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Research on Double-Layers optical information Encryption Based on Ghost Imaging
Optics Communications 455 (2020) 124585
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Research on Double-Layers optical information Encryption Based on Ghost Imaging Zhang Leihong, Zhang Zhisheng, Kang Yi, Ye Hualong, Xiong Rui, Yuan Xiao, Wang Zhaorui, Wang Kaimin, Zhang Dawei ∗ University of Shanghai for Science and Technology, Shanghai 200093, China
ARTICLE
INFO
Keywords: Optical information encryption Ghost imaging encryption Secondary encryption
ABSTRACT With the development of technology, digital images are greatly threatened during transmission. It is difficult to ensure the security of information in the early traditional encryption methods. Using different encryption technologies to form a secondary encryption can greatly improve the security of image encryption transmission, but facing the problems of low efficiency and poor accuracy. Based on ghost imaging and compressed sensing technology, this paper proposes a new optical information encryption algorithm: Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). In this paper, the feasibility of the algorithm is further studied and analyzed. Numerical simulations show that the algorithm can effectively improve the security. Experiments show that the algorithm can also improve the accuracy of restoration.
0. Introduction With the rapid development of Internet technology, Internet information spreads widely, and information security has received more and more attention. Due to the high parallelism, high speed and high storage, optical information encryption technology is favored by researchers. In recent years, many scholars have proposed different optical encryption methods, such as: ghost imaging encryption, chaotic encryption, dual random phase encryption, etc. [1–5]. K Klyshko [6] proposed a scheme about ghost imaging based on the entanglement behavior of two photon light. Shapiro and Bromber et al. [7] used a spatial light modulator (SLM) to achieve computational ghost imaging. F. Ferri et al. [8] proposed differential ghost imaging. This method reduces the influence of external environmental noise on the imaging quality. There are also many scholars who have proposed different ghost imaging methods [9–13]. In the field of encryption, Pere Clemente [14] first proposed an optical information encryption method based on computational ghost imaging, with non-locality imaging and good security. In 2015, Zhao Shengmei et al. [15] proposed a highperformance optical encryption based on CGI with QR encoding and compression sensing technology. In 2016, Yang Zhaohua et al. [16] proposed Parallel Compressive Ghost Imaging Based on Threshold Segmentation, which reduces the complexity of computer processing and the requirements of hardware. Although the above method improves the quality of some images and increases the speed of imaging, but the single encryption method has limitations. The consequences of being compromised are unimaginable. Secondary encryption improves
the security of the encryption system by combining two encryption technologies. However, the superposition of technology increases the complexity of the system. In the actual process, the information cannot be restored due to image degradation. A picture often contains a lot of information, in which the main feature information is dominant. It is the information that dominates the main content of the picture. In contrast, background information is in a relatively minor position. At present, most image encryption transmissions use the entire image information as a carrier, in this way, the encryption method of information is limited. This paper proposes a new encryption method: Double-Layered and Secondary Encryption Based on Ghost Imaging. This paper layered the information of a picture. This paper performed different secondary encryption for different levels of information. Different levels of information have different emphasis. The advantage of this method is that the information security and restoration quality of information is improved. In this paper, the layered optical encryption of image information is verified by experiments. This algorithm extends the method of secondary encryption based on ghost imaging. It provides a reference for further improving the accuracy of image gray information restoration. 1. Theoretical description 1.1. Computational ghost imaging Ghost imaging is a new imaging method. Unlike traditional imaging, ghost imaging is a non-local imaging. In optical encryption, ghost imaging encryption has advantages in security and reliability.
∗ Corresponding author. E-mail address: [email protected] (Z. Dawei).
https://doi.org/10.1016/j.optcom.2019.124585 Received 19 May 2019; Received in revised form 17 July 2019; Accepted 15 September 2019 Available online 18 September 2019 0030-4018/© 2019 Published by Elsevier B.V.
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Optics Communications 455 (2020) 124585
The principle of computing ghost imaging is shown in Fig. 1. There are N normal Gaussian random distribution matrices 𝜑𝑛 (𝑥, 𝑦) as a key and 𝜑𝑛 (𝑥, 𝑦) is evenly distributed over [0, 2𝜋]. Spatial light modulator (SLM) modulates the intensity of the light field. Each modulation produces a speckle field. The intensity distribution of the speckle field is I(𝑥, 𝑦). The modulated speckle field is irradiated onto the object 𝑇 (𝑥, 𝑦). The value of the light intensity transmitted through the object as 𝐵𝑛 . Repeat the measurement calculation N times to get N different { }𝑁 measurement values 𝐵𝑖 𝑖=1 . This process is shown in Eq. (1). 𝐼𝑛 (𝑥, 𝑦) is calculated according to the Fresnel propagation function as shown in the formula (2). 𝐵𝑛 =
∫
𝐼𝑛 (𝑥, 𝑦) 𝑇 (𝑥, 𝑦) 𝑑𝑥𝑑𝑦 [
] | | 𝐼𝑛 (𝑥, 𝑦) = |𝐸𝑖𝑛 (𝑥, 𝑦) 𝑒𝑥𝑝 𝑗𝜑𝑛 (𝑥, 𝑦) ⊗ ℎ𝑧 (𝑥, 𝑦)| | |
(1) Fig. 1. Principle of computational ghost imaging.
(2)
where ℎ𝑧 (𝑥, 𝑦) is the Fresnel diffraction function, and ⊗ stands for convolution. In the imaging process, this paper performs N times of sampling. Correlates the intensity distribution of the speckle field with the measured value of the light intensity, reconstructs the information to restore the original information, and completes the reconstruction. The reconstruction formula for computing ghost imaging is expressed as: 𝑇𝐺𝐼 (𝑥, 𝑦) =
𝑁 ) 1 ∑( 𝐵 − ⟨𝐵𝑛 ⟩ 𝐼𝑛 (𝑥, 𝑦) 𝑁 𝑛=1 𝑛
where f(x) is the pixel value of the point (x, y), L(x), g(x) is the divided image, Y(x) is the original image, and T is the threshold. The second step (the first encryption: watermark and scrambling): Load the image to be encrypted into the covered image with a certain weight. The specific method: (1) Use the main feature information as a watermark. (2) The watermark and covered image perform twodimensional discrete wavelet transform (DWT). (3) Decompose them into sub-images with different frequency domain characteristics. (4) Insert the low frequency part of the watermark into the low frequency of the covered image. After the insertion, the watermark information will be hidden in the covered image. The Insertion technique is alpha blending [17], formula as
(3)
where ⟨𝐵𝑛 ⟩ is the average value of the total light intensity measured n times. Compressed sensing computational ghost imaging uses the sparse characteristics of the information to obtain information at a rate lower than the Nyquist sampling limit. This method obtains a clearer picture with less sampling. The process expression is 𝑇𝐶𝑆 = T (𝑥, 𝑦) ∶ 𝑎𝑟𝑔𝑚𝑖𝑛 ‖𝛹 {T (𝑥, 𝑦)}‖ 𝐿1
𝛾𝐿𝐿 = 𝐾 ⋅ 𝛼𝐿𝐿 + 𝐺 ⋅ 𝛽𝐿𝐿
(6)
where 𝛼𝐿𝐿 is the low frequency part of the watermark, 𝛽𝐿𝐿 is the low frequency part of the covered image. K, G are scaling factors. The purpose of this is that the information of the main feature layer is hidden under the covered image. Once the information is attacked by illegal users, the method will act as a disguise and mislead the illegal user. Encryption for the background layer is fast scrambling by twodimensional Discrete Cosine Transform (DCT). In order to improve the encryption efficiency, this paper decided to use the bilinear interpolation [18] for the main feature layer. This paper compresses the information to form thumbnails, retains key pixels in the process of zooming out, removes redundant information, and reconstructs better images in ghost imaging with fewer samples. The image is magnified by a bilinear interpolation algorithm at the time of decryption. This processing can improve Double-Layered and Secondary encryption’s efficiency and reduce overall sampling time. The third step (the second encryption): the watermarked image and the scrambled image are encrypted by compressed sensing computational ghost imaging. Before the third step, the watermarked image is a two-dimensional image 𝑇 (𝑥, 𝑦). In the third step, the image is substituted into formula 1. Convert a two-dimensional image into a one-dimensional column vector. The intensity distribution function 𝐼𝑛 (𝑥, 𝑦) as a random matrix is also a measurement matrix in compressed sensing. At this point, the matrix expression of the encryption process is:
(4)
where ||⋅||𝐿1 is norm, 𝛹 means sparse representation; 1.2. Double-layers optical encryption This paper proposes a new encryption method — Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). As shown in Fig. 2, the encryption phase is mainly divided into three steps. The first step: Separates feature information from background. Divide the original image into the main feature layer and the background layer. The second step (First encryption): use the main feature information as the watermark. Then alpha blends [7] the watermark and the cover image. Quickly scramble background information. The third step: The watermarked image and the scrambled background image are encrypted by compressed sensing computational ghost imaging, respectively. Correspondingly, the decryption phase is also divided into three steps. The first step: Reconstruct the image by compressed sensing computational ghost image. The second step: Extract the main feature image and restore the background image. The third step: Integrate the main feature information into background.
⎡ 1 1 1 ⎤ ⎡ 𝐵1 ⎤ ⎢𝐼11 ⋯𝐼1𝑛 ⋯𝐼𝑛𝑛 ⎥ ⎡𝑇11 ⎤ ⎢ ⎥ ⎢ ⎥ ⎢𝐼 2 𝐼 2 2 ⎥ ⋮ ⎢ 𝐵2 ⎥ = ⎢ 11 ⋯ 1𝑛 ⋯𝐼𝑛𝑛 ⎥ ⎢⎢𝑇 ⎥⎥ ⎢ ⋮ ⎥ ⎢ ⎥ 1𝑛 ⎢𝐵 ⎥ ⎢ ⋮ ⋱ ⋮ ⋱ ⋮ ⎥ ⎢⎢ ⋮ ⎥⎥ ⎣ 𝑁⎦ ⎢ 𝑁 𝑁⎥ 𝑇 𝑁 ⎣𝐼 ⋯𝐼 ⋯𝐼 ⎦ ⎣ 𝑛𝑛 ⎦
1.2.1. Encryption The first step: Use the threshold segmentation technology to divide the information. Segment the main feature layer and the background layer. In the main feature layer, the background information has been cleared, and the main feature information in the background layer has been cleared. This paper uses threshold segmentation techniques to segment information. This paper selects the pixel value between the two peaks as the threshold value, and divide the information into two layers of the same size. The process is as follows { 𝐿 (𝑥) , 𝑓 (𝑥, 𝑦) > 𝑇 𝑌 (𝑥) = (5) 𝑔 (𝑥) 𝑓 (𝑥, 𝑦) ≤ 𝑇
11
1𝑛
(7)
𝑛𝑛
⎡ 𝐵1 ⎤ ⎢ ⎥ 𝐵 where ⎢ 2 ⎥ is the cipher text encrypted by compressed sensing com⎢ ⋮ ⎥ ⎢𝐵 ⎥ ⎣ 𝑁⎦ putational ghost imaging. 2
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Optics Communications 455 (2020) 124585
Fig. 2. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI).
1.2.2. Decryption The first step: Reconstruct the image by compressed sensing computational ghost imaging. Calculate the light intensity information 𝐼𝑛 (𝑥, 𝑦) by the key 𝜑𝑛 (𝑥, 𝑦). Associate 𝐼𝑛 (𝑥, 𝑦) with cipher text to reconstruct a two-dimensional image. The process expression is the same as Eq. (4). The second step: At this stage, the main feature image information and background image information are extracted from the reconstructed image. This paper performs the DWT on the reconstructed watermarked image after compressed sensing computational ghost imaging, then decompose it into sub-images, and then extract watermark from these sub-images [17]. The expression of this process is: ( ) 𝜀𝐿𝐿 − 𝐺 ⋅ 𝛽𝐿𝐿 ÷ K = 𝛼𝐿𝐿 (8) where K, G are scaling factors, 𝜀𝐿𝐿 is the low frequency part of the reconstructed watermarked image, and 𝛽𝐿𝐿 is an approximation of the low frequency part of the covered image. Different from the valuation used in [19], this paper considers that in the actual ghost imaging process, the image will degrade and affect the pixel value of the image. If this paper uses the estimate of the low frequency of the covered image before compressed sensing computational ghost imaging reconstruction, it will not extract valid information. Therefore, this paper have improved the approximation 𝛽𝐿𝐿 of the covered image in the experiment. This paper filters the reconstructed watermarked image to recover the covered image. Use the difference between the reconstructed watermarked image and the covered image to extract the watermark information 𝛼𝐻𝑌 , ( ) J ⋅ 𝜀𝐻𝑌 − 𝐺 ⋅ 𝛽𝐻𝑌 ÷ K = 𝛼𝐻𝑌 (9)
Fig. 3. Simulation results: (a) Original image (b) Main feature layer (c) Background layer (d) Covered image (e) Watermarked image (f) quickly scrambled image (g) Compressed sensing Computational ghost image (h) Extracted watermark (i) Final restored image.
where J, K, G are scaling factors, 𝜀𝐻𝑌 is the watermarked image reconstructed by compressed sensing computational ghost imaging, and
Fig. 4. Grayscale histogram: (a) Gray histogram of Main feature image (b) Gray histogram of Watermarked image.
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Optics Communications 455 (2020) 124585
Fig. 5. pixel correlation: (a) Pixel correlation of Main feature image in the horizontal direction (b) Pixel correlation of Watermarked image in the horizontal direction (c) Pixel correlation of Main feature image in the vertical direction (d) Pixel correlation of Watermarked image in the vertical direction (e) Pixel correlation of Main feature image in the diagonal direction (f) Pixel correlation of Watermarked image in the diagonal direction.
𝛽𝐻𝑌 is the difference between the reconstructed watermarked image and the covered image. This paper extracts the watermark from the reconstructed image and get the main feature information of the original image. Restore the background information of the original image from the reconstructed scrambled image. The third step: finally integrate the main feature information into background information.
the Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). This section uses MATLAB R2016a software simulation to achieve. The original image size is a 64×64 grayscale image. The simulation results are shown in Fig. 3. In Fig. 3, a (original image) is divided into b (main feature layer) and c (background layer). Blend b (main feature layer) into d (covered image) to form e (watermarked image). f is quickly scrambled by c.
2. Numerical simulation
g is the image after compressed sensing computational ghost imaging, extracts h from it. Restore background layer after compressed sensing
By combining bilinear interpolation technology and alpha blending technology, the security of compressed sensing ghost imaging encryption technology is further enhanced. This section will analyze
computational ghost imaging. Integrate the main feature information into background information. Reconstruct the final restored image i. 4
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Optics Communications 455 (2020) 124585
This paper uses information entropy, PSNR (peak signal-to-noise ratio), and CC (correlation coefficient) as quantitative indicators. Reconstructed images of LSGI (Double-Layered and Secondary Encryption Based on Ghost Imaging), CSGI (Compressed sensing ghost imaging), and DWGI (Digital watermarking combined with ghost imaging without double-layers) were analyzed. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI) has two different layers of sampling times. The average of sampling times of the main feature layer and the background layer is taken as the sampling number of LSGI. 2.1. Safety This paper uses the technique of alpha blending when we are encrypting. According to research [19], alpha blending can greatly reduce the correlation of adjacent pixels and improve the anti-attack capability. The histogram of the image is a method of statistical image features. The histogram distribution of different images is different. In other words, the greater the difference in the histogram distribution of the image, the smaller the correlation between the two images. The gray histogram of the main feature image and the watermarked image is shown in Fig. 4. We can find that there are different gray frequencies in the two images. It proves that the correlation between the two images has been reduced and the security is improved. At the same time, the pixels of the digital image are not independent. The adjacent pixel correlation distribution of the main feature image and the watermarked image is shown in Fig. 5. (a),(b) are the pixels correlation in the horizontal direction, (c),(d) are the pixels correlation in the vertical direction, (e),(f) are the pixels correlation in the diagonal direction. It can be seen that (1) the inter-pixel correlation of the main feature image are different from the inter-pixel correlation of the watermarked image. (2) It can be proved that alpha blending plays a good camouflage effect, which can hide important information and improve security.
Fig. 6. Information entropy.
Table 1 Correlation coefficients.
𝑝𝑖𝑗 𝑙𝑜𝑔𝑝𝑖𝑗
2000
3000
4000
55.5% 15.6% 18.9%
78.2% 18.2% 97.2%
89.9% 34.6% 99.0%
92.1% 44.1% 99.5%
The correlation coefficient (CC) reflects the relationship between the two variables. It indicates the degree of similarity between the original information and the restored information. The correlation coefficient is expressed by CC. The larger the CC value, the better the feasibility of the scheme. Calculation expression is: ⎧ 𝑁 1 ∑ ⎪ 𝑋 E (x) = ⎪ 𝑁 𝑖=1 𝑖 ⎪ 𝑁 )2 ⎪ 1 ∑( D (x) = 𝑥𝑖 − 𝐸 (𝑥) ⎨ 𝑁 ⎪ 𝑖=1 𝑁 ⎪ ∑ ⎪COV (x, y) = 1 (𝑋 − 𝐸(𝑋))(𝑦𝑖 − 𝐸(𝑦)) ⎪ 𝑁 𝑖=1 𝑖 ⎩ 𝑐𝑜𝑣 (𝑥, 𝑦) 𝐶𝐶 = √ √ 𝐷 (𝑥) 𝐷 (𝑦)
In order to objectively evaluate the effect of the LSGI encryption scheme, this paper analyzes LSGI (Double-Layered and Secondary Encryption Based on Ghost Imaging) and DWGI (Digital watermarking combined with ghost imaging without layer) through information entropy. The formula for information entropy is H=
1000
LSGI DWGI CSGI
2.3. Correlation coefficient
2.2. Information entropy
255 ∑
Sampling times
(11)
where x and y represent the pixel values of two adjacent pixel points in the image, respectively, and CC is the correlation coefficient of two adjacent pixel points. The correlation coefficients of the three encryption algorithms (LSGI, DWGI, CSGI) under different sampling times are shown in Table 1. From the row data in Table 1, we can find that (1) as the number of samples increases, LSGI restored information increases the similarity with the original image information, which is more similar to the target. (2) By observing the column data of Table 1, we can find that correlation coefficients of CSGI and LSGI is higher than DWGI. It indicates that two algorithms restore information closer to the original information. (3) The correlation coefficients of LSGI at 4000 samples is similar to CSGI, which exceeds 90%. It indicates that the reduction effect is better, but LSGI is a secondary encryption algorithm. The Security of LSGI is much higher than CSGI.
(10)
𝑖=0
where 𝑝𝑖𝑗 is the probability that a gray value appears in the image, obtained by a gray histogram Eq. (10) can reflect the gray value at a certain position and the comprehensive characteristics of the surrounding pixels. Information entropy can directly express the amount of information included in the image. If the information entropy H value is smaller, the more orderly the system is, the higher the image quality is. The information entropy of the two methods (LSGI and DWGI) under different sampling times is shown in Fig. 6. By observing the trend in Fig. 6, this paper finds that (1) as the number of samples increases, LSGI is smaller. This shows that the more samples are counted, the more orderly LSGI is. The quality of the restored encrypted information is getting higher and higher. (2) At the same time, the information entropy value of DWGI has a lot of fluctuations and instability. It indicates that with the increase of sampling times, the quality of the reduction does not improve, and DWGI is unstable. This can show the importance of stratification
2.4. Peak signal-to-noise ratio In the process of information transmission, it will inevitably be attacked by noise. In order to detect the anti-noise ability of the 5
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Optics Communications 455 (2020) 124585
Table 2 The restoration effect of LSGI after noise attack. Cropping ratio
0%
5%
10%
15%
20%
LSGI
Fig. 8. Experimental device.
Encryption step 3, this paper uses compressed sensing computational ghost imaging encryption, the experimental device (Fig. 8) is using a laser diode as the illumination source and using the camera lens model for Nikon AF-S DX 55–200 mm f∕4 − 5.6 G ED (68 mm*79 mm). Bucket Detect is POINTGREY (BFLY-PGE-50H5M). The capture card is M2i.2030-exp. this paper uses DMD. The object is a watermarked image and a background image that has been scrambled. This paper uses MATLAB software to generate multiple random Gaussian matrices, the matrix is used as the random phase template in this experiment; Step 2: Load these random phase templates onto the DMD chip; Step 3: Place the watermarked image in front of the camera lens; Step 4: Turn on the signal trigger and start the experiment; Step 5: The laser diode first illuminates the watermarked image, and then illuminates the DMD chip; Step 6: The bucket detector receives 4096 times of light diffracted from the object. Decryption Step 1: This paper calculates the signal detected by the barrel detector and the corresponding incident speckle field by MATLAB software. Decryption Step 2: Through the compressed sensing computational ghost image reconstruction, it is found that the image does have some degradation phenomenon. Therefore, according to the second step of the decryption phase, the main feature information is extracted by Eq. (9). At the same time, the background image information is restored. Decryption Step 3: Finally, the restored main feature information is merged with the background information to complete the final decryption. The experiment selected four groups of letter images to repeat the experiment. The results obtained are shown in Table 3. The information entropy, correlation coefficient and peak signal-to-noise ratio are used to objectively evaluate the reduction effect as shown in Table 4. Through experiments and observations in Table 4, this paper finds: (1). In the process of compressed sensing computational ghost imaging, the image has a certain degree of degradation, which has a great impact on the final information extraction. (2). The watermark caused by image degradation can be improved by the formula 8. (3). The experimental results are the same as the numerical simulation results. It proves that the method has certain feasibility.
Fig. 7. Peak signal-to-noise ratio.
algorithm, this paper simulates the noise attack on the three algorithms separately. For LSGI, DWGI and CSGI, This paper adds noise in the ghost image encryption. Noise is ‘‘salt and pepper’’. The result is shown in Fig. 7 . The peak signal to noise ratio (PSNR) is used for objective evaluation. Mathematical expression is ] [ 𝑚 (2 − 1)2 (12) PSNR = 10 × log10 𝑀𝑆𝐸 where MSE is the mean square error between the original image and the reconstructed image. It can be observed from the figure that (1) the PSNR of three algorithms decreases as the noise density increases. (2) Overall, as the noise density increases, the PSNR of LSGI is higher than DWGI. (3) Observe the trend of the graph. As the noise density increases, the PSNR value of LSGI decreases less. It indicates that LSGI has greater antinoise ability. The restoration effect of LSGI after noise attack is shown in Table 2. Through the analysis of 2.1–2.4, we found that if the layering technique is not used, the encryption method that digital watermark directly combined with ghost imaging is unstable. However DoubleLayered and Secondary Encryption Based on Ghost Imaging (LSGI) has excellent capabilities in restoring encrypted information quality and anti-noise attacks. 3. Experiment In the experimental chapter, this paper uses the combination of digital simulation and experiment. The experimental part is the compressed sensing computational ghost imaging encryption for the watermarked image that has been encrypted once. The rest process is digital simulation. Because DMD has higher precision for light modulation, this paper replaces the SLM in Fig. 1 with DMD in the experiment. Encryption steps 1–2. An image is segmented, and the main feature information of the image is used as a watermark. Use technology of alpha blending to complete an encryption. Prepare for compressed sensing computational ghost imaging encryption experiments.
4. Conclusion This paper proposes a new encryption method: Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). LSGI solves the 6
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Table 3 Experimental result.
Table 4 Objective evaluation. Image name
1: U
2: a
3: S
4: T
Information entropy Correlation coefficient Peak signal-to-noise ratio
4.05 65% 7.8
3.75 63% 17.6
2.83 89% 18.9
2.89 32% 11.2
[2] S. Liu, C. Guo, J.T. Sheridan, A review of optical image encryption techniques, Opt. Laser Technol. 57 (2014) 327–342. [3] A. Alfalou, C. Brosseau, Optical image compression and encryption methods, Adv. Opt. Photon. 1 (3) (2009) 589–636. [4] P. Refregier, B. Javidi, Optical image encryption based on input plane and fourier plane random encoding, Opt. Lett. 20 (7) (1995) 767–769. [5] Z. Liu, S. Liu, Double image encryption based on iterative fractional fourier transform, Opt. Commun. 275 (2007) 324–329. [6] D.N. Klyshko, Klyshko DN two-photon light influence of filtration and a new possible EPR experiment, Phys. Lett. A 128 (3–4) (1988) 133–137. [7] J.H. Shapiro, Computational ghost imaging, Phys. Rev. A 78 (6) (2008) 061802. [8] F. Ferri, Differential ghost imaging, Phys. Rev. Lett. 104 (25) (2010) 253603. [9] J.H. Shapiro, R.W. Boyd, The physics of ghost imaging, Quantum Inf. Process. 11 (4) (2012) 949–993. [10] Hongchao Liu, Jun Xiong, Properties of high-order ghost imaging with natural light, J. Opt. Soc. Amer. A 30 (5) (2013) 956–961. [11] Z. Liu, S. Tan, J. Wu, et al., Spectral Camera based on ghost imaging via sparsity constraints, Sci. Rep. 6 (2016) 25718. [12] Jie Chen, Wenli Gong, Shensheng Han, Sub-Rayleigh ghost imaging via sparsity constraints based on a digital micro-mirror device, Phys. Lett. A 377 (31) (2013) 1844–1847. [13] Baoqing Sun, Stephen S. Welsh, Matthew P. Edgar, Jeffrey H. Shapiro, Miles J. Padgett, Normalized ghost imaging, Opt. Express 20 (15) (2012) 16892–16901. [14] P. Clemente, V. Durán, E. Tajahuerce, et al., Optical encryption based on computational ghost imaging, Opt. Lett. 35 (14) (2010) 2391–2393. [15] S.M. Zhao, L. Wang, W. Liang, et al., High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique, Opt. Commun. 353 (2015) 90–95. [16] Z. Yang, L.I. Dapeng, H. Peng, et al., Parallel compressive ghost imaging based on threshold segmentation, Opt. Tech. 42 (4) (2016) 289–293. [17] Akhil Pratap Singh, Agya Mishra, Wavelet based watermarking on digital image, Indian J. Comput. Sci. Eng. 1 (2) (2011) 86–91. [18] K.T. Gribbon, A novel approach to real-time bilinear interpolation, DELTA 2004, 126-131. [19] Adil Bouhous, Karim Kemih, Adil bouhous karim kemih novel encryption method based on optical time-delay chaotic system and a wavelet for data transmission, Opt. Laser Technol. 108 (2018) 162–169.
shortcomings of the current secondary encryption algorithm and breaks through the limitation of traditional secondary encryption. Compared with compressed sensing ghost imaging encryption, LSGI combines more methods to become more secure. In the process of compressed sensing computational ghost imaging, this paper combines information segmentation technology. The layered algorithm proposed in this paper can greatly improve the quality of encryption information restoration. It improves the accuracy of secondary encryption and has strong immune effect on environmental noise. In the future, different information in a picture will be processed in the encryption process. This process will be safe and effective. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI) has broad prospects. Acknowledgments This research was funded by Natural Science Foundation of Shanghai, China (Grant No. 18ZR1425800, 14ZR1428400), the Open Project of Anhui Province Key Laboratory of Nondestructive Evaluation, China (Grant No. CGHBMWSJC03), and the National Natural Science Foundation of China (Grant No. 61875125, 61405115) References [1] O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, B. Javidi, Optical techniques for information security, Proc. IEEE 97 (6) (2009) 1128–1148.
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Research on Double-Layers optical information Encryption Based on Ghost Imaging Zhang Leihong, Zhang Zhisheng, Kang Yi, Ye Hualong, Xiong Rui, Yuan Xiao, Wang Zhaorui, Wang Kaimin, Zhang Dawei ∗ University of Shanghai for Science and Technology, Shanghai 200093, China
ARTICLE
INFO
Keywords: Optical information encryption Ghost imaging encryption Secondary encryption
ABSTRACT With the development of technology, digital images are greatly threatened during transmission. It is difficult to ensure the security of information in the early traditional encryption methods. Using different encryption technologies to form a secondary encryption can greatly improve the security of image encryption transmission, but facing the problems of low efficiency and poor accuracy. Based on ghost imaging and compressed sensing technology, this paper proposes a new optical information encryption algorithm: Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). In this paper, the feasibility of the algorithm is further studied and analyzed. Numerical simulations show that the algorithm can effectively improve the security. Experiments show that the algorithm can also improve the accuracy of restoration.
0. Introduction With the rapid development of Internet technology, Internet information spreads widely, and information security has received more and more attention. Due to the high parallelism, high speed and high storage, optical information encryption technology is favored by researchers. In recent years, many scholars have proposed different optical encryption methods, such as: ghost imaging encryption, chaotic encryption, dual random phase encryption, etc. [1–5]. K Klyshko [6] proposed a scheme about ghost imaging based on the entanglement behavior of two photon light. Shapiro and Bromber et al. [7] used a spatial light modulator (SLM) to achieve computational ghost imaging. F. Ferri et al. [8] proposed differential ghost imaging. This method reduces the influence of external environmental noise on the imaging quality. There are also many scholars who have proposed different ghost imaging methods [9–13]. In the field of encryption, Pere Clemente [14] first proposed an optical information encryption method based on computational ghost imaging, with non-locality imaging and good security. In 2015, Zhao Shengmei et al. [15] proposed a highperformance optical encryption based on CGI with QR encoding and compression sensing technology. In 2016, Yang Zhaohua et al. [16] proposed Parallel Compressive Ghost Imaging Based on Threshold Segmentation, which reduces the complexity of computer processing and the requirements of hardware. Although the above method improves the quality of some images and increases the speed of imaging, but the single encryption method has limitations. The consequences of being compromised are unimaginable. Secondary encryption improves
the security of the encryption system by combining two encryption technologies. However, the superposition of technology increases the complexity of the system. In the actual process, the information cannot be restored due to image degradation. A picture often contains a lot of information, in which the main feature information is dominant. It is the information that dominates the main content of the picture. In contrast, background information is in a relatively minor position. At present, most image encryption transmissions use the entire image information as a carrier, in this way, the encryption method of information is limited. This paper proposes a new encryption method: Double-Layered and Secondary Encryption Based on Ghost Imaging. This paper layered the information of a picture. This paper performed different secondary encryption for different levels of information. Different levels of information have different emphasis. The advantage of this method is that the information security and restoration quality of information is improved. In this paper, the layered optical encryption of image information is verified by experiments. This algorithm extends the method of secondary encryption based on ghost imaging. It provides a reference for further improving the accuracy of image gray information restoration. 1. Theoretical description 1.1. Computational ghost imaging Ghost imaging is a new imaging method. Unlike traditional imaging, ghost imaging is a non-local imaging. In optical encryption, ghost imaging encryption has advantages in security and reliability.
∗ Corresponding author. E-mail address: [email protected] (Z. Dawei).
https://doi.org/10.1016/j.optcom.2019.124585 Received 19 May 2019; Received in revised form 17 July 2019; Accepted 15 September 2019 Available online 18 September 2019 0030-4018/© 2019 Published by Elsevier B.V.
Z. Leihong, Z. Zhisheng, K. Yi et al.
Optics Communications 455 (2020) 124585
The principle of computing ghost imaging is shown in Fig. 1. There are N normal Gaussian random distribution matrices 𝜑𝑛 (𝑥, 𝑦) as a key and 𝜑𝑛 (𝑥, 𝑦) is evenly distributed over [0, 2𝜋]. Spatial light modulator (SLM) modulates the intensity of the light field. Each modulation produces a speckle field. The intensity distribution of the speckle field is I(𝑥, 𝑦). The modulated speckle field is irradiated onto the object 𝑇 (𝑥, 𝑦). The value of the light intensity transmitted through the object as 𝐵𝑛 . Repeat the measurement calculation N times to get N different { }𝑁 measurement values 𝐵𝑖 𝑖=1 . This process is shown in Eq. (1). 𝐼𝑛 (𝑥, 𝑦) is calculated according to the Fresnel propagation function as shown in the formula (2). 𝐵𝑛 =
∫
𝐼𝑛 (𝑥, 𝑦) 𝑇 (𝑥, 𝑦) 𝑑𝑥𝑑𝑦 [
] | | 𝐼𝑛 (𝑥, 𝑦) = |𝐸𝑖𝑛 (𝑥, 𝑦) 𝑒𝑥𝑝 𝑗𝜑𝑛 (𝑥, 𝑦) ⊗ ℎ𝑧 (𝑥, 𝑦)| | |
(1) Fig. 1. Principle of computational ghost imaging.
(2)
where ℎ𝑧 (𝑥, 𝑦) is the Fresnel diffraction function, and ⊗ stands for convolution. In the imaging process, this paper performs N times of sampling. Correlates the intensity distribution of the speckle field with the measured value of the light intensity, reconstructs the information to restore the original information, and completes the reconstruction. The reconstruction formula for computing ghost imaging is expressed as: 𝑇𝐺𝐼 (𝑥, 𝑦) =
𝑁 ) 1 ∑( 𝐵 − ⟨𝐵𝑛 ⟩ 𝐼𝑛 (𝑥, 𝑦) 𝑁 𝑛=1 𝑛
where f(x) is the pixel value of the point (x, y), L(x), g(x) is the divided image, Y(x) is the original image, and T is the threshold. The second step (the first encryption: watermark and scrambling): Load the image to be encrypted into the covered image with a certain weight. The specific method: (1) Use the main feature information as a watermark. (2) The watermark and covered image perform twodimensional discrete wavelet transform (DWT). (3) Decompose them into sub-images with different frequency domain characteristics. (4) Insert the low frequency part of the watermark into the low frequency of the covered image. After the insertion, the watermark information will be hidden in the covered image. The Insertion technique is alpha blending [17], formula as
(3)
where ⟨𝐵𝑛 ⟩ is the average value of the total light intensity measured n times. Compressed sensing computational ghost imaging uses the sparse characteristics of the information to obtain information at a rate lower than the Nyquist sampling limit. This method obtains a clearer picture with less sampling. The process expression is 𝑇𝐶𝑆 = T (𝑥, 𝑦) ∶ 𝑎𝑟𝑔𝑚𝑖𝑛 ‖𝛹 {T (𝑥, 𝑦)}‖ 𝐿1
𝛾𝐿𝐿 = 𝐾 ⋅ 𝛼𝐿𝐿 + 𝐺 ⋅ 𝛽𝐿𝐿
(6)
where 𝛼𝐿𝐿 is the low frequency part of the watermark, 𝛽𝐿𝐿 is the low frequency part of the covered image. K, G are scaling factors. The purpose of this is that the information of the main feature layer is hidden under the covered image. Once the information is attacked by illegal users, the method will act as a disguise and mislead the illegal user. Encryption for the background layer is fast scrambling by twodimensional Discrete Cosine Transform (DCT). In order to improve the encryption efficiency, this paper decided to use the bilinear interpolation [18] for the main feature layer. This paper compresses the information to form thumbnails, retains key pixels in the process of zooming out, removes redundant information, and reconstructs better images in ghost imaging with fewer samples. The image is magnified by a bilinear interpolation algorithm at the time of decryption. This processing can improve Double-Layered and Secondary encryption’s efficiency and reduce overall sampling time. The third step (the second encryption): the watermarked image and the scrambled image are encrypted by compressed sensing computational ghost imaging. Before the third step, the watermarked image is a two-dimensional image 𝑇 (𝑥, 𝑦). In the third step, the image is substituted into formula 1. Convert a two-dimensional image into a one-dimensional column vector. The intensity distribution function 𝐼𝑛 (𝑥, 𝑦) as a random matrix is also a measurement matrix in compressed sensing. At this point, the matrix expression of the encryption process is:
(4)
where ||⋅||𝐿1 is norm, 𝛹 means sparse representation; 1.2. Double-layers optical encryption This paper proposes a new encryption method — Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). As shown in Fig. 2, the encryption phase is mainly divided into three steps. The first step: Separates feature information from background. Divide the original image into the main feature layer and the background layer. The second step (First encryption): use the main feature information as the watermark. Then alpha blends [7] the watermark and the cover image. Quickly scramble background information. The third step: The watermarked image and the scrambled background image are encrypted by compressed sensing computational ghost imaging, respectively. Correspondingly, the decryption phase is also divided into three steps. The first step: Reconstruct the image by compressed sensing computational ghost image. The second step: Extract the main feature image and restore the background image. The third step: Integrate the main feature information into background.
⎡ 1 1 1 ⎤ ⎡ 𝐵1 ⎤ ⎢𝐼11 ⋯𝐼1𝑛 ⋯𝐼𝑛𝑛 ⎥ ⎡𝑇11 ⎤ ⎢ ⎥ ⎢ ⎥ ⎢𝐼 2 𝐼 2 2 ⎥ ⋮ ⎢ 𝐵2 ⎥ = ⎢ 11 ⋯ 1𝑛 ⋯𝐼𝑛𝑛 ⎥ ⎢⎢𝑇 ⎥⎥ ⎢ ⋮ ⎥ ⎢ ⎥ 1𝑛 ⎢𝐵 ⎥ ⎢ ⋮ ⋱ ⋮ ⋱ ⋮ ⎥ ⎢⎢ ⋮ ⎥⎥ ⎣ 𝑁⎦ ⎢ 𝑁 𝑁⎥ 𝑇 𝑁 ⎣𝐼 ⋯𝐼 ⋯𝐼 ⎦ ⎣ 𝑛𝑛 ⎦
1.2.1. Encryption The first step: Use the threshold segmentation technology to divide the information. Segment the main feature layer and the background layer. In the main feature layer, the background information has been cleared, and the main feature information in the background layer has been cleared. This paper uses threshold segmentation techniques to segment information. This paper selects the pixel value between the two peaks as the threshold value, and divide the information into two layers of the same size. The process is as follows { 𝐿 (𝑥) , 𝑓 (𝑥, 𝑦) > 𝑇 𝑌 (𝑥) = (5) 𝑔 (𝑥) 𝑓 (𝑥, 𝑦) ≤ 𝑇
11
1𝑛
(7)
𝑛𝑛
⎡ 𝐵1 ⎤ ⎢ ⎥ 𝐵 where ⎢ 2 ⎥ is the cipher text encrypted by compressed sensing com⎢ ⋮ ⎥ ⎢𝐵 ⎥ ⎣ 𝑁⎦ putational ghost imaging. 2
Z. Leihong, Z. Zhisheng, K. Yi et al.
Optics Communications 455 (2020) 124585
Fig. 2. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI).
1.2.2. Decryption The first step: Reconstruct the image by compressed sensing computational ghost imaging. Calculate the light intensity information 𝐼𝑛 (𝑥, 𝑦) by the key 𝜑𝑛 (𝑥, 𝑦). Associate 𝐼𝑛 (𝑥, 𝑦) with cipher text to reconstruct a two-dimensional image. The process expression is the same as Eq. (4). The second step: At this stage, the main feature image information and background image information are extracted from the reconstructed image. This paper performs the DWT on the reconstructed watermarked image after compressed sensing computational ghost imaging, then decompose it into sub-images, and then extract watermark from these sub-images [17]. The expression of this process is: ( ) 𝜀𝐿𝐿 − 𝐺 ⋅ 𝛽𝐿𝐿 ÷ K = 𝛼𝐿𝐿 (8) where K, G are scaling factors, 𝜀𝐿𝐿 is the low frequency part of the reconstructed watermarked image, and 𝛽𝐿𝐿 is an approximation of the low frequency part of the covered image. Different from the valuation used in [19], this paper considers that in the actual ghost imaging process, the image will degrade and affect the pixel value of the image. If this paper uses the estimate of the low frequency of the covered image before compressed sensing computational ghost imaging reconstruction, it will not extract valid information. Therefore, this paper have improved the approximation 𝛽𝐿𝐿 of the covered image in the experiment. This paper filters the reconstructed watermarked image to recover the covered image. Use the difference between the reconstructed watermarked image and the covered image to extract the watermark information 𝛼𝐻𝑌 , ( ) J ⋅ 𝜀𝐻𝑌 − 𝐺 ⋅ 𝛽𝐻𝑌 ÷ K = 𝛼𝐻𝑌 (9)
Fig. 3. Simulation results: (a) Original image (b) Main feature layer (c) Background layer (d) Covered image (e) Watermarked image (f) quickly scrambled image (g) Compressed sensing Computational ghost image (h) Extracted watermark (i) Final restored image.
where J, K, G are scaling factors, 𝜀𝐻𝑌 is the watermarked image reconstructed by compressed sensing computational ghost imaging, and
Fig. 4. Grayscale histogram: (a) Gray histogram of Main feature image (b) Gray histogram of Watermarked image.
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Z. Leihong, Z. Zhisheng, K. Yi et al.
Optics Communications 455 (2020) 124585
Fig. 5. pixel correlation: (a) Pixel correlation of Main feature image in the horizontal direction (b) Pixel correlation of Watermarked image in the horizontal direction (c) Pixel correlation of Main feature image in the vertical direction (d) Pixel correlation of Watermarked image in the vertical direction (e) Pixel correlation of Main feature image in the diagonal direction (f) Pixel correlation of Watermarked image in the diagonal direction.
𝛽𝐻𝑌 is the difference between the reconstructed watermarked image and the covered image. This paper extracts the watermark from the reconstructed image and get the main feature information of the original image. Restore the background information of the original image from the reconstructed scrambled image. The third step: finally integrate the main feature information into background information.
the Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). This section uses MATLAB R2016a software simulation to achieve. The original image size is a 64×64 grayscale image. The simulation results are shown in Fig. 3. In Fig. 3, a (original image) is divided into b (main feature layer) and c (background layer). Blend b (main feature layer) into d (covered image) to form e (watermarked image). f is quickly scrambled by c.
2. Numerical simulation
g is the image after compressed sensing computational ghost imaging, extracts h from it. Restore background layer after compressed sensing
By combining bilinear interpolation technology and alpha blending technology, the security of compressed sensing ghost imaging encryption technology is further enhanced. This section will analyze
computational ghost imaging. Integrate the main feature information into background information. Reconstruct the final restored image i. 4
Z. Leihong, Z. Zhisheng, K. Yi et al.
Optics Communications 455 (2020) 124585
This paper uses information entropy, PSNR (peak signal-to-noise ratio), and CC (correlation coefficient) as quantitative indicators. Reconstructed images of LSGI (Double-Layered and Secondary Encryption Based on Ghost Imaging), CSGI (Compressed sensing ghost imaging), and DWGI (Digital watermarking combined with ghost imaging without double-layers) were analyzed. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI) has two different layers of sampling times. The average of sampling times of the main feature layer and the background layer is taken as the sampling number of LSGI. 2.1. Safety This paper uses the technique of alpha blending when we are encrypting. According to research [19], alpha blending can greatly reduce the correlation of adjacent pixels and improve the anti-attack capability. The histogram of the image is a method of statistical image features. The histogram distribution of different images is different. In other words, the greater the difference in the histogram distribution of the image, the smaller the correlation between the two images. The gray histogram of the main feature image and the watermarked image is shown in Fig. 4. We can find that there are different gray frequencies in the two images. It proves that the correlation between the two images has been reduced and the security is improved. At the same time, the pixels of the digital image are not independent. The adjacent pixel correlation distribution of the main feature image and the watermarked image is shown in Fig. 5. (a),(b) are the pixels correlation in the horizontal direction, (c),(d) are the pixels correlation in the vertical direction, (e),(f) are the pixels correlation in the diagonal direction. It can be seen that (1) the inter-pixel correlation of the main feature image are different from the inter-pixel correlation of the watermarked image. (2) It can be proved that alpha blending plays a good camouflage effect, which can hide important information and improve security.
Fig. 6. Information entropy.
Table 1 Correlation coefficients.
𝑝𝑖𝑗 𝑙𝑜𝑔𝑝𝑖𝑗
2000
3000
4000
55.5% 15.6% 18.9%
78.2% 18.2% 97.2%
89.9% 34.6% 99.0%
92.1% 44.1% 99.5%
The correlation coefficient (CC) reflects the relationship between the two variables. It indicates the degree of similarity between the original information and the restored information. The correlation coefficient is expressed by CC. The larger the CC value, the better the feasibility of the scheme. Calculation expression is: ⎧ 𝑁 1 ∑ ⎪ 𝑋 E (x) = ⎪ 𝑁 𝑖=1 𝑖 ⎪ 𝑁 )2 ⎪ 1 ∑( D (x) = 𝑥𝑖 − 𝐸 (𝑥) ⎨ 𝑁 ⎪ 𝑖=1 𝑁 ⎪ ∑ ⎪COV (x, y) = 1 (𝑋 − 𝐸(𝑋))(𝑦𝑖 − 𝐸(𝑦)) ⎪ 𝑁 𝑖=1 𝑖 ⎩ 𝑐𝑜𝑣 (𝑥, 𝑦) 𝐶𝐶 = √ √ 𝐷 (𝑥) 𝐷 (𝑦)
In order to objectively evaluate the effect of the LSGI encryption scheme, this paper analyzes LSGI (Double-Layered and Secondary Encryption Based on Ghost Imaging) and DWGI (Digital watermarking combined with ghost imaging without layer) through information entropy. The formula for information entropy is H=
1000
LSGI DWGI CSGI
2.3. Correlation coefficient
2.2. Information entropy
255 ∑
Sampling times
(11)
where x and y represent the pixel values of two adjacent pixel points in the image, respectively, and CC is the correlation coefficient of two adjacent pixel points. The correlation coefficients of the three encryption algorithms (LSGI, DWGI, CSGI) under different sampling times are shown in Table 1. From the row data in Table 1, we can find that (1) as the number of samples increases, LSGI restored information increases the similarity with the original image information, which is more similar to the target. (2) By observing the column data of Table 1, we can find that correlation coefficients of CSGI and LSGI is higher than DWGI. It indicates that two algorithms restore information closer to the original information. (3) The correlation coefficients of LSGI at 4000 samples is similar to CSGI, which exceeds 90%. It indicates that the reduction effect is better, but LSGI is a secondary encryption algorithm. The Security of LSGI is much higher than CSGI.
(10)
𝑖=0
where 𝑝𝑖𝑗 is the probability that a gray value appears in the image, obtained by a gray histogram Eq. (10) can reflect the gray value at a certain position and the comprehensive characteristics of the surrounding pixels. Information entropy can directly express the amount of information included in the image. If the information entropy H value is smaller, the more orderly the system is, the higher the image quality is. The information entropy of the two methods (LSGI and DWGI) under different sampling times is shown in Fig. 6. By observing the trend in Fig. 6, this paper finds that (1) as the number of samples increases, LSGI is smaller. This shows that the more samples are counted, the more orderly LSGI is. The quality of the restored encrypted information is getting higher and higher. (2) At the same time, the information entropy value of DWGI has a lot of fluctuations and instability. It indicates that with the increase of sampling times, the quality of the reduction does not improve, and DWGI is unstable. This can show the importance of stratification
2.4. Peak signal-to-noise ratio In the process of information transmission, it will inevitably be attacked by noise. In order to detect the anti-noise ability of the 5
Z. Leihong, Z. Zhisheng, K. Yi et al.
Optics Communications 455 (2020) 124585
Table 2 The restoration effect of LSGI after noise attack. Cropping ratio
0%
5%
10%
15%
20%
LSGI
Fig. 8. Experimental device.
Encryption step 3, this paper uses compressed sensing computational ghost imaging encryption, the experimental device (Fig. 8) is using a laser diode as the illumination source and using the camera lens model for Nikon AF-S DX 55–200 mm f∕4 − 5.6 G ED (68 mm*79 mm). Bucket Detect is POINTGREY (BFLY-PGE-50H5M). The capture card is M2i.2030-exp. this paper uses DMD. The object is a watermarked image and a background image that has been scrambled. This paper uses MATLAB software to generate multiple random Gaussian matrices, the matrix is used as the random phase template in this experiment; Step 2: Load these random phase templates onto the DMD chip; Step 3: Place the watermarked image in front of the camera lens; Step 4: Turn on the signal trigger and start the experiment; Step 5: The laser diode first illuminates the watermarked image, and then illuminates the DMD chip; Step 6: The bucket detector receives 4096 times of light diffracted from the object. Decryption Step 1: This paper calculates the signal detected by the barrel detector and the corresponding incident speckle field by MATLAB software. Decryption Step 2: Through the compressed sensing computational ghost image reconstruction, it is found that the image does have some degradation phenomenon. Therefore, according to the second step of the decryption phase, the main feature information is extracted by Eq. (9). At the same time, the background image information is restored. Decryption Step 3: Finally, the restored main feature information is merged with the background information to complete the final decryption. The experiment selected four groups of letter images to repeat the experiment. The results obtained are shown in Table 3. The information entropy, correlation coefficient and peak signal-to-noise ratio are used to objectively evaluate the reduction effect as shown in Table 4. Through experiments and observations in Table 4, this paper finds: (1). In the process of compressed sensing computational ghost imaging, the image has a certain degree of degradation, which has a great impact on the final information extraction. (2). The watermark caused by image degradation can be improved by the formula 8. (3). The experimental results are the same as the numerical simulation results. It proves that the method has certain feasibility.
Fig. 7. Peak signal-to-noise ratio.
algorithm, this paper simulates the noise attack on the three algorithms separately. For LSGI, DWGI and CSGI, This paper adds noise in the ghost image encryption. Noise is ‘‘salt and pepper’’. The result is shown in Fig. 7 . The peak signal to noise ratio (PSNR) is used for objective evaluation. Mathematical expression is ] [ 𝑚 (2 − 1)2 (12) PSNR = 10 × log10 𝑀𝑆𝐸 where MSE is the mean square error between the original image and the reconstructed image. It can be observed from the figure that (1) the PSNR of three algorithms decreases as the noise density increases. (2) Overall, as the noise density increases, the PSNR of LSGI is higher than DWGI. (3) Observe the trend of the graph. As the noise density increases, the PSNR value of LSGI decreases less. It indicates that LSGI has greater antinoise ability. The restoration effect of LSGI after noise attack is shown in Table 2. Through the analysis of 2.1–2.4, we found that if the layering technique is not used, the encryption method that digital watermark directly combined with ghost imaging is unstable. However DoubleLayered and Secondary Encryption Based on Ghost Imaging (LSGI) has excellent capabilities in restoring encrypted information quality and anti-noise attacks. 3. Experiment In the experimental chapter, this paper uses the combination of digital simulation and experiment. The experimental part is the compressed sensing computational ghost imaging encryption for the watermarked image that has been encrypted once. The rest process is digital simulation. Because DMD has higher precision for light modulation, this paper replaces the SLM in Fig. 1 with DMD in the experiment. Encryption steps 1–2. An image is segmented, and the main feature information of the image is used as a watermark. Use technology of alpha blending to complete an encryption. Prepare for compressed sensing computational ghost imaging encryption experiments.
4. Conclusion This paper proposes a new encryption method: Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI). LSGI solves the 6
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Optics Communications 455 (2020) 124585
Table 3 Experimental result.
Table 4 Objective evaluation. Image name
1: U
2: a
3: S
4: T
Information entropy Correlation coefficient Peak signal-to-noise ratio
4.05 65% 7.8
3.75 63% 17.6
2.83 89% 18.9
2.89 32% 11.2
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shortcomings of the current secondary encryption algorithm and breaks through the limitation of traditional secondary encryption. Compared with compressed sensing ghost imaging encryption, LSGI combines more methods to become more secure. In the process of compressed sensing computational ghost imaging, this paper combines information segmentation technology. The layered algorithm proposed in this paper can greatly improve the quality of encryption information restoration. It improves the accuracy of secondary encryption and has strong immune effect on environmental noise. In the future, different information in a picture will be processed in the encryption process. This process will be safe and effective. Double-Layered and Secondary Encryption Based on Ghost Imaging (LSGI) has broad prospects. Acknowledgments This research was funded by Natural Science Foundation of Shanghai, China (Grant No. 18ZR1425800, 14ZR1428400), the Open Project of Anhui Province Key Laboratory of Nondestructive Evaluation, China (Grant No. CGHBMWSJC03), and the National Natural Science Foundation of China (Grant No. 61875125, 61405115) References [1] O. Matoba, T. Nomura, E. Perez-Cabre, M. Millan, B. Javidi, Optical techniques for information security, Proc. IEEE 97 (6) (2009) 1128–1148.
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