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New variable-order fractional chaotic systems for fast image encryption.

Guo-Cheng Wu1, Zhen-Guo Deng2, Dumitru Baleanu3

  • 1Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, People's Republic of China.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces novel variable-order fractional chaotic systems with a short memory concept, enhancing image encryption security and efficiency. The new models demonstrate rich chaotic dynamics and improved performance in practical applications.

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Area of Science:

  • Chaos theory
  • Fractional calculus
  • Cryptography

Background:

  • Fractional-order systems offer complex dynamics.
  • Existing chaotic systems have limitations in security and efficiency.
  • Image encryption requires robust and fast algorithms.

Purpose of the Study:

  • To propose new variable-order fractional chaotic systems.
  • To introduce a short memory concept for Caputo derivatives.
  • To apply these systems to block image encryption.

Main Methods:

  • Utilizing a piecewise constant function for fractional order definition.
  • Employing the predictor-corrector method for numerical solutions.
  • Extending the concept to fractional difference equations.

Main Results:

  • Demonstrated rich chaotic dynamics in the proposed systems.
  • Achieved generalized chaotic behaviors in fractional difference equations.
  • Successfully applied the models to block image encryption with varying fractional orders per block.

Conclusions:

  • The new variable-order fractional chaotic systems provide enhanced security for image encryption.
  • The proposed method significantly reduces encryption time.
  • This approach offers a promising direction for secure and efficient image encryption.