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The large key space image encryption algorithm based on modulus synchronization between real and complex

P Muthukumar1, Nasreen Khan2

  • 1PG & Research Department of Mathematics, Gobi Arts & Science College, Gobichettipalayam, 638 453 Tamil Nadu India.

Multimedia Tools and Applications
|October 24, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel fractional-order hyper-chaotic system and a modulus synchronization method for real and complex systems. This enables a new, secure image encryption algorithm with a large key space.

Keywords:
Complex fractional-order systemsCoronavirus imageDigital image encryptionHyper-chaosModulus synchronization

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Fractional Calculus Applications
  • Complex Systems Analysis

Background:

  • Hyper-chaotic systems exhibit complex dynamical behaviors crucial for secure communications.
  • Fractional-order systems offer enhanced complexity and unpredictability compared to integer-order systems.
  • Synchronization of fractional-order systems is essential for secure information processing.

Purpose of the Study:

  • To construct and analyze a new fractional-order real hyper-chaotic system and its complex variable counterpart.
  • To propose a novel modulus synchronization scheme for synchronizing real and complex fractional-order systems.
  • To develop a new modulus synchronization-based encryption algorithm for digital images.

Main Methods:

  • Analysis of dynamical properties including stability of equilibrium points, phase plots, Lyapunov spectrum, and bifurcation analysis.
  • Design of non-linear controllers based on Lyapunov stability theory for achieving modulus synchronization.
  • Implementation and validation of a modulus synchronization encryption algorithm for digital images.

Main Results:

  • Successful construction and dynamical analysis of a new fractional-order real and complex hyper-chaotic system.
  • Demonstration of a novel modulus synchronization scheme for real and complex fractional-order systems.
  • Validation of a new image encryption algorithm based on modulus synchronization, showing a large key space and high efficacy compared to existing methods.

Conclusions:

  • The proposed fractional-order hyper-chaotic systems exhibit rich dynamical behaviors.
  • The novel modulus synchronization scheme effectively synchronizes disparate fractional-order systems.
  • The developed image encryption algorithm offers a secure and efficient solution for digital image protection.