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Abstract：
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.
摘要：
经典的一维混沌映射具有许多理想的特性，非常适合许多不同的科学领域，尤其是密码学。在本文中,我们提出了一种通过使用一维（1D）混沌映射来构造高维（HD）循环对称混沌映射的想法。以两个构造的三维循环对称混沌映射为例，命名为三维循环对称Logistic映射(3D-CSLM)和三维循环对称切比雪夫映射(3D-CSCM),分别。数值实验表明，新地图具有更好的动力学性能，它们的参数范围更广，与原始地图相比。此外，为了验证它在图像加密中的效果，提出了一种基于3D-CSLM和DNA编码的图像加密算法。DNA方法用于图像加密可以提高置换和扩散的效率。首先,该算法使用3D-CSLM生成混沌序列，用于DNA操作规则选择和像素置换。然后通过DNA的XOR运算实现扩散,最后形成一个加密的图像。仿真实验结果表明,该方案具有良好的安全性能和较强的抗攻击能力。
