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A New Hyperchaotic 4D-FDHNN System with Four Positive Lyapunov Exponents and Its Application in Image Encryption.

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This study introduces a novel hyperchaotic four-dimensional fractional discrete Hopfield neural network (4D-FDHNN) system for secure image encryption. The proposed system utilizes fractal-based confusion and Hilbert dynamic random diffusion for enhanced security and efficiency.

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Area of Science:

  • Computational Neuroscience
  • Chaos Theory
  • Cryptography

Background:

  • The need for robust image encryption methods is growing.
  • Existing chaotic systems may lack sufficient complexity for advanced security applications.

Purpose of the Study:

  • To propose a novel hyperchaotic four-dimensional fractional discrete Hopfield neural network (4D-FDHNN) system.
  • To design a secure image encryption scheme utilizing the proposed chaotic system.

Main Methods:

  • Verification of chaotic dynamics using iterative trajectory, phase diagrams, attractor diagrams, 0-1 test, sample entropy, and Lyapunov exponents.
  • Image encryption incorporating a fractal-like model for confusion and a Hilbert dynamic random diffusion method.

Main Results:

  • The 4D-FDHNN system exhibits hyperchaotic behavior with four positive Lyapunov exponents.
  • The proposed encryption scheme demonstrates high complexity and security through fractal confusion and dynamic diffusion.
  • Simulation and security analyses confirm the algorithm's efficiency and resilience against common attacks.

Conclusions:

  • The developed 4D-FDHNN system provides a strong foundation for secure communication.
  • The novel image encryption scheme offers enhanced security and efficiency compared to existing methods.
  • The proposed approach is effective in resisting various cryptanalytic attacks.