基于级联混沌系统和量子Baker映射的图像加密算法

doi:10.3969/j.issn.1671-1122.2023.12.006

摘要/Abstract

摘要：

量子图像加密借助于量子纠缠和叠加特性来提高算法效率，同时，与传统的图像加密算法相比，其在信息传递的安全性上更具优越性。针对量子图像仅在空间域或变换域不能充分置乱混淆的问题，文章提出了空间域和变换域操作相结合的置乱混淆方法。首先，通过量子Baker映射对图像像素的位置进行空间域的置乱。其次，利用量子比特旋转改变空间域像素的灰度信息，其中旋转角度由级联混沌系统产生的伪随机序列来确定；然后，将空间域的量子态转换到傅里叶变换域，并在傅里叶域进行量子比特旋转；最后，利用量子傅里叶逆变换将变换域信息转换到空间域得到密文图像。由于Baker映射周期更长，使得本文算法的密钥空间更大。另外，基于级联混沌系统的旋转参数生成可以减轻密钥传输负担。仿真实验结果验证了本文算法的安全性和有效性，且在复杂度上优于经典图像加密算法。

关键词: 量子图像处理, 图像安全, 量子Baker映射, 级联混沌系统, 图像加密

Abstract:

Quantum image encryption can greatly improve the efficiency with help of quantum entanglement and superposition characteristics, and has advantages over traditional image encryption algorithms in ensuring the security of information transmission. Aiming at the problem that quantum images could not be fully scrambled and confused only in the spatial domain or the transform domain, a scramble and confusion method combining the spatial domain and the transform domain was proposed. Firstly, the positions of image pixels were scrambled in spatial domain by quantum Baker map. Secondly, the gray information of pixels in spatial domain was changed by the rotation of quantum bits. The rotation angle was determined by the pseudo-random sequence generated by the cascade chaotic system. Then, the quantum state in the spatial domain was converted to the Fourier transform domain, and the quantum bits were rotated in the Fourier domain. Finally, the information in the transform domain was converted to the spatial domain by the inverse quantum Fourier transform to obtain the ciphertext image. Because the Baker map has a longer period, the key space of the proposed algorithm is larger. In addition, the rotation parameter generation based on the cascade chaotic system can reduce the burden of keys transmission. Numerical simulation results verify the security and effectiveness of the proposed algorithm, and the complexity is superior to the classical image encryption algorithm.

Key words: quantum image processing, image security, quantum Baker map, cascade chaotic system, image encryption

中图分类号:

TP309

刘兴斌, 刘聪. 基于级联混沌系统和量子Baker映射的图像加密算法[J]. 信息网络安全, 2023, 23(12): 49-58.

LIU Xingbin, LIU Cong. Image Encryption Algorithm Based on Cascade Chaotic System and Quantum Baker Map[J]. Netinfo Security, 2023, 23(12): 49-58.

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图像	水平	垂直	对角线
明文Baboon	0.5709	0.6681	0.5799
密文Baboon	0.0050	0.0101	0.0374
明文Peppers	0.9454	0.9104	0.8742
密文Peppers	0.0028	0.0297	0.0115
明文Bridge	0.8883	0.8990	0.8415
密文Bridge	0.0227	-0.0343	-0.0227

图像	信息熵
明文Baboon	7.1273
密文Baboon	7.7300
明文Peppers	7.5918
密文Peppers	7.7414
明文Bridge	5.7062
密文Bridge	7.7432

评价指标		对比方法
评价指标		本文算法	文献[15] 算法	文献[16] 算法	文献[25]算法
信息熵		7.7568	7.7456	7.7566	7.7602
相关系数	水平方向	0.0101	0.0121	0.0135	0.0116
	垂直方向	0.0018	0.0054	0.0034	0.0023
	对角方向	0.0087	0.0142	0.0082	0.0086