Image encryption algorithm based on a new chaotic system with Rubik's cube transform and Brownian motion model

In this paper a new two-dimensional chaotic map based on Logistic map and Chebyshev map is proposed. The performance analysis and evaluation show the proposed map has a very wide range of chaos and good ergodicity. Further, a new image encryption algorithm is designed using the chaotic map with Rubik's Cube transform and Brownian motion model. The encryption process is ‘confusion - Rubik's cube transformation - diffusion’. In the confusion stage, a method combining Brownian motion theory and chaotic sequence is proposed. Then combining the advantages of chaotic system and Rubik's cube, a Rubik's Cube transformation algorithm is proposed. The scrambled pixel matrix and the chaotic matrix are spliced into a hexahedron structure, and the Rubik's Cube is dynamically scrambled through a pseudo-random sequence. Finally, the XOR operation is performed on the basis of the two-dimensional Hénon chaotic map. The experimental results show that the algorithm has the advantages of large key space, strong robustness and high security, and can resist common cryptanalysis attacks.