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Generalized triangle group based S-box construction for secure image encryption.

Aqsa Zafar Abbasi1, Ayesha Rafiq1, Ines Hilali Jaghdam2

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Summary

This study introduces a novel S-box design using Generalized Triangle Groups (GTG) for enhanced RGB image encryption. The new method offers superior nonlinearity and cryptanalysis resistance compared to existing techniques.

Keywords:
Algebraic CryptographyGeneralized Triangle GroupRGB Image EncryptionS-Box

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Area of Science:

  • Cryptography and Network Security
  • Applied Mathematics
  • Digital Image Processing

Background:

  • Cyber image security is critical for transmitting sensitive data over insecure networks.
  • Existing image encryption methods often suffer from poor security, efficiency, or flexibility.
  • Conventional S-box designs and chaotic maps have limitations in resisting cryptanalysis.

Purpose of the Study:

  • To propose a new S-box design method using Generalized Triangle Groups (GTG) for robust image encryption.
  • To evaluate the cryptographic properties and performance of the proposed S-box in an RGB image encryption system.
  • To demonstrate the superiority of the GTG-based approach over state-of-the-art methods.

Main Methods:

  • Mathematical parameterization of GTG to create nonlinear and bijective S-boxes.
  • Analysis of cryptographic attributes: nonlinearity, differential uniformity, Strict Avalanche Criterion (SAC), and attack resistance.
  • Integration of the designed S-boxes into an RGB image encryption scheme for substitution and permutation.

Main Results:

  • The proposed S-box exhibits high nonlinearity (112) and a balanced SAC (≈0.50).
  • Achieved excellent resistance against linear and differential attacks with high entropy (≈8.0), NPCR (>99.8%), and UACI (≈33.3%).
  • Demonstrated superior diffusion and confusion characteristics compared to existing algorithms.

Conclusions:

  • The GTG-based S-box design offers enhanced nonlinearity, diffusion, and confusion for RGB image encryption.
  • The proposed scheme provides improved cryptanalysis resistance and comparable computational efficiency.
  • This method represents a significant advancement in secure image communication over networks.