Research of pseudorandom number generation by nonalgebraic method
| Project/Area Number |
17540111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Mie University |
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Principal Investigator |
YAGUCHI Hirotake Mie University, Faculty of Education, Professor, 教育学部, 教授 (40157970)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | pseudorandom number / algorithm / chaos mapping / hash function / 数値計算 |
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| Research Abstract |
The aim of this research is to investigate nonalgebraic and nonrecursive pseudorandom number generators (RNGs) which have different algorithm from other RNGs. Random number generators which are used now-a-days, such as the feed back shift register RNG, the Mersenne Twister RNG and so on, are designed so that they generate random numbers (RNs) sequentially on a single computer. Therefore it is not so easy to adjust their algorithm to parallel computations for recent parallel computers. However our random number generator SSR (Simplified Shift-Real) RNG directly generates the k-th random number by using chaos mappings Ф_x, x∈[1,2), and is suitable for parallel computations.
Up to this interval of research, it was known to generate a long sequence of RNGs using Ф^<24>_x(1). Fundamental research for improvement of randomness and for generation of GNs which have long digit was in the earlier stage.
In the first half of this research, by the joint work with Kubo, I. (Hiroshima Institute of Tec
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hnology), we clarified the properties of Ф, theoretically, and obtained the probability distribution H(t) of Ф_x(1), x ∈[1,2). From this we had a result that if we use Ф^<24>_x(ω_0)-Ф^<24>_x(ν_0) instead of Ф^<24>_x(1) for appropriately chosen ω_0 and ν_0, the randomness of SSR RNs is remarkably improved by virtue of the chaotic property of Ф_x.
In the latter half of the research interval we investigated the integralization of the SSR RNG. The SSR RNG essentially uses floating computations; and a floating point system usually depends on a computer system (especially on MPU). So SSIR occasionally generates slightly different RNs if a computer system is different. To avoid this problem we introduce the SSI RNG which has the same mechanism of SSR and uses no floating point computations. The SSI is realized by multiplicatioin and shift of 64-bit integers. The statistical tests supplied by NIST of USA show us that the properties of SSI RNG are of the same level with those of other well-known RNGs. These results were reported at the international conference MCQMC 2006. Because the algorithm of SSI does not depend on the length of the digit of RNs, it can be applied to generate long-digit RNs. As a preliminary result we constructed the hash function SSI160 which has 160-bit hashed values. Research of application of SSI will be continued in the future. Less
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Report
(3 results)
Research Products
(11 results)
