二维超混沌系统的研究及在图像加密中的应用

构建了一个基于二维超混沌方程的非线性混沌映射,采用直方图、吸引子图的分析方法,研究了二维超混沌方程的特性;然后在该混沌方程的基础上,提出了一种新型的图像加密算法,其具体方法是先将彩色图像分离成红、绿、蓝三个分量,然后分别采用排序,异或,先排序后异或的方法进行加密。仿真结果表明,该加密算法对明文和密文都非常敏感,对初始密钥十分敏感,初值敏感性能达到10-10;密文图像的信息熵为7.908 563 896 646 1,非常接近理想值8;红、绿、蓝三个分量加密图像和明文图像之间的水平相关性系数差值分别是0.961 465 408 259 75、0.951 712 655 336 949、0.962 750 222 811 646。文章采用的加密方法完全改变了明文图像的像素值,使密文能够抵御攻击,仿真实验结果表明该加密算法具有良好的加密效果和安全性。

Research on Two-dimension Hyperchaos System and Its Application on Image Encryption

We construct a nonlinear chaos map based on two-dimensional hyperchaotic equation and study the characteristics of two-dimensional hyperchaotic equation by analysis methods of histogram and attractor. Then based on the chaotic equation,we put forward a new image encryption algorithm. The specific method is to separate a color original image into red,green and blue components,then we use sequence,XOR,sequence first then XOR to encrypt. The simulation shows that the proposed encryption algorithm is quite sensitive to plaintext and ciphertext as well as the initial key. The initial condition is up to 10-10. The information entropy of ciphertext image is 7.908 563 896 646 157,which is close to the ideal value of 8. The difference value of correlation coefficient between the encrypted image and the plain image of three RGB components respectively are 0.961 465 408 259 75,0.951 712 655 336 949,0.962 750 222 811 646. The proposed encryption method has completely changed the pixel values of the plaintext,so that the ciphertext can reject attack. The simulation shows that the encryption algorithm has great encrypting effect and safety.