中文摘要：

提出一个利用广义Logistic映射构造的二维非线性混沌映射，采用相图、分岔图分析方法，研究该混沌映射的非线性动态特性；利用该二维混沌方程生成混沌序列，将混沌序列进行优化改进，生成密钥序列；采用输出反馈的加密方式，改变图像的像素，达到加密的目的。实验仿真结果表明：该加密算法对明文和密文都非常敏感，混沌序列的选择极其敏感地依赖于明文，有效地提高了抵御选择明文攻击的能力；密文图像信息熵为7.974 3，接近理想值8.000 0，因而加密图像像素具有类随机均匀分布特性；加密图像和明文图像之间的相关性非常小，相邻像素具有零相关特性，而且密钥空间达到299 bit，加密方法大大改变了明文图像的像素，使得密文能够抵御统计攻击；本算法有很高的安全性，具有良好的加密效果。

英文摘要：

A nonlinear coupled two-dimensional generalized Logistic chaotic mapping was proposed by using phase maps and bifurcation graphics, and the complex nonlinear dynamic activities of two-dimensional formula were studied. By using the coupled two-dimensional generalized Logistic chaotic mapping a chaotic sequence was generated, then the chaotic sequence was optimized into secret key stream, and output-feedback technology was introduced in this encryption algorithm, which changes pixels. The results show that the encryption algorithm is extremely sensitive to the key and the encrypted image, the choice of chaotic sequence sensitively depends on the plaintext that enhances the ability of resisting the chosen plaintext attack, and the information entropy of the cipher image is 7.974 3, which is very close to the ideal value 8.000 0. The encrypted image has random-like distribution behavior of grey values, and the correlation between the encrypted image and the plain image is close to 0. The adjacent pixels have zero co-correlat ion properties, and the encryption method changes the pixel of the original image greatly, which makes the ciphertext resist statistical attack, and the algorithm has the advantages of large space, and the key space reaches 299 bit.