Chaos-based image encryption systems are essential for securing sensitive digital content. To address existing limitations and enhance security, we first present a new discrete model called the 2D Sinusoidal-Logarithmic-Exponential Modulation System (2D-SLEMS). Analysis of its dynamics reveals that for values of \(\theta \in (0, 1)\) , the system demonstrates a hyperchaotic characteristic, where the phase-plane trajectories are highly irregular and densely fill the space. This dynamic behavior makes the system a promising candidate for cryptographic purposes. Next, we propose a novel color image encryption scheme based on the 2D-SLEMS, incorporating a novel non-equilibrium dynamic S-box substitution method. In this scheme, we initially propose a method that links the plaintext to generate the system’s parameters and initial conditions for the 2D-SLEMS, ensuring that the encryption process exhibits a high level of sensitivity to the plaintext through the iterative control of the system. The scheme constructs four types of S-boxes of varying sizes: 6-bit, 8-bit, 10-bit, and 12-bit. The plaintext image is transformed into a bit matrix corresponding to the red, green, and blue (RGB) channels, where each row contains a 24-bit value. A column permutation is applied to the bit matrix, followed by the division of each 24-bit row into 6-bit, 8-bit, and 10-bit groups, with each group being substituted using its corresponding S-box. Subsequently, the 24-bit data is grouped into two 12-bit blocks and substituted using a 12-bit S-box. Finally, a pixel-level permutation and diffusion process is applied to generate the encrypted ciphertext image. The proposed image encryption scheme offers strong security. With a key space of \(2^{499}\) , the system shows excellent resistance to statistical analysis, as indicated by near-zero correlation coefficients. The NPCR and UACI values of 99.6006% and 33.4760% demonstrate high plaintext sensitivity, while the cipher image information entropy of 7.999277 suggests near-random images. These results confirm the robustness and security of the proposed encryption system.
