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Related Experiment Videos

Properties making a chaotic system a good pseudo random number generator.

Massimo Falcioni1, Luigi Palatella, Simone Pigolotti

  • 1Dipartimento di Fisica and Center for Statistical Mechanics and Complexity--INFM, Università di Roma La Sapienza P.le A. Moro 2, Rome 00185, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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We explored properties for deterministic algorithms to generate pseudo-random numbers, proposing the multidimensional Anosov symplectic map. This chaotic map offers high entropy, dimensionality, and long periods for robust random number generation.

Area of Science:

  • Chaos theory
  • Number theory
  • Computational mathematics

Background:

  • Deterministic algorithms can produce pseudo-random number sequences.
  • Key properties include high Kolmogorov-Sinai entropy, high dimensionality, and long periods.
  • The suitability of such algorithms is crucial for various computational applications.

Purpose of the Study:

  • To identify essential properties for deterministic pseudo-random number generation.
  • To propose and evaluate the multidimensional Anosov symplectic (cat) map as a pseudo-random number generator.
  • To analyze the chaotic features of the cat map relevant to random number generation.

Main Methods:

  • Discussed theoretical properties of deterministic pseudo-random number generators.
  • Proposed the multidimensional Anosov symplectic map.

Related Experiment Videos

  • Investigated chaotic features and their survival in a discrete-state version numerically.
  • Performed comparative testing against other generators.

    • Main Results:

    • Identified high Kolmogorov-Sinai entropy, high dimensionality, and long periods as critical properties.
    • Demonstrated the suitability of the multidimensional Anosov symplectic map.
    • Showcased chaotic features contributing to pseudo-randomness.
    • Confirmed the survival of key chaotic features in the discrete version.

    Conclusions:

    • The multidimensional Anosov symplectic map is a promising candidate for pseudo-random number generation.
    • Its chaotic properties are well-suited for producing high-quality random sequences.
    • Numerical investigations validate its effectiveness, especially in discrete-state implementations.