Compressed optical encryption and decryption methods based on ghost imaging and image authentication

Abstract

This invention discloses a compressed optical encryption scheme based on ghost imaging and image authentication. During encryption, the target object is illuminated using Hadamard speckle lighting, and the intensity of the reflected light is collected by a bucket detector. To improve data transmission security, a steganography method is introduced to hide the data. The collected bucket signals are encoded into a series of random binary speckle sequences and hidden within a projection pattern used to illuminate the authentication image. During the measurement of the authentication image, diffraction data is collected using the bucket detector to obtain the sequence authentication key data. Once the receiver is authenticated, the corresponding key is sent to recover the secret image. This invention introduces an authentication method, improves the security of information transmission, compresses the data, and the proposed encryption method has high decryption quality and security.

Description

Technical Field

[0001] This invention relates to the field of image technology, and in particular to a compressed optical encryption and decryption method based on ghost imaging and image authentication. Background Technology

[0002] Ghost imaging, as a novel imaging technique, possesses nonlocality, meaning it can reconstruct the target object in an optical path that does not contain information about the target object. This characteristic enables imaging in complex media. Furthermore, ghost imaging reconstructs target object information through correlation operations using multiple samples, thus showing great potential in complex environments and information compression. The earliest ghost imaging technology can be traced back to 1995, when Pittman's group at the University of Maryland proposed an imaging scheme based on a two-photon entangled light source, experimentally verifying the feasibility of the theory. With the development of GI technology, in 2008, Shapiro proposed the theory of computational ghost imaging, greatly simplifying the experimental optical path of ghost imaging by using a spatial light modulator to generate active illumination speckle. Since then, computational ghost imaging has experienced rapid development, with many new theories and methods being proposed.

[0003] Recently, ghost imaging technology has been widely used in image encryption. Compared with traditional optical encryption schemes, ghost imaging-based encryption has lower experimental requirements, lower cost, and simpler ciphertext, significantly reducing the required storage space. However, the input and output of ghost imaging encryption exhibit a linear relationship, making it vulnerable to chosen-plaintext attacks. To improve its security, researchers have proposed many encryption schemes. In 2010, scholars first applied CGI technology to optical image encryption, which greatly simplified the ciphertext storage space. In 2014, scholars hid multiple markers within the same image to achieve ghost imaging encryption. In 2015, scholars proposed an optical encryption scheme based on QR coding and compressed sensing technology. In 2021, scholars proposed an optical color image encryption method based on Hadamard single-pixel imaging and Arnold transform.

[0004] Currently, most encryption methods based on ghost imaging use a large number of illumination patterns as keys to encode the pixel values ​​of the image, and the collected bucket signals are used as ciphertext. Encrypting large-pixel images typically requires storing and transmitting a large number of illumination patterns, resulting in a massive amount of measurements and data, thus significantly limiting its practical application. Furthermore, ghost imaging encryption exhibits a linear input-output relationship, making it vulnerable to attacks and interference from thieves; therefore, the security of the encryption system needs further improvement. Summary of the Invention

[0005] The purpose of this invention is to provide a compressed optical encryption and decryption method based on ghost imaging and image authentication. This invention introduces an authentication method, improving security during information transmission, and compresses the data. Furthermore, the proposed encryption method offers high decryption quality and security.

[0006] The technical solution of this invention: a compressed optical encryption and decryption method based on ghost imaging and image authentication, comprising the following steps:

[0007] Encryption process:

[0008] (1) Image compression sampling: The target object is illuminated using Hadamard speckle, and the intensity of the reflected light from the object is collected by a barrel detector to obtain the light intensity value D;

[0009] (2) Data Steganography: The collected light intensity values ​​D are encoded into a series of random binary matrices {P} O}, and obtain the key k1;

[0010] (3) Generate authentication key: Generate the random binary matrix {P} O The key is hidden within the projection pattern used to illuminate the authentication image, and the key k2, ciphertext C, and authentication key k are obtained.

[0011] Decryption process:

[0012] (a) Authentication: The receiver performs an association operation based on the authentication key k and the ciphertext C to recover a blurred image, and sends the image back to the sender for identity authentication. After successful authentication, the sender sends the key k1 and key k2 to the receiver.

[0013] (b) Decryption: Recover the secret image using keys k1 and k2.

[0014] The compressed optical encryption and decryption method based on ghost imaging and image authentication described above includes the following steps in the image compression sampling:

[0015] 1.1. Using a computer to generate lighting patterns, by adjusting the impulse function σ H (u,v) is subjected to inverse Hadamard transform to generate Hadamard speckle I(x,y) for projection:

[0016]

[0017] Where (x,y) represents the spatial coordinates, H -1 This represents the inverse Hadamard transform, where (u,v) represents the Hadamard domain coordinates, and the impulse function is expressed as:

[0018]

[0019] In the formula: (u0, v0) is an initial position coordinate of the Hadama domain;

[0020] Another group of speckles with elemental values ​​opposite to those of the Hadamard speckle is represented as follows:

[0021] I - (x,y)=1-I + (x,y);

[0022] I + (x,y) and I-(x,y) represent a pair of complementary Hadamard speckle patterns;

[0023] 1.2 Project the generated Hadamard speckle pattern sequentially onto the secret image, and use a bucket detector to record the intensity value D of the reflected light in turn:

[0024] D i =∫∫I i (x,y)O(x,y)dxdy;

[0025] Among them I i (x,y) represents the i-th Hadamard speckle pattern in the projection, and O(x,y) represents the target object to be encrypted.

[0026] The aforementioned compressed optical encryption and decryption method based on ghost imaging and image authentication includes the following steps in data steganography:

[0027] 2.1. Two one-dimensional arrays {D1} and {D2} are obtained by combining the light intensity values ​​D. The two arrays {D1} and {D2} are concatenated into a single array {D}.

[0028] 2.2 Reset the one-dimensional array {D} into a two-dimensional matrix S, and use the reset two-dimensional matrix S as the additional key k1;

[0029] 2.3. Using pixel value decomposition, the two-dimensional matrix S is decomposed into a series of random binary matrices {P}. O The value at each position in a two-dimensional matrix S is equal to the sum of the values ​​at the corresponding positions in all random matrices.

[0030] S(i,j)={P1(i,j)+P2(i,j)+…+P k (i,j)};

[0031] Among them, P k Let (i,j) represent the k-th matrix of the decomposition, and (i,j) represent the position coordinates of the matrix.

[0032] In the aforementioned compressed optical encryption and decryption method based on ghost imaging and image authentication, step 2.1 uses two scaling factors λ1 and λ2 during stitching. To make corrections:

[0033]

[0034] in Represents splicing, and These represent the average values ​​of arrays {D1} and {D2}, respectively.

[0035] The aforementioned compressed optical encryption and decryption method based on ghost imaging and image authentication includes the following steps for generating the authentication key:

[0036] 3.1 Generate a set of random binary matrices {P} on a computer. NO};

[0037] 3.2, The matrix {P} O Randomly insert into matrix {P} NO Generate a new random matrix {P} in}, use the inserted position sequence as the additional key k2, and use the random matrix {P} as the ciphertext C;

[0038] 3.3. Illuminate the authentication map with the generated random matrix {P} and collect the reflected light intensity sequence {B} of the authentication map using a bucket detector;

[0039] B i =∫∫P i (x,y)T(x,y)dxdy;

[0040] Among them, P i (x,y) represents the i-th random speckle image of the projection; T(x,y) represents the authentication image;

[0041] 3.4. Binarize the sequence {B} with the threshold set as the average value of the sequence. Use the binarized sequence as the authentication key k.

[0042] The aforementioned compressed optical encryption and decryption method based on ghost imaging and image authentication uses a nonlinear correlation algorithm for authentication.

[0043] NC(x,y)=|IFT{|FT(T)·[FT(T′)] * | w-1 ·FT(T′)·[FT(T)] *}| 2 ;

[0044] Where FT(·) represents the two-dimensional Fourier transform, IFT(·) represents the two-dimensional inverse Fourier transform, T represents the authentication map, T′ represents the reconstructed authentication map, and w represents the nonlinear intensity;

[0045] Once a relevant peak appears in the authentication graph, it indicates successful authentication. The sender then sends additional keys k1 and k2 to the receiver.

[0046] The aforementioned compressed optical encryption and decryption method based on ghost imaging and image authentication includes the following decryption steps:

[0047] b.1 The receiver uses key k2 to extract the random binary matrix {P} from the ciphertext {P}. O};

[0048] b.2, Next, for all random binary matrices {P} O The pixel values ​​of} are summed to obtain a two-dimensional matrix S:

[0049]

[0050] b.3. Use key k1 to obtain a one-dimensional array {D} from the two-dimensional matrix S;

[0051] b.4. Perform a difference operation on the array {D} to obtain the Hadamard coefficients H(u,v):

[0052] H(u,v)=D + -D - ;

[0053] Where D + and D - These are the measurements corresponding to a pair of Hadamard speckle patterns, where (u,v) represents the Hadamard domain coordinates.

[0054] b.5. Fill the obtained Hadamard coefficients into the corresponding Hadamard spectrum in sequence, and perform inverse Hadamard transform on the Hadamard spectrum to recover the secret image information.

[0055] Compared with existing technologies, the advantages of this invention are as follows: (1) The sampling system of this invention, based on ghost imaging technology, enables the encryption of multiple images, compressing information while ensuring the quality of the decrypted image. (2) This invention uses steganography to encode secret information into a series of random binary speckles, which has strong anti-interference and anti-loss capabilities during transmission and is not easily suspected or detected by eavesdroppers. (3) This invention introduces an authentication method based on single-pixel imaging, using ciphertext illumination authentication maps to generate authentication keys. The receiver needs to be authenticated before decryption, increasing the system's security. Attached Figure Description

[0056] Figure 1 The following is a schematic diagram of the experimental setup for this invention: a digital projector (DLP), a secret image O(x,y), a bucket detector (SPD), a data acquisition card (DAQ), and a computer (PC);

[0057] Figure 2 For encryption flowchart;

[0058] Figure 3 For the decryption flowchart;

[0059] Figure 4 The simulation results are as follows: (a)(b) secret image; (c) authentication image; (d) recovered authentication image; (e)(f) decrypted image; (g) authentication result;

[0060] Figure 5 The authentication graph (a) and authentication result (b) are decrypted using the wrong key, and the authentication graph (c) and authentication result (d) are decrypted using the correct key.

[0061] Figure 6 The following are the decryption results using the wrong key: (a) the authentication graph; (b) the authentication graph decrypted using only the correct key k; (c)(d) the secret image decrypted using only the correct key k; (e)(f) the secret image decrypted using only the correct keys k and k2; (g)(h) the secret image decrypted using only the correct keys k and k1.

[0062] Figure 7 The decrypted secret images and their corresponding mean square errors under different noise intensities;

[0063] Figure 8 Secret images decrypted under different cropping ratios. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0065] Example: A compressed optical encryption and decryption method based on ghost imaging and image authentication. In this example, the experimental setup is shown in the figure. The encryption system includes a digital projector (DLP), an image to be encoded O(x,y), a bucket detector (SPD), a data acquisition card (DAQ), and a computer. The DLP projects the computer-generated coded speckle pattern onto the secret image, and the bucket detector sequentially collects and records the reflected light intensity values ​​of the objects. The image compression sampling and authentication key generation processes both utilize the aforementioned experimental setup.

[0066] The specific implementation of the method described in this invention includes the following steps:

[0067] The encryption process is as follows Figure 2 As shown:

[0068] (1) Image compression sampling, including the following steps:

[0069] 1.1 Using computer-generated lighting patterns, the Hadamard speckle pattern I(x,y) can be generated by adjusting the impulse function σ. H (u,v) is generated by inverse Hadamard transform:

[0070]

[0071] Where (x,y) represents the spatial coordinates, H -1 This represents the inverse Hadamard transform, where (u,v) represents the Hadamard domain coordinates, and the impulse function is expressed as:

[0072]

[0073] In the formula: (u0, v0) is an initial position coordinate of the Hadamard domain, which can be assigned according to the selected sampling strategy.

[0074] Another group of speckles with elemental values ​​opposite to those of the Hadamard speckle is represented as follows:

[0075] I - (x,y)=1-I + (x,y);

[0076] In the formula, I + (x,y) and I-(x,y) represent a pair of complementary Hadamard speckle patterns;

[0077] 1.2 Project the generated Hadamard speckle pattern sequentially onto the secret image, and use a bucket detector to record the intensity value D of the reflected light in turn:

[0078] D i =∫∫I i (x,y)O(x,y)dxdy;

[0079] Among them, I i (x,y) represents the i-th Hadamard speckle pattern in the projection, and O(x,y) represents the target object to be encrypted.

[0080] (2) Data steganography includes the following steps:

[0081] 2.1 In this embodiment, two secret images are encrypted with a sampling rate of 25%. After compressed sampling, two one-dimensional arrays {D1} and {D2} are obtained by combining the light intensity values ​​D. These two one-dimensional arrays {D1} and {D2} are then concatenated. To ensure a uniform distribution of the resulting arrays, two scaling factors λ1 and λ2 are used during the concatenation process. To make corrections:

[0082]

[0083] in, Represents splicing, and Let {D1} and {D2} represent the average values ​​of arrays {D2} and {D1}, respectively; in this step, This ensures that the distribution ranges of the two arrays are similar, while ×λ1 is used to transform the values ​​of the generated array {D} to the range we need.

[0084] 2.2 Reset the one-dimensional array {D} into a two-dimensional matrix S, and use the reset two-dimensional matrix S as the additional key k1;

[0085] 2.3. Using pixel value decomposition, matrix S is decomposed into a series of random binary matrices {P}. O The value at each position in matrix S is equal to the sum of the values ​​at the corresponding positions in all random matrices.

[0086] S(i,j)={P1(i,j)+P2(i,j)+...+P k (i,j)};

[0087] Among them, P k Let (i,j) represent the k-th matrix of the decomposition, and (i,j) represent the position coordinates of the matrix.

[0088] (3) Generate authentication keys, including the following steps:

[0089] 3.1 An authentication method based on a single-pixel imaging system is introduced into the encryption system. To this end, a set of random matrices {P} is generated on the computer. NO};

[0090] 3.2, The matrix {P} O Randomly insert into matrix {P} NO Generate a new random matrix {P} in}, use the inserted position sequence as the additional key k2, and use {P} as the ciphertext;

[0091] 3.3. Illuminate the authentication map with the newly generated random matrix {P}, and collect the light intensity values ​​{B} of the authentication map using a bucket detector:

[0092] B i =∫∫P i (x,y)T(x,y)dxdy;

[0093] Among them, P i (x,y) represents the i-th random speckle pattern in the projection, and T(x,y) represents the authentication image to be authenticated.

[0094] 3.4. Binarize the sequence {B} with the threshold set as the average value of the sequence. Use the binarized sequence as the authentication key k.

[0095] Decryption steps are as follows Figure 3 As shown:

[0096] (a) The certification process is as follows Figure 3 As shown in Figure (a), the steps include:

[0097] a.1 The receiver first performs an association operation on the obtained key and ciphertext to recover a blurry image, and then sends the image back to the sender for authentication.

[0098] a.2 The sender authenticates the received image against the images in the authentication database using a non-linear correlation algorithm:

[0099] NC(x,y)=|IFT{|FT(T)·[FT(T′)] * | w-1 ·FT(T′)·[FT(T)] *}| 2 ;

[0100] Where FT(·) represents the two-dimensional Fourier transform, IFT(·) represents the two-dimensional inverse Fourier transform, T represents the authentication map, T′ represents the reconstructed authentication map, and w represents the nonlinear intensity;

[0101] Once a relevant peak appears in the authentication graph, it indicates successful authentication. The sender then sends the additional keys k1 and k2 to the receiver.

[0102] (b) The decryption process is as follows: Figure 3 As shown in Figure (b), the steps include:

[0103] b.1 The receiver uses key k2 to extract the random matrix {P} from the ciphertext {P}. O};

[0104] b.2, Next, for all random matrices {P} O The pixel values ​​of} are summed to obtain matrix S:

[0105]

[0106] b.3. Use key k1 to extract the one-dimensional array {D} from S;

[0107] b.4. Perform a difference operation on the array {D} to obtain the Hadamard coefficients H(u,v):

[0108] H(u,v)=D + -D - ;

[0109] Where D + and D - These are the measurements corresponding to a pair of Hadamard speckle patterns, where (u,v) represents the Hadamard domain coordinates.

[0110] b.5. Fill the obtained Hadamard coefficients into the corresponding Hadamard spectrum in sequence, and perform inverse Hadamard transform on the Hadamard spectrum to recover the secret image information.

[0111] To further illustrate the technical solution of this invention, two 128×128 pixel images, Pepper and House, were selected as secret images, and a 128×128 pixel image, Boat, was selected as the authentication image. First, 8192 Hadamard speckle images generated by a computer were projected onto the two secret images respectively. The bucket detector then sequentially collected the light intensity values ​​D into two one-dimensional arrays. and

[0112] Next, the resulting arrays are concatenated into a single array. It is important to note that the scaling factor λ1 used must be ensured. The array values ​​fluctuate below 4000. Then, a one-dimensional array... The matrix is ​​reset to a 128×128 two-dimensional matrix S, and the reset sequence is used as the additional key k1. Using pixel value decomposition, the two-dimensional matrix S is decomposed into 4000 random 128×128 binary matrices.

[0113] Secondly, the two-dimensional matrix S is scrambled and decomposed into 4000 random binary matrices. matrix Random insertion matrix Generate ciphertext The inserted position sequence serves as the additional key k2. Using the ciphertext... An illumination authentication graph is used to generate the authentication key, and bucket detectors record measurements {B}. {B} is binarized, with a threshold set to the average value of the sequence; the binarized sequence is used as the authentication key k. Finally, the ciphertext and authentication key k are sent to the recipient via public and secret channels, respectively.

[0114] The result obtained by performing calculations based on the encryption flowchart is as follows: Figure 4 As shown in the figure, (a) and (b) represent two secret images, (c) represents an image in the authentication database held by the sender, (d) is the reconstruction result after the receiver obtains the key and ciphertext, and (e) and (f) represent the recovered secret images with peak signal-to-noise ratios (PSNR) of 24.2 dB and 25.8 dB, respectively. It can be seen that a relatively high-quality image can still be recovered after decryption. (g) is the authentication result when the nonlinear strength is 0.2, with a nonlinear correlation coefficient of 0.09. The figure shows a clear correlation peak in the authentication image. Numerical simulation results verify the feasibility of our proposed compressed optical encryption scheme based on ghost imaging and image authentication.

[0115] Next, the security capabilities of the scheme were tested, starting with an analysis of the key. The authentication graph and result obtained when decryption is performed using an incorrect key k are shown below. Figure 5 As shown in (a) and (b), from Figure 5 (a) shows no image-related information, and the corresponding results also indicate a noise distribution without any relevant peaks. The authentication graph and authentication graph results obtained when decrypted using the correct authentication key k are as follows: Figure 5 As shown in (c) and (d), the authentication results exhibit a significant peak, indicating successful authentication, but the reconstructed authentication graph still lacks any image information. These results demonstrate that using an incorrect authentication key fails authentication, and unauthorized users cannot obtain any secret image information.

[0116] To further test the system's security, an analysis was conducted on unauthorized users attempting to brute-force the encryption system. Figure 6 As shown, without knowing the encryption scheme of this invention, when an eavesdropper intercepts the key k, they can only recover the authentication image (b) through correlation operations, resulting in a blurry image that does not contain object information. Even if the encryption scheme of this invention is leaked, with only the key k, the eavesdropper cannot obtain any image of the secret object, as shown in Figures (c) and (d). When the eavesdropper understands the encryption scheme of this invention and intercepts the keys k and k2, they can only recover a grayscale speckle image and cannot obtain any useful information, as shown in Figures (e) and (f). When the keys k and k1 are leaked, an unauthorized person can only obtain a blurry outline of a secret image, as shown in Figures (g) and (h). Only when an unauthorized person obtains all the keys k, k1, and k2 and understands the encryption scheme of this invention can they recover the information of the secret image. It is evident that this invention has excellent security performance and is very difficult to crack.

[0117] Finally, the embodiments of the present invention perform noise attacks and pruning attacks on the ciphertext to verify the robustness of the encryption system. To verify the anti-interference capability of the method, Gaussian noise is selected for the noise attack, such as... Figure 7 As shown in the figure, it can be seen that as the noise intensity increases, the MSE of the reconstructed image gradually increases, and the quality of the reconstructed image gradually decreases. When the noise intensity is 0.4, the decrypted image still has a clear outline, with only some details lost, indicating that the method has good anti-interference attack capabilities. Next, the anti-cropping capability of the encryption system is verified by cropping the ciphertext. The cropping ratio of the ciphertext is represented by dividing the cropped ciphertext by the total ciphertext, and is set to 2.5%, 5%, 7.5%, and 10% respectively. The anti-cropping capability of the encryption system is evaluated by the visual quality of the image. The results of the reconstructed image are shown in the figure. Figure 8 As shown, from Figure 8 It can be seen that as the cropping ratio increases, the details of the reconstructed image are gradually lost. When the cropping ratio is 10%, the outline of the encrypted image can still be distinguished, indicating that the method has good anti-cropping capability.

[0118] In summary, this invention introduces an authentication method, which improves the security of information transmission, compresses the data, and the proposed encryption method has high decryption quality and security.

Claims

1. A compressed optical encryption and decryption method based on ghost imaging and image authentication, characterized in that: Includes the following steps: Encryption process: (1) Image compression sampling: The target object is illuminated using Hadamard speckle, and the intensity of the reflected light from the object is collected by a barrel detector to obtain the light intensity value D; (2) Data Steganography: This includes the following steps: 2.

1. Two one-dimensional arrays {D1} and {D2} are obtained by combining the light intensity values ​​D. The two arrays {D1} and {D2} are concatenated into a single array {D}. 2.2 Reset the one-dimensional array {D} into a two-dimensional matrix S, and use the reset sequence as the additional key k1; 2.

3. Using pixel value decomposition, the two-dimensional matrix S is decomposed into a series of random binary matrices {P}. O The value at each position in a two-dimensional matrix S is equal to the sum of the values ​​at the corresponding positions in all random matrices. S(i,j)={P1(i,j)+P2(i,j)+…+P k (i,j)}; Among them, P k Let (i,j) represent the k-th matrix of the decomposition, and (i,j) represent the position coordinates of the matrix. (3) Generate authentication key: This includes the following steps: 3.1 Generate a set of random binary matrices {P} on a computer. NO }; 3.2, The matrix {P} O Randomly insert into matrix {P} NO Generate a new random matrix {P} in}, use the inserted position sequence as the additional key k2, and use the random matrix {P} as the ciphertext C; 3.

3. Illuminate the authentication map with the generated random matrix {P} and collect the reflected light intensity sequence {B} of the authentication map using a bucket detector; B i =∫∫P i (x,y)T(x,y)dxdy; Among them, P i (x,y) represents the i-th random speckle image of the projection; T(x,y) represents the authentication image; 3.

4. Binarize the sequence {B}, setting the threshold to the average value of the sequence. Use the binarized sequence as the authentication key k. Decryption process: (a) Authentication: The receiver performs an association operation based on the authentication key k and the ciphertext C to recover a blurred image, and sends the image back to the sender for identity authentication. After successful authentication, the sender sends the key k1 and key k2 to the receiver. (b) Decryption: Recover the secret image using keys k1 and k2.

2. The compressed optical encryption and decryption method based on ghost imaging and image authentication according to claim 1, characterized in that: The compressed sampling of the image includes the following steps: 1.

1. Using a computer to generate lighting patterns, by adjusting the impulse function σ H (u,v) is subjected to inverse Hadamard transform to generate Hadamard speckle I(x,y) for projection: Where (x,y) represents the spatial coordinates, H -1 This represents the inverse Hadamard transform, where (u,v) represents the Hadamard domain coordinates, and the impulse function is expressed as: In the formula: (u0, v0) is an initial position coordinate of the Hadama domain; Another group of speckles with elemental values ​​opposite to those of the Hadamard speckle is represented as follows: I - (x,y)=1-I + (x,y); I + (x,y) and I - (x,y) represent a pair of complementary Hadamard speckle patterns; 1.2 Project the generated Hadamard speckle pattern sequentially onto the secret image, and use a bucket detector to record the intensity value D of the reflected light in turn: D i =∫∫I i (x,y)O(x,y)dxdy; Among them, I i (x,y) represents the i-th Hadamard speckle pattern of the projection, and O(x,y) represents the target object to be encrypted.

3. The compressed optical encryption and decryption method based on ghost imaging and image authentication according to claim 1, characterized in that: In step 2.1, two scaling factors λ1 and λ2 were used during the splicing process. To make corrections: in Represents splicing, and These represent the average values ​​of arrays {D1} and {D2}, respectively.

4. The compressed optical encryption and decryption method based on ghost imaging and image authentication according to claim 1, characterized in that: The authentication is performed using a nonlinear correlation algorithm. NC(x,y)=|IFT{FT(T)·[FT(T')] * | w-1 ·FT(T')·[FT(T)] * }| 2 ; Where FT(·) represents the two-dimensional Fourier transform, IFT(·) represents the two-dimensional inverse Fourier transform, T represents the authentication map, T′ represents the reconstructed authentication map, and w represents the nonlinear intensity; Once a relevant peak appears in the authentication graph, it indicates successful authentication. The sender then sends additional keys k1 and k2 to the receiver.

5. The compressed optical encryption and decryption method based on ghost imaging and image authentication according to claim 1, characterized in that: The decryption process includes the following steps: b.1 The receiver uses key k2 to extract the random binary matrix {P} from the ciphertext {P}. O }; b.2, Next, for all random binary matrices {P} O The pixel values ​​of} are summed to obtain a two-dimensional matrix S: b.

3. Use key k1 to obtain a one-dimensional array {D} from the two-dimensional matrix S; b.

4. Perform a difference operation on the array {D} to obtain the Hadamard coefficients H(u,v): H(u,v)=D + -D - ; Where D + and D - These are the measurements corresponding to a pair of Hadamard speckle patterns, where (u,v) represents the Hadamard domain coordinates. b.

5. Fill the obtained Hadamard coefficients into the corresponding Hadamard spectrum in sequence, and perform inverse Hadamard transform on the Hadamard spectrum to recover the secret image information.

Images