Novel 2D nonlinear sine-log-sqrt-logistic map and staircase block scrambling for a rapid image encryption algorithm

Abstract

In this paper, we propose a nonlinear 2-dimensional hyperchaotic map, called the 2D nonlinear sine-log-sqrt-logistic map (2D-NSLSLM), which introduces both the logarithmic function and the square root function. By incorporating the square root and logarithmic functions, the complexity of its nonlinear characteristics is further enhanced. This increases the dynamic complexity of the system and makes the system difficult to predict. Compared to some 2D chaotic maps, the 2D-NSLSLM exhibits higher sensitivity, a wider chaotic range, and more complex chaotic behavior. To explore its applications, 2D-NSLSLM is applied to formulate an image encryption algorithm with a new structure. The proposed algorithm consists of three steps: three rounds of staircase block scrambling, followed by one round of fast diffusion, and concluding with an additional round of staircase block scrambling. The simulation experiments prove that the structure not only has good anti-multiple-noise attacks and anti-differential attack ability, that is, it cleverly balances the robustness and anti-different attack ability, but also greatly improves the encryption speed. Through experiments and comparisons involving local Shannon entropy, information entropy, chosen plaintext attacks, and differential attacks, the results indicate that the new algorithm provides very secure encryption.