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Updated: Sep 18, 2025

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Robust Image Encryption with 2D Hyperchaotic Map and Dynamic DNA-Zigzag Encoding.

Haijun Zhang1,2, Xiaojiao Liu2, Kehan Chen2

  • 1Chongqing Research Institute, Changchun University of Science and Technology, Chongqing 401135, China.

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|June 26, 2025
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Summary
This summary is machine-generated.

A new two-dimensional exponent-logarithm-sine chaotic map (2D-ELSCM) offers strong randomness for secure image encryption. The proposed scheme uses DNA encoding and Zigzag transform for robust data protection.

Keywords:
DNA-zigzag encodinghyperchaotic mapimage encryptionshuffle algorithm

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Area of Science:

  • Cryptography and Information Security
  • Applied Mathematics
  • Computer Science

Background:

  • Chaotic maps are essential for secure encryption due to their complex dynamics.
  • Existing chaotic maps often lack sufficient randomness or complexity for advanced security needs.
  • Image encryption requires robust methods to protect sensitive visual data.

Purpose of the Study:

  • To introduce a novel two-dimensional hyperchaotic map, the 2D exponent-logarithm-sine chaotic map (2D-ELSCM).
  • To develop and evaluate a secure image encryption scheme based on the 2D-ELSCM.
  • To assess the encryption scheme's performance against various security metrics and potential attacks.

Main Methods:

  • Design of the 2D-ELSCM using exponential, logarithmic, and sine functions.
  • Evaluation of chaotic properties using Largest Lyapunov Exponent (LLE), Permutation Entropy (PE), Sample Entropy (SE), Kolmogorov Entropy (KE), and the 0-1 test.
  • Implementation of an image encryption scheme involving improved Knuth-Durstenfeld shuffle (IKDS), DNA encoding, and Zigzag transform.
  • Generation of chaotic map initial conditions using SHA-512 hash of plaintext and an external key.

Main Results:

  • The 2D-ELSCM demonstrated high chaos with LLE=8.3175, PE=0.9998, SE=1.9826, KE=2.1117, and 0-1 test result=0.9970.
  • The map successfully passed NIST randomness tests, confirming its complexity.
  • The encryption scheme achieved near-zero correlation coefficients, average NPCR of 99.6090%, and UACI of 33.4707% for encrypted images.
  • The scheme showed strong resistance to attacks and excellent encryption quality.

Conclusions:

  • The 2D-ELSCM is a highly random and complex chaotic map suitable for cryptographic applications.
  • The proposed image encryption scheme offers significant security improvements and robustness.
  • The integration of the novel chaotic map and advanced encryption techniques provides a promising solution for secure image transmission and storage.