Properties making a chaotic system a good Pseudo Random Number Generator

Abstract

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed.

10 pages, 3 figures, new version, title changed and minor corrections

References in corpus (6)

• Predictability: a way to characterize Complexity
• Chaos or Noise - Difficulties of a Distinction
• Pseudo Random Coins Show More Heads Than Tails
• Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
• Entropy of Pseudo Random Number Generators
• Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards

Cited by in corpus (16)

• Recommendations and illustrations for the evaluation of photonic random number generators
• A dynamical approach to generate chaos in a micromechanical resonator
• New Enhanced Chaotic Number Generators
• Periodicity Analysis of the Logistic Map over Ring ${\mathbb{Z}}_{3^n}$
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• Anosov C-systems and random number generators
• Evaluating Quality of Chaotic Pseudo-Random Generators: Application to Information Hiding
• Randomness Quality of CI Chaotic Generators: Applications to Internet Security
• Random Numbers from a Delay Equation
• Maximally Chaotic Dynamical Systems and Fundamental Interactions
• The Graph Structure of the Generalized Discrete Arnold's Cat Map
• Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
• Role of Symmetry and Geometry in a chaotic Pseudo-Random Bit Generator
• Device-independent Shannon entropy certification
• Maximally chaotic dynamical systems of Anosov-Kolmogorov