Improved Lorenz chaotic map with dynamic zig-zag pattern for high-security digital image encryption

Abstract

This study proposes a secure image encryption framework based on an improved Lorenz chaotic map combined with a dynamic zig-zag permutation strategy. The improved chaotic mapping introduces dynamic perturbations to increase the complexity of chaotic trajectories and expand the key space, while the dynamic zig-zag traversal enhances pixel-level diffusion and minimizes residual pixel correlations during the permutation stage. Experimental evaluation was conducted on multiple RGB images with a resolution of 512×512 pixels. The proposed method achieved mean squared error (MSE) values of approximately 1800–1900 and peak signal-to-noise ratio (PSNR) values around 15.8 dB, indicating significant structural distortion between plaintext and cipher images. In addition, the obtained unified average changing intensity (UACI) (~33.4%) and number of pixels change rate (NPCR) (~99.61%) values approach the theoretical ideals, demonstrating strong resistance against statistical and differential attacks. Comparative analysis shows that the proposed framework provides stronger statistical robustness than conventional Lorenz-based encryption schemes. Furthermore, the decryption process successfully reconstructs the original images without information loss, confirming the correctness and reversibility of the scheme. These results indicate that integrating dynamic perturbations with adaptive zig-zag permutation effectively improves diffusion strength, key space complexity, and overall encryption robustness for secure multimedia image transmission.