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Generalized double-humped logistic map-based medical image encryption.

Samar M Ismail1, Lobna A Said2, Ahmed G Radwan3,2

  • 1Faculty of IET, German University in Cairo (GUC), Cairo 11865, Egypt.

Journal of Advanced Research
|July 24, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a generalized Double Humped (DH) logistic map for secure pseudo-random number generation (PRNG). This enhanced map offers greater control and randomness for image encryption, improving secure communication of medical images.

Keywords:
Double-humpedImage encryptionMLENPCRNegative bifurcationUACI

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Cryptography and Information Security
  • Computational Mathematics

Background:

  • Pseudo-random number generation (PRNG) is crucial for secure communication.
  • Existing logistic maps may lack sufficient control and randomness for advanced applications.
  • Image encryption requires robust and efficient PRNG techniques.

Purpose of the Study:

  • To design and analyze a generalized Double Humped (DH) logistic map for enhanced PRNG.
  • To develop an image encryption algorithm utilizing the proposed generalized DH map.
  • To evaluate the security and robustness of the encryption system for medical images.

Main Methods:

  • Design of the generalized Double Humped (DH) logistic map with a new control parameter.
  • Analysis of the map's dynamic behavior: fixed points, stability, Lyapunov exponent, and bifurcation diagrams.
  • Development of an image encryption algorithm based on the generalized DH map's PRNG.
  • Comprehensive security analysis: key sensitivity, key-space, histogram, correlation, MAE, NPCR, UACI, noise attack robustness, and NIST tests.

Main Results:

  • The generalized DH map offers improved control over the chaotic range and exhibits a zooming effect in its bifurcation diagram.
  • The proposed image encryption algorithm demonstrates high security and robustness against various attacks.
  • The system achieves efficient and secure transfer of medical images (MRI, X-ray).
  • NIST test results confirm the efficiency and randomness of the generated sequences.

Conclusions:

  • The generalized DH logistic map provides a powerful tool for designing controllable and random PRNG sequences.
  • The developed image encryption system offers a secure and reliable solution for medical image communication.
  • The proposed method outperforms previous approaches in terms of security and controllability.