||||||||
| アクセス権 | open access | |||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
| 権利情報 | ||||||||||
| 権利情報 | Copyright (c) 2003 Elsevier Science | |||||||||
| 主題 | ||||||||||
| 主題Scheme | Other | |||||||||
| 主題 | Random number generation | |||||||||
| 主題 | ||||||||||
| 主題Scheme | Other | |||||||||
| 主題 | Fourier transform | |||||||||
| 主題 | ||||||||||
| 主題Scheme | Other | |||||||||
| 主題 | Statistical test | |||||||||
| 主題 | ||||||||||
| 主題Scheme | NDC | |||||||||
| 主題 | 350 | |||||||||
| 内容記述 | ||||||||||
| 内容記述 | We introduce a non-empirical test on pseudorandom number generators (prng), named sum-discrepancy test. We compute the distribution of the sum of consecutive m outputs of a prng to be tested, under the assumption that the initial state is uniformly randomly chosen. We measure its discrepancy from the ideal distribution, and then estimate the sample size which is necessary to reject the generator. These tests are effective to detect the structure of the outputs of multiple recursive generators with small coefficients, in particular that of lagged Fibonacci generators such as random() in BSD-C library, as well as add-with-carry and subtract-with-borrow generators like RCARRY. The tests show that these generators will be rejected if the sample size is of order 106. We tailor the test to generators with a discarding procedure, such as ran_array and RANLUX, and exhibit empirical results. It is shown that ran_array with half of the output discarded is rejected if the sample size is of the order of 4×1010. RANLUX with luxury level 1 (i.e. half of the output discarded) is rejected if the sample size is of the order of 2×108, and RANLUX with luxury level 2 (i.e. roughly 3/4 is discarded) will be rejected for the sample size of the order of 2.4×1018. In our previous work, we have dealt with the distribution of the Hamming weight function using discrete Fourier analysis. In this work, we replace the Hamming weight with the continuous sum, using a classical Fourier analysis, i.e. Poisson's summation formula and Levy's inversion formula. | |||||||||
| 言語 | en | |||||||||
| 出版者 | ||||||||||
| 出版者 | Elsevier Science | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | AO | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_b1a7d7d4d402bcce | |||||||||
| 関連情報 | ||||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | 10.1016/S0378-4754(02)00227-6 | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | isVersionOf | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://dx.doi.org/10.1016/S0378-4754(02)00227-6 | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 0378-4754 | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | AA00723761 | |||||||||
| 開始ページ | ||||||||||
| 開始ページ | 431 | |||||||||
| 書誌情報 |
Mathematics and Computers in Simulation Mathematics and Computers in Simulation 巻 62, 号 3-6, p. 431-442, 発行日 2003-03 |
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| 旧ID | 15036 | |||||||||
