Symmetric Grayscale Image Encryption Based on Quantum Operators with Dynamic Matrices

Image encryption is crucial for ensuring the confidentiality and integrity of digital images, preventing unauthorized access and alterations. However, existing encryption algorithms often involve complex mathematical operations or require specialized hardware, which limits their efficiency and practicality. To address these challenges, we propose a novel image encryption scheme based on the emulation of fundamental quantum operators from a multi-braided quantum group in the sense of Durdevich. These operators—coproduct, product, and braiding—are derived from quantum differential geometry and enable the dynamic generation of encryption values, avoiding the need for computationally intensive processes. Unlike quantum encryption methods that rely on physical quantum hardware, our approach simulates quantum behavior through classical computation, enhancing accessibility and efficiency. The proposed method is applied to grayscale images with 8-, 10-, and 12-bit depth per pixel. To validate its effectiveness, we conducted extensive experiments, including visual quality metrics (PSNR, SSIM), randomness evaluation using NIST 800-22, entropy and correlation analysis, key sensitivity tests, and execution time measurements. Additionally, comparative tests against AES encryption demonstrate the advantages of our approach in terms of performance and security. The results show that the proposed method provides a high level of security while maintaining computational efficiency.