A novel image encryption scheme based on Logistic cosine cascade maps

Abstract A two-dimensional Logistic cosine cascade map (2D-LCCM) and a three-dimensional Logistic cosine cascade map (3D-LCCM) are proposed based on a logistic map and infinite collapse cascade model. We analyze the chaotic properties of 2D-LCCM and 3D-LCCM, such as Lyapunov exponential spectrum, attractors, and complexity, which show that the 2D-LCCM and 3D-LCCM are hyperchaotic and have large chaotic regions. We also proposed a DNA encryption algorithm based on double chaotic maps. 2D-LCCM was used for scrambling and 3D-LCCM for diffusion. First, the sequence no-duplicate zigzag transform (SNZT) is used to scramble the plaintext. Z-transform is applied to the permutation sequence to make the sequence more random. Then a repetition-free permutation associated with the plaintext is applied to each block, and the pixel position is effectively scrambled. Finally, DNA diffusion is performed using DNA coding to diffuse pixel values. Simulation results show that the algorithm has a good encryption effect, high efficiency and anti-interference performance. Therefore, the proposed new hyperchaotic map and DNA encryption algorithm can be effectively applied to the process of image encryption.