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From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology.

Luciana De Micco1,2,3, Maximiliano Antonelli1,2,3, Osvaldo Anibal Rosso4

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This study introduces a new method for creating Pseudo-Random Number Generators (PRNGs) from continuous-time chaotic systems. The approach ensures chaotic behavior and eliminates correlations, leading to PRNGs that pass rigorous statistical tests.

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NISTPRNGchaosdiehardpermutation complexitypermutation entropystatistical properties

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Area of Science:

  • Chaos theory applications in electronics
  • Information theory in random number generation

Background:

  • Continuous-time chaotic systems are underutilized for Pseudo-Random Number Generators (PRNGs) due to temporal correlations and computational demands.
  • Selection of time step and discretization significantly impacts the statistical and chaotic properties of these systems.

Purpose of the Study:

  • To analyze the influence of time step and discretization on chaotic systems for PRNG applications.
  • To develop a methodology for generating high-quality PRNGs from continuous-time chaotic systems.
  • To ensure generated sequences exhibit chaotic oscillation while minimizing inner and temporal correlations.

Main Methods:

  • Interpreting the time step as a parameter for discrete maps.
  • Applying information theory quantifiers like permutation entropy and complexity.
  • Evaluating generated sequences using Marsaglia Diehard and NIST statistical test suites.

Main Results:

  • A methodology was developed to maintain chaotic oscillation and destroy temporal correlations in continuous-time chaotic systems.
  • The proposed Pseudo-Random Number Generators (PRNGs) demonstrate excellent statistical properties and high throughput.
  • Generated sequences successfully passed both Marsaglia Diehard and NIST tests.

Conclusions:

  • The proposed method effectively transforms continuous-time chaotic systems into reliable PRNGs.
  • The methodology is versatile and applicable to various continuous-time chaotic systems.
  • Hardware implementation of the proposed PRNGs is resource-efficient.