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General image encryption algorithm based on deep learning compressed sensing and compound chaotic system

Chen Wei Guo Yuan Jing Shi-Wei

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General image encryption algorithm based on deep learning compressed sensing and compound chaotic system

Chen Wei, Guo Yuan, Jing Shi-Wei
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  • Many image compression and encryption algorithms based on traditional compressed sensing and chaotic systems are time-consuming, have low reconstruction quality, and are suitable only for grayscale images. In this paper, we propose a general image compression encryption algorithm based on a deep learning compressed sensing and compound chaotic system, which is suitable for grayscale images and RGB format color images. Color images can be directly compressed and encrypted, but grayscale images need copying from 1 channel to 3 channels. First, the original image is divided into multiple 3 × 33 × 33 non-overlapping image blocks and the bilinear interpolation Bilinear and convolutional neural network are used to compress the image, so that the compression network has no restriction on the sampling rate and can obtain high-quality compression of image. Then a composite chaotic system composed of a two-dimensional cloud model and Logistic is used to encrypt and decrypt the compressed image (sliding scrambling and vector decomposition), and finally the decrypted image is reconstructed. In the reconstruction network, the convolutional neural network and bilinear interpolation Bilinear are mainly responsible for reconstructing the contour structure information, and the fully connected layer is mainly responsible for reconstructing and combining the color information to reconstruct a high-quality image. For grayscale images, we also need to calculate the average value of the corresponding positions of the 3 channels of the reconstructed image, and change the 3 channels into 1 channel. The experimental results show that the general image encryption algorithm based on deep learning compressed sensing and compound chaos system has great advantages in data processing quality and computational complexity. Although in the network the color images are used for training, the quality of grayscale image reconstruction is still better than that of other algorithms. The image encryption algorithm has a large enough key space and associates the plaintext hash value with the key, which realizes the encryption effect of one image corresponding to one key, thus being able to effectively resist brute force attacks and selective plaintext attacks. Compared with it in the comparison literature, the correlation coefficient is close to an ideal value, and the information entropy and the clear text sensitivity index are also within a critical range, which enhances the confidentiality of the image.
      Corresponding author: Guo Yuan, guoyuan171@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61872204), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F2017029), the Fundamental Research Funds for the Higher Education Institutions of Heilongjiang Province, China (Grant No. 135109236), and the Graduate Innovation Research Project, China (Grant No. YJSCX2019042)
    [1]

    Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289Google Scholar

    [2]

    Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489Google Scholar

    [3]

    Candes E J, Wakin M B 2008 IEEE Signal Process. Mag. 25 21Google Scholar

    [4]

    Mousavi A, Patel A B, Baraniuk R G 2015 53rd Annual Allerton Conference on Communication, Control, and Computing Monticello, USA, September 29–October 2, 2015 p1336

    [5]

    练秋生, 富利鹏, 陈书贞, 石保顺 2019 自动化学报 45 2082Google Scholar

    Lian Q S, Fu L P, Chen S Z, Shi B S 2019 Acta Autom. Sin. 45 2082Google Scholar

    [6]

    Kulkarni K, Lohit S, Turaga P, Kerviche R, Ashok A 2016 IEEE Conference on Computer Vision and Pattern Recognition Las Vegas, USA, June 26–30, 2016 p449

    [7]

    Yao H T, Dai F, Zhang SL, Zhang Y D, Tian Q, Xu C S 2019 Neurocomputing 359 483Google Scholar

    [8]

    李静, 向菲, 张军朋 2019 电子设计工程 27 84Google Scholar

    Li J, Xian F, Zhang J P 2019 Int. Electr. Elem. 27 84Google Scholar

    [9]

    Hu X C, Wei L S, Chen W, Chen Q Q, Guo Y 2020 IEEE Access 8 12452Google Scholar

    [10]

    庄志本, 李军, 刘静漪, 陈世强 2020 物理学报 69 040502Google Scholar

    Zhuang Z B, Li J, Liu J Y, Chen S Q 2020 Acta Phys. Sin. 69 040502Google Scholar

    [11]

    Zhang D, Liao X F, Yang B, Zhang Y S 2018 Multim. Tools Appl. 77 2191Google Scholar

    [12]

    石航, 王丽丹 2019 物理学报 68 200501Google Scholar

    Shi H, Wang L D 2019 Acta Phys. Sin. 68 200501Google Scholar

    [13]

    Gong L H, Qiu K D, Deng C Z, Zhou N R 2019 Opt. Laser Technol. 115 257Google Scholar

    [14]

    Qin W, Peng X 2010 Opt. Lett. 35 118Google Scholar

    [15]

    Liu Y N, Niu H Q, Li Z L 2019 Chin. Phys. Lett. 36 044302Google Scholar

    [16]

    Li C B, Yin W T, Jiang H, Zhang Y 2013 Comput. Optim. Appl. 56 507Google Scholar

    [17]

    Dong W S, Shi G M, Li X, Ma Y, Huang F 2014 IEEE Trans. Image Process. 23 3618Google Scholar

    [18]

    Metzler C A, Maleki A, Baraniuk R G 2016 IEEE Trans. Inf. Theory 62 5117Google Scholar

    [19]

    Guo Y, Jing S W, Zhou Y Y, Xu X, Wei L S 2020 IEEE Access 8 9896Google Scholar

    [20]

    Belazi A, El-Latif A A, Belghith S 2016 Signal Process. 128 155Google Scholar

    [21]

    Hua Z Y, Zhou Y C, Pun C M, Chen C 2015 Inf. Sci. 297 80Google Scholar

    [22]

    Wu Y, Zhou Y C, Saveriades G, Agaian S S, Noonan J P, Natarajan P 2013 Inf. Sci. 222 323Google Scholar

  • 图 1  滑动置乱流程图

    Figure 1.  Flow chart for scrambling.

    图 2  彩色图像的压缩重构网络(采样率MR = 0.18)

    Figure 2.  Color image compression and reconstruction network, sampling rate MR = 0.18.

    图 3  BCNN模型与全连接层分别重构的Lena和Sea图像 (a) Lena (灰度); (b) Lena (彩色); (c) Sea (灰度); (d) Sea (彩色)

    Figure 3.  Lena and Sea images reconstructed from BCNN model and fully connected layer respectively: (a) Lena (gray); (b) Lena (color); (c) Sea (gray); (d) Sea (color).

    图 4  整个算法流程图

    Figure 4.  Entire algorithm flow chart.

    图 5  Lena (gray)图像明文与密文在水平、竖直、斜线3个方向的相关分布图 (a) 明文图像的相关分布图; (b)密文图像的相关分布图

    Figure 5.  Correlation distribution of the plaintext and ciphertext in the horizontal, vertical and oblique directions of Lena (gray) images: (a) Correlation distribution of plaintext; (b) correlation distribution of ciphertext.

    图 6  在密文图像上添加高斯噪声或椒盐噪声后重构出的Lena图像 (a), (b)使用的网络在训练时没有添加高斯噪声; (c), (d)使用的网络在训练时添加了强度为0.10的高斯噪声

    Figure 6.  Lena image reconstructed by adding Gaussian noise or salt and pepper noise to the ciphertext image: The networks used in (a) and (b) did not add Gaussian noise during training; the networks used in (c) and (d) are trained with Gaussian noise with an intensity of 0.10.

    图 7  Lena图像的密文被剪切后的重构结果 (a)剪切不同大小后的密文; (b), (c)使用的网络在训练时没有添加高斯噪声; (d), (e)使用的网络在训练时添加了强度为0.10的高斯噪声

    Figure 7.  Reconstruction result after ciphertext cut of Lena image: (a) Cut ciphertexts of different sizes; the networks used in (b) and (c) did not add Gaussian noise during training; the networks used in (d) and (e) are trained with Gaussian noise with an intensity of 0.10.

    图 8  选择明文攻击效果图

    Figure 8.  Effect pictures of chosen plaintext attack.

    图 9  Lena (gray), Peppers (gray), Lena (color), Peppers (color)图像在明文与密文上的直方图 (a)明文直方图; (b)密文直方图

    Figure 9.  Histograms of Lena (gray), Peppers (gray), Lena (color), Peppers (color) images in plain text and ciphertext: (a) Plain text histogram; (b) ciphertext histogram.

    表 1  重构的灰度图像在不同算法、不同采样率下的PSNR

    Table 1.  PSNR of reconstructed gray images under different algorithms and different sampling rates.

    采样率算法LenaMonarchFlinstones平均PSNR
    0.25TVAL328.6727.7724.0527.84
    NLR-CS29.3925.9122.4328.05
    D-AMP28.0026.3925.0228.17
    ReconNet26.5424.3122.4525.54
    DR2-Net29.4227.9526.1928.66
    MSRNet30.2128.9026.6729.48
    FCLBCNN31.0929.9727.5729.71
    0.10TVAL324.1621.1618.8822.84
    NLR-CS15.3014.5912.1814.19
    D-AMP22.5119.0016.9421.14
    ReconNet23.8321.1018.9222.68
    DR2-Net25.3923.1021.0924.32
    MSRNet26.2823.9821.7225.16
    FCLBCNN26.9324.5822.0825.41
    0.04TVAL319.4616.7314.8818.39
    NLR-CS11.6111.628.9610.58
    D-AMP16.5214.5712.9315.49
    ReconNet21.2818.1916.3019.99
    DR2-Net22.1318.9316.9320.80
    MSRNet22.7619.2617.2821.41
    FCLBCNN23.3319.5917.1721.51
    0.01TVAL311.8711.099.7511.31
    NLR-CS5.956.384.455.30
    D-AMP5.736.204.335.19
    ReconNet17.8715.3913.9617.27
    DR2-Net17.9715.3314.0117.44
    MSRNet18.0615.4113.8317.54
    FCLBCNN18.1215.6313.9017.62
    DownLoad: CSV

    表 2  在BSD500测试集上不同算法、不同采样率下的平均PSNR和平均SSIM

    Table 2.  Mean PSNR and SSIM of different algorithms and different sampling rates on the BSD500 test set.

    算法MR = 0.08MR = 0.10MR = 0.18MR = 0.25MR = 0.53
    PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
    ReconNet23.280.612125.480.7241
    DR2-Net24.260.660327.560.7961
    MSRNet24.730.683727.930.8121
    FCLBCNN (gray)24.830.705628.190.840032.870.9392
    FCLBCNN (color)27.940.825232.070.9279
    DownLoad: CSV

    表 3  Lena图像在各阶段的效果(采样率MR = 0.53 (灰度), 0.18 (彩色))

    Table 3.  Lena image effects at various stages, sampling rate MR = 0.53 (gray), 0.18 (color).

    原图采样率压缩图像置乱图像密文图像重构图像PSNRSSIM
    0.5336.43870.9715
    0.1832.55160.9456
    DownLoad: CSV

    表 4  不同加密算法的相关系数比较

    Table 4.  Comparison of correlation coefficients of different encryption algorithms.

    测试图像方向明文(gray)密文
    本文(gray)本文(color)文献[20]文献[21]
    Lena水平0.93960.0010–0.0024–0.00480.0011
    竖直0.9639–0.00660.0012–0.01120.0098
    斜线0.9189–0.00390.0035–0.0045–0.0227
    Peppers水平0.9769–0.0004–0.0023–0.00560.0071
    竖直0.97720.00890.0063–0.0162–0.0065
    斜线0.9625–0.00770.0004–0.0113–0.0165
    平均值水平0.0003–0.0024–0.00520.0041
    竖直0.00120.0038–0.01370.0017
    斜线–0.00580.0020–0.0079–0.0196
    DownLoad: CSV

    表 5  不同加密算法得到的信息熵的比较

    Table 5.  Comparison of the entropy obtained by different encryption algorithms.

    测试图像明文(gray)密文
    本文(gary)本文(color)文献[12]
    Lena7.30357.99497.99447.9544
    Peppers7.43447.99567.99527.9633
    DownLoad: CSV

    表 6  不同加密算法得到的局部信息熵比较

    Table 6.  Comparison of the local entropy obtained by different encryption algorithms.

    测试图像局部信息熵(gray/color)临界值
    $\begin{array}{l} u_{0.05}^{* - } = 7.9019 \\ u_{0.05}^{* + } = 7.9030 \end{array}$$\begin{array}{l} u_{0.01}^{* - } = 7.9017 \\ u_{0.01}^{* + } = 7.9032 \end{array}$$\begin{array}{l} u_{0.001}^{* - } = 7.9015 \\ u_{0.001}^{* + } = 7.9034 \end{array}$
    Lena7.9024/7.9027PassPassPass
    Peppers7.9027/7.9023PassPassPass
    DownLoad: CSV

    表 7  不同加密算法得到的NPCR比较

    Table 7.  Comparison of NPCR obtained by different encryption algorithms.

    测试图像NPCR (gray/color)NPCR理论临界值
    $N_{0.05}^* = 99.5693\% $$N_{0.01}^* = 99.5527\% $$N_{0.001}^* = 99.5341\% $
    Lena0.9960/0.9961PassPassPass
    Lena[12]0.9954/—FailFailPass
    Lena[20]0.9962/—PassPassPass
    Peppers0.9959/0.9957PassPassPass
    Peppers[12]0.9944/—FailFailFail
    Peppers[20]0.9963/—PassPassPass
    DownLoad: CSV

    表 8  不同加密算法得到的UACI比较

    Table 8.  Comparison of UACI obtained by different encryption algorithms.

    测试图像UACI (gray/color)UACI理论临界值
    $\begin{array}{l} u_{0.05}^{* - } = 33.2824\% \\ u_{0.05}^{* + } = 33.6447\% \end{array}$$\begin{array}{l} u_{0.01}^{* - } = 33.2255\% \\ u_{0.01}^{* + } = 33.7016\% \end{array}$$\begin{array}{l} u_{0.001}^{* - } = 33.1594\% \\ u_{0.001}^{* + } = 33.7677\% \end{array}$
    Lena0.3352/0.3357PassPassPass
    Lena[12]0.3303/—FailFailFail
    Lena[20]0.3370/—FailPassPass
    Peppers0.3333/0.3331PassPassPass
    Peppers[12]0.3305/—FailFailFail
    Peppers[20]0.3369/—FailPassPass
    DownLoad: CSV

    表 9  本文压缩加密算法与在原图上直接使用本文加密算法的耗时对比

    Table 9.  Time-consuming comparison that the compression encryption algorithm of this article and the encryption algorithm of this article directly used on the original image.

    图像大小压缩重构(gray/color)加解密(gray/color)总时间(gray/color)编程工具平台
    256 × 2560.21/0.200.66/0.650.87/0.85Pycharm + Pytorchi5-8500 CPU
    0.93/2.810.93/2.81
    512 × 5120.91/0.892.51/2.513.42/3.40
    3.89/11.963.89/11.96
    1024 × 10244.81/4.629.40/9.4214.21/14.04
    15.84/48.5115.84/48.51
    DownLoad: CSV
  • [1]

    Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289Google Scholar

    [2]

    Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489Google Scholar

    [3]

    Candes E J, Wakin M B 2008 IEEE Signal Process. Mag. 25 21Google Scholar

    [4]

    Mousavi A, Patel A B, Baraniuk R G 2015 53rd Annual Allerton Conference on Communication, Control, and Computing Monticello, USA, September 29–October 2, 2015 p1336

    [5]

    练秋生, 富利鹏, 陈书贞, 石保顺 2019 自动化学报 45 2082Google Scholar

    Lian Q S, Fu L P, Chen S Z, Shi B S 2019 Acta Autom. Sin. 45 2082Google Scholar

    [6]

    Kulkarni K, Lohit S, Turaga P, Kerviche R, Ashok A 2016 IEEE Conference on Computer Vision and Pattern Recognition Las Vegas, USA, June 26–30, 2016 p449

    [7]

    Yao H T, Dai F, Zhang SL, Zhang Y D, Tian Q, Xu C S 2019 Neurocomputing 359 483Google Scholar

    [8]

    李静, 向菲, 张军朋 2019 电子设计工程 27 84Google Scholar

    Li J, Xian F, Zhang J P 2019 Int. Electr. Elem. 27 84Google Scholar

    [9]

    Hu X C, Wei L S, Chen W, Chen Q Q, Guo Y 2020 IEEE Access 8 12452Google Scholar

    [10]

    庄志本, 李军, 刘静漪, 陈世强 2020 物理学报 69 040502Google Scholar

    Zhuang Z B, Li J, Liu J Y, Chen S Q 2020 Acta Phys. Sin. 69 040502Google Scholar

    [11]

    Zhang D, Liao X F, Yang B, Zhang Y S 2018 Multim. Tools Appl. 77 2191Google Scholar

    [12]

    石航, 王丽丹 2019 物理学报 68 200501Google Scholar

    Shi H, Wang L D 2019 Acta Phys. Sin. 68 200501Google Scholar

    [13]

    Gong L H, Qiu K D, Deng C Z, Zhou N R 2019 Opt. Laser Technol. 115 257Google Scholar

    [14]

    Qin W, Peng X 2010 Opt. Lett. 35 118Google Scholar

    [15]

    Liu Y N, Niu H Q, Li Z L 2019 Chin. Phys. Lett. 36 044302Google Scholar

    [16]

    Li C B, Yin W T, Jiang H, Zhang Y 2013 Comput. Optim. Appl. 56 507Google Scholar

    [17]

    Dong W S, Shi G M, Li X, Ma Y, Huang F 2014 IEEE Trans. Image Process. 23 3618Google Scholar

    [18]

    Metzler C A, Maleki A, Baraniuk R G 2016 IEEE Trans. Inf. Theory 62 5117Google Scholar

    [19]

    Guo Y, Jing S W, Zhou Y Y, Xu X, Wei L S 2020 IEEE Access 8 9896Google Scholar

    [20]

    Belazi A, El-Latif A A, Belghith S 2016 Signal Process. 128 155Google Scholar

    [21]

    Hua Z Y, Zhou Y C, Pun C M, Chen C 2015 Inf. Sci. 297 80Google Scholar

    [22]

    Wu Y, Zhou Y C, Saveriades G, Agaian S S, Noonan J P, Natarajan P 2013 Inf. Sci. 222 323Google Scholar

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Publishing process
  • Received Date:  29 June 2020
  • Accepted Date:  10 August 2020
  • Available Online:  07 December 2020
  • Published Online:  20 December 2020

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