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New method for the random number generation.

Many researches in a rich variety of sciences, including quantum, statistical, and nuclear physics, quantum chemistry, material science, and many others, rely heavily in their research on the use of random numbers. The most efficient way of generating sequences of random numbers is based on deterministic recursive rules, which produce pseudorandom numbers. The design of the incrementally powerful random number generators (RNG) that behave as realizations of independent uniformly distributed random variables and approximate ``true randomness'' [1] remains one of the major challenges for computational science.

A new method for constructing high-quality pseudorandom numbers generators (RNG) developed by Lev Barash and Lev Shchur [2] marks a breakthrough in the field. Traditionally, random numbers (RN) are the coordinates of some periodic trajectory, and correlations exist both along the trajectory and between bits of the given number. The proposed approach to making numbers less correlated is to generate an ensemble of uncorrelated trajectories, and use one bit (represented by two digits 0 and 1) from the position of each trajectory to construct s-bit number from s coordinates. Generation of the ensemble of trajectories is naturally parallel computation.

The series of generators are developed using new method with the efficient realizations for Pentium processors, making our RNGs  competitive with the best known generators. Generators were tested with the battery of calibrated sets of tests



Shown in the figure is neither Vasily Kandinsky nor Kasimir Malevich artistic work, but the visualization of the approach developed in [2]. Each region of the suprematic square denoted with the specific color, is coded by the five bits of the random numbers. The more bits included, the richer picture will appear and will be plotted, and more randomness will be generated.

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[1] D. Knuth, The art of the computer programming, Vol. 2, (Addison-Wesley, Cambridge, 1981)

[2] L. Barash and L.N. Shchur, Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation, arxiv.org: physics/0409069, Phys. Rev. E 73, 036701 (2006)

(c) ИТФ им. Л.Д. Ландау РАН,

(с) отдел прикладных сетевых исследований НЦЧ РАН