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

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.