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Updated: May 28, 2026

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3D-TCM-Driven Bit-Level Image Encryption via S-Box Feedback Algorithm.

Jie Zhang1, Wenjie Zhou1, Mingxu Wang2

  • 1School of Electronics and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary
This summary is machine-generated.

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A new three-dimensional chaotic map (3D-TCM) enhances image encryption by improving complexity and stability. The proposed scheme offers strong security against attacks, validated by statistical tests.

Area of Science:

  • Cryptography
  • Applied Mathematics
  • Computer Science

Background:

  • Existing low-dimensional chaotic maps have limited dynamical complexity and stability, hindering their use in effective image encryption.
  • Dynamic degradation in current chaotic maps compromises the security of encrypted images.

Purpose of the Study:

  • To develop a novel three-dimensional chaotic map (3D-TCM) with enhanced dynamical complexity and stability for improved image encryption.
  • To design and evaluate a secure image encryption scheme utilizing the proposed 3D-TCM.

Main Methods:

  • A novel three-dimensional chaotic map (3D-TCM) was constructed and its dynamical properties were analyzed.
  • A plaintext-related image encryption scheme was developed, integrating bit-level permutation and S-box-based diffusion with the 3D-TCM.
Keywords:
S-box constructionchaos-based encryptionhyperchaotic systemsecure image encryption

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Main Results:

  • The 3D-TCM demonstrated superior dynamical complexity and stability compared to existing maps.
  • The proposed encryption scheme achieved high information entropy, low pixel correlation, and favorable NPCR/UACI values.
  • The scheme successfully passed the NIST SP800-22 statistical tests, indicating robust security.

Conclusions:

  • The novel 3D-TCM offers significant advantages in dynamical complexity and stability for image encryption.
  • The developed image encryption scheme provides strong resistance to differential attacks and exhibits overall robustness.
  • The findings suggest the proposed 3D-TCM and encryption scheme are effective for secure image data protection.