基于指数-余弦离散混沌映射的图像加密算法研究

为了增强图像数据传输的安全性，该文提出一种新型的2维指数-余弦离散混沌映射系统。该系统通过向1维余弦混沌系统中引入指数和高次幂非线性项来构造新型混沌映射。引入的非线性项对1维余弦混沌系统的迭代过程进行扰动得到更饱满的混沌相轨。利用Lyapunov指数谱、系统分岔图等对该系统的混沌动力学性质进行了验证。基于此混沌映射，该文提出一种新型的混沌图像加密算法。该算法通过“置乱-扩散-置乱”等加密环节，使得加密后的数据具有很好的数据安全性。加密图像数据的安全性分析也表明2维指数-余弦混沌映射具有较强的算法鲁棒性以及加密安全性。

A Novel Image Encryption Algorithm Based on Exponent-cosine Chaotic Mapping

In order to enhance the security of image data transmission, a novel two-dimensional exponent - cosine chaotic map is proposed. In this system, a new chaotic map is constructed by introducing exponent and high-power nonlinear terms into one dimensional cosine chaotic system. The nonlinear term is introduced to perturb the iterative process of one-dimensional cosine chaotic system to obtain fuller chaotic phase orbits. Lyapunov exponential spectrum and system bifurcation diagram are used to verify the features of chaotic system. Based on the chaotic map, a novel image encryption algorithm is proposed. The encrypted data has good encryption security by following a “scrambling-diffusion-scrambling” strategy. Security analysis of encrypted image data also shows that the two-dimensional exponential - cosine chaotic map has strong robustness and encryption security.