Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size
Landau Institute for Theoretical Physics - 142432 Chernogolovka, Russia
Accepted: 13 May 2011
The behavior of a family of dissipative dynamical systems representing transformations a of a two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.
PACS: 02.70.Uu – Applications of Monte Carlo methods / 02.50.Ng – Distribution theory and Monte Carlo studies / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2011