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Chaos in a ring circuit.

E Farcot1, S Best2, R Edwards3

  • 1School of Mathematical Sciences, University of Nottingham, United Kingdom.

Chaos (Woodbury, N.Y.)
|May 3, 2019
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Summary
This summary is machine-generated.

This study introduces a novel ring-shaped logic circuit for a True Random Number Generator (TRNG). It utilizes chaotic dynamics for intrinsic randomness, offering a robust alternative to noise-based generators.

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Area of Science:

  • * Electrical Engineering
  • * Chaos Theory
  • * Computer Science

Background:

  • * Existing True Random Number Generators (TRNGs) often depend on physical noise sources, which can be unreliable.
  • * Idealized deterministic systems in current TRNGs are typically oscillatory, lacking inherent randomness.
  • * A robust TRNG design is needed that does not solely rely on external noise.

Purpose of the Study:

  • * To propose a ring-shaped logic circuit design for a True Random Number Generator (TRNG).
  • * To explore the use of chaotic dynamics for intrinsic randomness in TRNGs.
  • * To develop and analyze mathematical models for the proposed circuit.

Main Methods:

  • * Development of mathematical models using differential equations with steep sigmoid transfer functions.
  • * Analysis of the hard step-function limit, leading to a Glass network model.
  • * Investigation of the system's state space diagram and global attractor structure.
  • * Combination of analytical results and numerical simulations.

Main Results:

  • * The proposed circuit exhibits chaotic dynamics, ensuring intrinsic randomness.
  • * The global attractor is characterized by intertwined periodic paths with unpredictable trajectory alternations.
  • * The system demonstrates symmetry and invariance under cyclic group action.
  • * Symmetric chaos was confirmed through analytical and numerical methods.

Conclusions:

  • * The ring-shaped logic circuit based on chaotic dynamics provides a robust TRNG design.
  • * This approach offers intrinsic randomness, superior to noise-dependent methods.
  • * The validated chaotic behavior ensures reliable random number generation in hardware implementations.