Random Numbers from a Delay Equation

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• 作者：Julian Self ; Michael C. Mackey
• 关键词：Pseudorandom number generator (PRNG) ; Random number generator (RNG) ; Differential delay equation (DDE) ; Deterministic chaos
• 刊名：Journal of Nonlinear Science
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：26
• 期：5
• 页码：1311-1327
• 全文大小：1,226 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Mathematical and Computational Physics
  Mechanics
  Applied Mathematics and Computational Methods of Engineering
  Economic Theory
  
• 出版者：Springer New York
• ISSN：1432-1467
• 卷排序：26

文摘

Delay differential equations can have “chaotic” solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01’s very stringent “Big Crush” battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here.