Improvement of pseudorandom number generators from viewpoint of algebra and statistics

2013 Fiscal Year Final Research Report

• Project/Area Number: 22740075
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Ehime University (2011-2013); Kure National College of Technology (2010)
• Principal Investigator: HARAMOTO Hiroshi 愛媛大学, 教育学部, 講師 (40511324)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Keywords: 擬似乱数 / 代数学 / 応用数学 / 統計数学

Research Abstract

(1) We proposes an adaptive modification of statistical tests, in particular TestU01. This procedure automatically increases the sample size, and tests the PRNG again. It stops when the p-value falls in a clearly rejectable range. (2) We have implemented the codes of the jumping-ahead for MT19937 and WELL19937, in C and C++ languages. These are distributed from a homepage. (3) we report a method to compute the weight distribution of the second to the sixth lowest bits of several PRNGs by using MacWilliams identity.

Research Products

• [Journal Article] A non-empirical test on the second to the sixth least significant bits of pseudorandom number generators (2013)
  • Author(s): Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, Yuki Otsuka
  • Journal Title: Monte Carlo and Quasi-Monte Carlo Methods 2012 Pages: 417-426
  • Peer Reviewed
• [Journal Article] MacWilliams 恒等式による擬似乱数列の下位ビットの分布計算 (2012)
  • Author(s): 原本博史, 松本眞, 西村拓士, 大塚祐樹
  • Journal Title: 日本応用数理学会2012年度年会講演予稿集 Pages: 43-44
• [Presentation] An approximation of the weight distribution of the n-th bits of pseudorandom number generators (2014)
  • Author(s): Hiroshi Haramoto, Makoto Matsumoto
  • Organizer: Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC2014)
  • Place of Presentation: ルーヴェン・ベルギー
  • Year and Date: 2014-04-09
• [Presentation] MacWilliams 恒等式による擬似乱数の非統計的検定 (2012)
  • Author(s): 原本博史, 松本眞, 西村拓士, 大塚祐樹
  • Organizer: Workshop on Galois point and related topics
  • Place of Presentation: 山形大学
  • Year and Date: 2012-09-16
• [Presentation] MacWilliams 恒等式による擬似乱数列の下位ビットの分布計算 (2012)
  • Author(s): 原本博史, 松本眞, 西村拓士, 大塚祐樹
  • Organizer: 日本応用数理学会2012年年会
  • Place of Presentation: 稚内市
  • Year and Date: 2012-08-29
• [Presentation] A non-empirical test on the second to the sixth lowest bits of pseudorandom number generators (2012)
  • Author(s): Hiroshi Haramoto
  • Organizer: Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation
  • Place of Presentation: 東京大学
  • Year and Date: 2012-06-13
• [Presentation] A non-empirical test on the second to the sixth least significant bits of pseudorandom number generators (2012)
  • Author(s): Hiroshi Haramoto, Makoto Matsumoto, Takuji Nishimura, Yuki Otsuka
  • Organizer: Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2012)
  • Place of Presentation: シドニー・オーストラリア
  • Year and Date: 2012-02-13
• [Book] 線形代数 (2013)
  • Author(s): 河東泰之他(編), 原本博史(共著)
  • Total Pages: 121-139
  • Publisher: サイエンス社
• [Book] 線形代数問題集 (2013)
  • Author(s): 河東泰之他(編), 原本博史(共著)
  • Total Pages: 70-89
  • Publisher: サイエンス社
• [Book] 基礎数学 (2012)
  • Author(s): 河東泰之他(編), 原本博史(共著)
  • Total Pages: 206-220
  • Publisher: サイエンス社
• [Book] 基礎数学問題集 (2012)
  • Author(s): 河東泰之他(編), 原本博史(共著)
  • Total Pages: 82-93
  • Publisher: サイエンス社
• [Remarks]
  • URL: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/JUMP/index.html