CLSM-IEA: a novel cosine-logistic-sine map and its application in a new image encryption scheme

Chaotic systems have initial value sensitivity, unpredictability, and random-like properties, which are widely employed in image encryption schemes. However, many existing encryption schemes are deficient in security due to the shortcomings of the adopted chaotic maps and designed encryption algorithms, such as the discontinuous chaotic ranges, unevenly distributed trajectories, and the fixed orders to process the pixels. To solve these problems, we propose a new two-dimensional cosine-logistic-sine map (2D-CLSM), which is shown to have an extensive chaotic range and complex chaotic behaviors in terms of trajectory, bifurcation diagram, Lyapunov exponent, sample entropy, permutation entropy and TestU01. Furthermore, a new 2D-CSLM-based image encryption algorithm (CLSM-IEA) is designed, which includes the chaotic efficient permutation and random multi-directional diffusion operations. The chaotic efficient permutation is designed to quickly separate adjacent pixels into different positions randomly according to chaotic sequences generated from the 2D-CLSM. The random multi-directional diffusion secretly processes the pixels in diverse directions, the processes of which are determined by the chaotic matrix. The simulation analysis reveals that the proposed encryption algorithm has a higher security level than some state-of-the-art algorithms.