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收稿：2019-08-06，
修回：2020-2-10，
录用：2020-2-17，
纸质出版：2020-07-16
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目的
2
随着互联网通信和多媒体技术的快速发展，单幅图像加密技术难以满足日益增长的数据传输需求。为提高图像加密系统的传输效率，同时保证安全性和鲁棒性，本文构建一种基于gyrator变换和多分辨率奇异值分解（multi-resolution singular value decomposition，MRSVD）的多图像加密算法。
方法
2
首先，将明文图像每两幅组合为复数矩阵，利用改进的logistic映射生成混沌相位掩模，对复数矩阵进行gyrator域的双随机相位编码。其次，将变换后矩阵的实部分量和虚部分量组合为实数矩阵并进行多分辨率奇异值分解。最后，使用正交系数矩阵对多分辨率奇异值分解的结果进行线性组合得到密文图像。
结果
2
实验结果表明，使用本文算法得到的解密图像的峰值信噪比大于300 dB，解密图像质量相较于对比算法的解密图像质量更好；密钥发生微小改变前后密文相关系数（correlation coefficient，CC）远小于0.20，明文像素值发生微小变化时像素变化率（number of pixels change rate，NPCR）与归一化平均变化强度（unified average changing intensity，UACI）分别约为0.999 0和0.333 7；密钥空间大小为5.616 9×10
60
，可以抵御蛮力攻击；当密文图像受到一定强度的高斯白噪声和剪切攻击时，本文算法能够较好地恢复明文图像。
结论
2
所提出的多图像加密算法在高质量恢复明文图像的同时具有较高的安全性和较强的鲁棒性，可以应用于图像的内容保护与安全传输。
Objective
2
The rapid development of the Internet communication and multimedia technology has allowed the convenient transmission of substantial video
image
and other multimedia data through networks at any moment. On the one hand
these data may be leaked in the transmission process and illegally used due to the openness and sharing of the internet. On the other hand
several images may contain sensitive information
such as human body images that can potentially reveal the privacy information of one person
including gender
weight
and health status. Remote sensing images may include important information
such as geographical location
sensor parameters
and the spectral characteristics of ground objects. Therefore
the protection of image content and secure communication have become important issues in the field of information security. Since the double random phase encoding (DRPE) was proposed
numerous encryption schemes
such as fractional Fourier transform
gyrator transform
Fresnel transform
and multiparameter discrete fractional Fourier transform
have been introduced in other domains. The majority of such algorithms focus on a single image. Multi-image encryption technology has been widely investigated in recent years to meet the growing demand for data transmission. This paper introduces a multi-image encryption algorithm based on gyrator transform and multiresolution singular value decomposition (MRSVD).
Method
2
First
every two images are combined into a complex matrix by precoding and then DRPE in the gyrator domain is performed
where chaotic phase masks are constructed using a modified logistic map. Second
the real and imaginary parts of the transformed results are spliced into a real matrix. MRSVD is implemented to improve the security. With a given mean and variance values
a Gaussian matrix is generated and an orthogonal coefficient matrix is obtained by singular value decomposition. Cipher images are obtained by linear combination of the MRSVD results. Plaintext images can be recovered using an authorized key through the reverse encryption process. The phase masks
rotation angles of gyrator transforms
and parameter of Gaussian matrix are generated by using the modified logistic map
which makes the storage and transmission convenient. The initial states of the modified logistic map are closely related to plaintext images
and this condition results in high-level security.
Result
2
Numerical simulations are performed on 120 grayscale images to demonstrate the feasibility and reliability of the proposal. The peak signal-to-noise ratio (PSNR) values of the decrypted images by using the proposed method with granted keys are larger than 300 dB. This result indicates that the quality of the decrypted images by using the proposed method is better than that obtained using other methods. The histograms of cipher images obey the Gaussian distribution
which is different from the results of plaintext images. The correlation coefficient value of cipher images is much less than 0.20 when keys are slightly changed. The decrypted results with a key that deviates from the correct value of 10
-15
are chaotic. The average PSNR value is approximately 8.516 1 dB
and the average structural similarity is close to 0. When the pixel values of plaintext images increase by a small amount
the average number of pixel change rate and the unified average changing intensity are approximately 0.999 0 and 0.333 7
respectively. The key space is up to 5.616 9×10
60
which can resist a brute force attack. For the cipher images attacked by Gaussian white noise and cropping
the proposed algorithm can still recover plaintext images and shows better robustness than two other algorithms.
Conclusion
2
A multilevel multi-image encryption approach based on gyrator transform and MRSVD is proposed in this study. The chaotic random phase masks and real-valued cipher image is convenient to storage and transmit. The identity orthogonal matrix obtained by singular value decomposition is utilized to share the MRSVD results. Such utilization increases the security of ciphertext. Experimental results demonstrate that the proposed method can restitute plaintext images with high quality and achieves high security and strong robustness. It can be applied for the protection of image content and secure communication.
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