Image Encryption Based on Chebyshev Map and Infinite Collapse Map
Huizong Li, Bin Ge · Recent Patents on Engineering · 2025
Introduction: The transmission and storage of unencrypted images over networks can lead to privacy breaches, exposing sensitive visual content. Image encryption techniques provide an effective solution to safeguard private data. Conventional encryption algorithms often rely on one-dimensional chaotic maps, which suffer from limitations such as restricted chaotic orbits and narrow parameter ranges. To address these shortcomings, this study introduces a novel two-dimensional chaotic map, 2D-CICM (Two-Dimensional Chebyshev and Infinite Collapse Map), combining the Chebyshev map and the Infinite Collapse map. The randomness of 2D-CICM is rigorously validated through attractor analysis, Lyapunov exponent evaluation, and the 0-1 test. Additionally, an image encryption algorithm leveraging 2D-CICM is proposed. Method: The initial values and parameters of the chaotic map are dynamically generated based on the plaintext image';s dimensions and pixel values. The scrambling phase employs dual-level permutation, targeting both pixel positions and bit-level data. In the diffusion phase, two sets of chaotic sequences, along with plaintext image information, are utilized to alter pixel values, producing the ciphertext image. The proposed 2D-CICM algorithm is currently under patent application and incorporates technological innovations designed to broaden its applicability. Results: Simulations demonstrate that 2D-CICM exhibits robust performance, including an expansive key space (>2309), high key sensitivity (failure to decrypt with 10-14 key perturbations), nearideal entropy (7.9994 for Lena image), and resistance to differential attacks (NPCR 99.6126%, UACI 33.4681%). Discussion: By integrating the Chebyshev map and the Infinite Collapse map, the 2D-CICM algorithm addresses several limitations of traditional chaotic maps, such as narrow parameter ranges and discontinuous chaotic orbits. It effectively withstands diverse cryptographic attacks, ensuring superior security Conclusion: The 2D-CICM algorithm offers strong security guarantees and holds significant potential for applications in network information security and secure image communication.