Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

TL;DR

This paper introduces a new pseudorandom number generator based on dissipative dynamical systems, demonstrating its statistical robustness, equidistribution, and efficiency comparable to existing generators.

Contribution

It proposes a novel generator using dissipative dynamical systems with proven statistical independence and equidistribution properties, supported by extensive testing.

Findings

Achieves equidistribution of bit sequences

Proves statistical independence of bits at certain distances

Performs well in standard statistical tests

Abstract

The behavior of a family of dissipative dynamical systems representing transformations of 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.