New variable-order fractional chaotic systems for fast image encryption

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.