A novel 2D Log-Logistic–Sine chaotic map for image encryptionA novel 2D Log-Logistic–Sine chaotic map for image encryptionM. Wang et al.

Chaotic maps, with their unpredictability, sensitivity to initial conditions and control parameters, are highly suitable for cryptographic applications. However, most chaotic maps have drawbacks such as low complexity and insufficient security. To improve the dynamic complexity of chaotic maps, a novel 2D log-logistic–sine chaotic map (2D-LLSCM) based on nonlinear log function has been introduced. The introduction of this function significantly increases the nonlinear complexity of the chaotic map. In contrast to existing two-dimensional chaotic systems, the proposed 2D-LLSCM demonstrates an expanded chaotic scope and a more complex dynamic behavior. Besides, to break the gap between integer lossless image encryption and lossy mathematical-transform-based encryption schemes, an image encryption scheme using the 2D-LLSCM and nonlinear log-polar transform is designed. The chaotic matrix and the nonlinear log-polar transform are jointly employed to scramble and diffuse the plaintext. Moreover, the parameters employed in the log-polar transform are devised as cipher keys, thereby further expanding the key space. The experiments confirm the effectiveness enhancement of the proposed scheme, while the security analysis underscores its ability to resist various attacks.