Construction of high-dimensional cyclic symmetric chaotic map with one-dimensional chaotic map and its security application.

Classical one-dimensional chaotic map has many ideal characteristics which is quite suitable for many different kinds of scientific fields, especially cryptography. In this paper, we propose an idea of constructing high-dimensional (HD) cyclic symmetric chaotic maps by using one-dimensional (1D) chaotic map. Two constructed 3D cyclic symmetric chaotic maps are taken as the examples, named three-dimensional cyclic symmetric logistic map (3D-CSLM) and three-dimensional cyclic symmetric Chebyshev map (3D-CSCM), respectively. Numerical experiments show that the new maps possesses better dynamical performances, and their parameters have a wider range, compared with the original map. Furthermore, to verify its effect in image encryption, a novel image encryption algorithm based on 3D-CSLM and DNA coding is proposed. DNA method for image encryption can improve the efficiency of permutation and diffusion. Firstly, the algorithm uses 3D-CSLM to generate chaotic sequences for DNA operation rule selection and pixel permutation. Then through the DNA XOR operation to achieve diffusion, and finally form an encrypted image. Several simulation tests results indicate that the proposal has a promising security performance and strong anti-attack ability.