本文提出一种量子混沌与折叠算法相结合的图像加密系统。该系统的主要思想是通过量子混沌映射和二维Logistic映射分别进行Arnold变换, 得到两个由伪随机数组成的与灰度图像大小相等的矩阵Q、E, 然后利用这两个矩阵对图像分别进行以下操作: 一是利用矩阵Q对图像从4个方向进行“折叠操作”, 二是使用前一个像素值与当前像素值进行异或, 然后将异或得到的值加上E对应的值, 以对当前像素值进行修改, 从而达到图像扩散的效果, 增加差分攻击的难度。利用MATLAB对测试图像进行模拟仿真分析, 结果显示, 经该加密系统加密后的图像, 其水平、竖直和对角线方向像素值的相关性分别为0.001 006、0.000 152、0.000 789, 信息熵H(s)=7.997 3。一系列的实验结果表明该加密系统具有很高的安全性和随机性。

An image encryption system combining quantum chaos with folding algorithm was proposed. The main idea of the proposed algorithm is to make Arnold transform through quantum chaos map and 2D Logistic map respectively, to generate the matrix Q and the matrix E, and the two matrices were made of pseudo random numbers and identical to grayscale image. Then, such matrices were used for two operations on the image and to achieve image encryption, as follows: one was to achieve “folding operation” on image at four directions by application of matrix Q and another was to execute nonequivalence of the former pixel value and present pixel value, plus the values after nonequivalence with E corresponding value, so the modification of present pixel value was obtained and the effect of image diffusion was realized and the difficulty of the differential attack was increased. Simulation analysis on tested image was conducted by application of MATLAB and the results show that for images encrypted by such encryption system, the correlations of pixel value at horizontal, vertical and diagonal directions are 0.001 006, 0.000 152 and 0.000 789 respectively, with entropy H(s)=7.997 3. The results of a series of tests show that the proposed encryption system has highly security and randomness.