Quantum Colour Image Encryption Algorithm Based on Chaotic Systems
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摘要: 为了提高图像安全性，将混沌系统引入到量子图像加密领域. 首先通过Chen混沌将图像按位异或；然后将彩色图像表示为量子的叠加态，通过Logistic混沌序列产生幺正矩阵对量子图像进行置乱；再次产生一个混沌序列对每个像素的红绿蓝三基色进行随机互换，达到对量子图像加密的目的；最后，在经典计算机上进行了模拟实验，结果表明加密后图像直方图更为平滑，像素平均分布在0～255范围内，图像相邻像素相关性低，加密图像红绿蓝像素相关系数平均值分别为0.001 6、0.001 7和0.003 8，并且密钥敏感性高，能有效抵抗穷举攻击和统计攻击，算法具有良好的有效性和可行性.Abstract: To enhance the security of image data, the incorporation of a chaotic system with quantum image encryption was proposed. Bitwise XOR operation was performed on a test image by applying the Chen chaotic system, and the obtained colour image was expressed as a quantum superposition state. The unitary matrix generated by the logistic chaotic sequence was then employed for scrambling the quantum image. In addition, to achieve the objective of quantum image encryption, another chaotic sequence was generated for randomly interchanging the red, green, and blue colour components of each pixel in the quantum image. Results obtained from simulation experiments conducted on a classical computer demonstrate that the grey histogram of the encrypted image is smooth, and the pixel intensity range is distributed uniformly between the values of 0 to 255. The correlation between adjacent pixels is found to be low, with the correlation coefficient values being 0.001 6, 0.001 7, and 0.003 8 for the red, green, and blue channels, respectively. Furthermore, the high key sensitivity of the proposed algorithm can effectively resist high intensity, exhaustive, and statistical attacks. Hence, the proposed algorithm can feasibly provide the required security for image data.
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Key words:
- chaotic system /
- image encryption /
- quantum information /
- quantum algorithm
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表 1 Lena图像的相关系数
Table 1. Values of correlation coefficients for Lena’s image
图像 水平方向 垂直方向 对角方向 R G B R G B R G B Lena 0.969 5 0.981 0 0.940 5 0.942 8 0.945 2 0.894 1 0.917 9 0.923 1 0.852 3 加密后图像 –0.001 5 0.000 2 0.002 9 –0.003 2 0.001 0 –0.001 2 0.000 3 0.003 9 0.007 4 文献[8] –0.020 2 0.005 8 –0.001 3 –0.001 2 –0.010 8 0.000 3 –0.000 6 0.011 9 0.008 9 
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表 2 NPCR像素改变率
Table 2. Number pixels change rate values of images obtained before and after performing encryption
图像 NPCR Lean原图像与加密图像 0.995 9 Peppers原图像与加密图像 0.996 2
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