Optical asymmetric encryption and decryption method and system based on synchronous compression wavelet transform

Abstract

The invention belongs to the technical field of optical encryption and information security, and particularly provides an optical asymmetric encryption and decryption method and system based on synchronous compressed wavelet transform, and the method comprises the steps: multiplying a to-be-encrypted image by a first random phase mask, encrypting a first modulation image, and obtaining a preliminary encryption result; multiplying the preliminary encryption result by a second random phase mask, and encrypting the second modulation image to obtain an intermediate encryption result; decomposing the intermediate encryption result into sub-blocks with different frequencies through one-dimensional Haar synchronous compression wavelet transform; the high-frequency coefficient in the horizontal direction is stored as a final encryption result, and encryption of the to-be-encrypted image is completed; and storing the low-frequency coefficient, the high-frequency coefficient in the vertical direction and the high-frequency coefficient in the diagonal direction as a decryption key for decrypting a final encryption result. According to the technical scheme, shear attacks, noise attacks, known plaintext attacks, selected plaintext attacks and special attacks can be effectively resisted.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of optical encryption technology and information security technology, and particularly relates to an optical asymmetric encryption and decryption method and system based on synchronous compression wavelet transform. BACKGROUND

[0002] As a main means of protecting image information security, image encryption technology has been widely studied in recent years and has become one of the research hotspots in the field of image information security. Image encryption is to encode meaningful image information into meaningless code by disturbing the pixel position or size of the image, so as to protect the information security of the image. According to the technical means used in the encrypted image, the image encryption method can be divided into digital image encryption method and optical image encryption method. Among them, optical image encryption has the advantages of high speed, large capacity, parallelism and the ability to quickly realize convolution and correlation operation. Optical image encryption methods are usually divided into symmetric and asymmetric. In the symmetric encryption system, the encryption system is vulnerable to chosen-plaintext and known-plaintext attacks due to its linearity or symmetry.

[0003] In order to improve the security of the encryption system, researchers have proposed to introduce nonlinear operations or construct asymmetric encryption systems in the encryption system. Phase truncation, as one of the most representative technologies in the field of asymmetric encryption, has been widely studied in the field of image encryption in recent years. The main advantage of the asymmetric encryption system based on phase truncation is that it can resist chosen-plaintext attacks, but cannot resist special attacks. Therefore, the development, design and research of asymmetric image encryption systems have become the focus and important research direction in the field of information security. It is of positive and important significance to propose a safe and effective asymmetric optical encryption algorithm to promote the progress of the field of image encryption research. SUMMARY

[0004] The present application provides an optical asymmetric encryption and decryption method and system based on synchronous compression wavelet transform, which is designed to solve the problems that the existing DRPE (double random phase encoding) system is difficult to resist known-plaintext attacks and chosen-plaintext attacks, and the asymmetric encryption system based on phase truncation cannot resist special attacks. An optical asymmetric encryption algorithm based on synchronous compression wavelet transform (SWT) is designed, which can realize image encryption while effectively resisting clipping attacks, noise attacks, known-plaintext attacks, chosen-plaintext attacks and special attacks.

[0005] To achieve the above purpose, the present application provides the following scheme: The optical asymmetric encryption and decryption method based on synchronous compression wavelet transform comprises: Multiplying the image to be encrypted with a first random phase mask to obtain a first modulation image, and encrypting the first modulation image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain a preliminary encryption result; Multiplying the preliminary encryption result with a second random phase mask to obtain a second modulation image, and encrypting the second modulation image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain an intermediate encryption result; Decomposing the intermediate encryption result into sub-blocks of different frequencies by one-dimensional Haar synchronous compression wavelet transform to obtain low-frequency coefficients CA, high-frequency coefficients CH in a horizontal direction, high-frequency coefficients CV in a vertical direction, and high-frequency coefficients CD in a diagonal direction; Saving the high-frequency coefficients CH in the horizontal direction as a final encryption result to complete the encryption of the image to be encrypted, and saving the low-frequency coefficients CA, the high-frequency coefficients CV in the vertical direction, and the high-frequency coefficients CD in the diagonal direction as a decryption key for decrypting the final encryption result.

[0006] Preferably, the calculation formula for obtaining the preliminary encryption result is as follows: , wherein, the image to be encrypted is an M×N pixel image, the preliminary encryption result is represented by, the first random phase mask is represented by, , the fractional Fourier transform is represented by, and the parameters of the fractional Fourier transform are represented by i, and i represents an imaginary unit, and the random function is represented by.

[0007] Preferably, the calculation formula for obtaining the intermediate encryption result is as follows: , wherein, the intermediate encryption result is represented by, , and the parameters of the fractional Fourier transform are represented by.

[0008] Preferably, the method for decrypting the final encryption result comprises: performing inverse synchronous compression wavelet transform on the final encryption result and the decryption key to obtain a preliminary decryption result; multiplying the preliminary decryption result after inverse fractional Fourier transform with a conjugate plate of the second random phase mask to obtain an intermediate decryption result; The intermediate decryption result is multiplied by a conjugate plate of the first random phase mask after inverse fractional Fourier transform, and a final decryption result is obtained.

[0009] Preferably, the calculation formula for obtaining the preliminary decryption result is as follows: , Wherein, represents the preliminary decryption result, represents the inverse fractional Fourier transform, represents the low-frequency coefficient, represents the final encryption result, high-frequency coefficient in the vertical direction, high-frequency coefficient in the diagonal direction, represents the wavelet transform base.

[0010] Preferably, the calculation formula for obtaining the intermediate decryption result is as follows: , Wherein, represents the intermediate decryption result, represents the conjugate plate of the second random phase mask, .

[0011] Preferably, the calculation formula for obtaining the final decryption result is as follows: , Wherein, represents the final decryption result, represents the conjugate plate of the first random phase mask, .

[0012] The application also provides an optical asymmetric encryption and decryption system based on synchronous compression wavelet transform, which is used for realizing the method and comprises: A preliminary encryption module is configured to multiply a to-be-encrypted image and a first random phase mask to obtain a first modulated image, encrypt the first modulated image in a fractional Fourier transform domain by using a double random phase encoding technology, and obtain a preliminary encryption result. An intermediate encryption module is configured to multiply the preliminary encryption result and a second random phase mask to obtain a second modulated image, encrypt the second modulated image in a fractional Fourier transform domain by using a double random phase encoding technology, and obtain an intermediate encryption result. A wavelet transform module is configured to decompose the intermediate encryption result into sub-blocks of different frequencies by one-dimensional Haar synchronous compression wavelet transform, and obtain a low-frequency coefficient CA, a high-frequency coefficient CH in a horizontal direction, a high-frequency coefficient CV in a vertical direction, and a high-frequency coefficient CD in a diagonal direction. A key generation module is configured to save the high-frequency coefficient CH in the horizontal direction as a final encryption result, complete encryption of the image to be encrypted, save the low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction and the high-frequency coefficient CD in the diagonal direction as a decryption key, and decrypt the final encryption result.

[0013] Compared with the prior art, the present application has the following advantages: compared with the existing double random phase encoding encryption algorithm and the asymmetric encryption algorithm based on phase truncation, the present application mainly studies the security against noise attack, cutting attack, chosen-plaintext attack, known-plaintext attack and special attack, proposes an encryption module composed of an asymmetric optical encryption system, designs an optical asymmetric image encryption and decryption method based on SWT, and has the following advantages: (1) the method can resist a certain degree of cutting attack and noise attack; (2) compared with the symmetric system based on double random phase encoding, the method proposed by the present application can resist chosen-plaintext attack and known-plaintext attack; (3) compared with the widely used asymmetric encryption system based on phase truncation, the method proposed by the present application can resist special attack; (4) the optical asymmetric image encryption and decryption method based on SWT proposed by the present application can be applied to audio asymmetric encryption. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings described in the following embodiments are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0015] Figure 1 The encryption principle diagram provided by the present application is shown in the figure; Figure 2 The decryption principle diagram provided by the present application is shown in the figure; Figure 3 The original gray-scale image to be encrypted, the encrypted result and the decrypted result are shown in the figure: Figure 3 (a) in the figure is the original gray-scale image; Figure 3 (b) in the figure is the encrypted result; Figure 3 (c) in the figure is the decrypted result; Figure 4 The histogram distribution of the original image and the encrypted image is shown in the figure; Figure 4 (a) in the figure is the histogram distribution of the original image; Figure 4 (b) in the figure is the histogram distribution of the encrypted image; Figure 5 The images decrypted from (b) in different key conditions are shown in the figure; Figure 3 (b) in the figure is the histogram distribution of the encrypted image; Figure 5(a) shows the decryption result when the key RMP1 is incorrect; Figure 5 (b) shows the decryption result when the key RMP2 is incorrect; Figure 5 (c) is the key α1 Decryption result when an error occurs; Figure 5 (d) is the key α2 Decryption result when an error occurs; Figure 5 (e) is the key. β1 Decryption result when an error occurs; Figure 5 f is the key β2 Decryption result when an error occurs; Figure 6 Decrypted image under conditions of a shearing attack; Figure 6 (a) is an encrypted image subjected to a 1 / 16 shearing attack; Figure 6 (b) is from Figure 6 The result decrypted in (a); Figure 6 Image (c) is an encrypted image subjected to a 1 / 4 shearing attack; Figure 6 (d) is from Figure 6 The result decrypted in (c); Figure 7 The decrypted image under Gaussian noise attack conditions; Figure 7 (a) shows the decryption result when subjected to 0.01 times Gaussian noise; Figure 7 (b) shows the decryption result when subjected to 0.05 times Gaussian noise. Figure 7 (c) shows the decryption result when subjected to 0.1 times Gaussian noise attack; Figure 7 (d) shows the decryption result when subjected to 0.2 times Gaussian noise. Figure 8 For pseudo-plaintext images and decrypted images under chosen-plaintext attacks; Figure 8 Image (a) is a pseudo-plaintext image; Figure 8 (b) shows the decryption result obtained using the pseudo-key; Figure 9 This refers to the specific attack results targeting the encryption method designed in this invention; Figure 9 Image (a) is the image recovered after 100 iterations; Figure 9 (b) is a graph showing the correlation coefficient between the decrypted image recovered through a special attack and the original image as a function of the number of iterations. Figure 10 This is a schematic diagram of the optical path according to an embodiment of the present invention. Detailed Implementation

[0016] The technical solutions in the embodiments of the present application will be described clearly and completely below with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work are within the scope of the present application.

[0017] In order to make the above objectives, characteristics and advantages of the present application more apparent, the present application will be further described in detail below with the drawings and specific embodiments.

[0018] Embodiment one: As shown in the figure, the optical asymmetric encryption and decryption method based on synchronous compression wavelet transform includes: Figure 1 S1: multiplying the image to be encrypted (i.e. the original image) by the first random phase mask to obtain the first modulated image, and using the double random phase encoding technology to encrypt the first modulated image in the fractional Fourier transform domain to obtain the preliminary encryption result. As shown in the figure, the further embodiment is that the calculation formula of the preliminary encryption result is as follows: Figure 1 , wherein, is the image (gray image) to be encrypted with MxN pixels, represents the preliminary encryption result, represents the first random phase mask, , represents the fractional Fourier transform, and are the parameters of the fractional Fourier transform, and can both be used as additional keys to enhance the security of the encryption system. In addition, any optical transform can be used instead of the fractional Fourier transform for encryption. represents the imaginary unit, represents the random function. in the formula Figure 1 represents the optical transform, and the fractional Fourier transform is used in the present application. .

[0019] S2: multiplying the preliminary encryption result by the second random phase mask to obtain the second modulated image, and using the double random phase encoding technology to encrypt the second modulated image in the fractional Fourier transform domain to obtain the intermediate encryption result. The further embodiment is that the calculation formula of the intermediate encryption result is as follows: , wherein, represents the intermediate encryption result, , and ​Parameters of the fractional Fourier transform.

[0020] S3: decompose the intermediate encryption result into sub-blocks of different frequencies by one-dimensional Haar synchronous compression wavelet transform, to obtain low-frequency coefficients CA, high-frequency coefficients CH in horizontal direction, high-frequency coefficients CV in vertical direction, and high-frequency coefficients CD in diagonal direction. The expression is as follows: .

[0021] wherein, SWT represents synchronous compression wavelet transform.

[0022] S4: save the high-frequency coefficients CH in horizontal direction as the final encryption result , to complete the encryption of the image to be encrypted; save the low-frequency coefficients CA, the high-frequency coefficients CV in vertical direction, and the high-frequency coefficients CD in diagonal direction as the decryption key , to decrypt the final encryption result.

[0023] , , Two random phase masks and used in the encryption process , , , Three square matrices generated in the encryption process are used to decrypt the image as the decryption key. The decryption process is shown in Figure 2 . Figure 2 wherein, ISWT represents one-dimensional Haar synchronous compression inverse wavelet transform; represents inverse optical transform, and inverse fractional Fourier transform is used in the present application; represents the preliminary decryption result; represents RPM 2 the conjugate board of ; represents the preliminary decryption result obtained by the second inverse fractional Fourier transform; represents RPM 1 the conjugate board of ; represents the final decryption image.

[0024] Further embodiments are that the method for decrypting the final encryption result comprises: the final encryption result is multiplied by the decryption key The inverse synchronous compression wavelet transform is performed to obtain a preliminary decryption result Further embodiments are characterized in that the calculation formula for obtaining the preliminary decryption result is as follows: , Wherein, represents the preliminary decryption result, represents the inverse fractional Fourier transform, represents the low-frequency coefficient, represents the final encryption result, high-frequency coefficient in the vertical direction, high-frequency coefficient in the diagonal direction, represents the wavelet transform base.

[0025] The preliminary decryption result is multiplied by the conjugate plate of the second random phase mask RPM2 after inverse fractional Fourier transform to obtain an intermediate decryption result Further embodiments are characterized in that the calculation formula for obtaining the intermediate decryption result is as follows: , Wherein, represents the intermediate decryption result, represents the conjugate plate of the second random phase mask, .

[0026] The intermediate decryption result is multiplied by the conjugate plate of the first random phase mask RPM1 after inverse fractional Fourier transform to obtain a final decryption result .

[0027] Further embodiments are characterized in that the calculation formula for obtaining the final decryption result is as follows: , Wherein, represents the final decryption result, represents the conjugate plate of the first random phase mask, .

[0028] The present application uses random phase masks and , the parameters of fractional Fourier transform , , , for encryption, and uses a private key for decryption of the ciphertext, because the key used for encryption is different from the key used for decryption, thereby realizing asymmetric encryption.

[0029] Figure 3 Image (a) is the original image to be encrypted. The resulting grayscale encrypted image is obtained after encryption using the proposed encryption algorithm. Figure 3 As shown in (b). From Figure 3 As can be seen in (b), the information of the original image is encrypted. When all keys are correct and the image is not attacked, all the information of the encrypted image can be completely restored to obtain the original image (e.g., ...). Figure 3 (As shown in (c)). This demonstrates that the encryption and decryption of images using this method is successful.

[0030] Figure 4 (a) represents the original text. Figure 3 Histogram distribution of (a), Figure 4 (b) is the encrypted version. Figure 3 (b) Histogram distribution. By comparison, it can be seen that the peak values ​​and histogram distributions of the ciphertext and the original image are completely different. Therefore, it is impossible to obtain any useful information about the original image by analyzing the histogram distribution of the ciphertext.

[0031] Furthermore, when one key is incorrect while the others are correct, the decryption result of the color image is as follows: Figure 5 (a) Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 Middle (e) and Figure 5 As shown in (f), the correlation coefficients between the decrypted image and the attacked original image are calculated to be 0.0825, 0.0127, 0.3765, 0.3921, 0.1485, and 0.1586, respectively. Therefore, the security of this encryption system can be guaranteed. Figure 5 The key mentioned above is the parameter of the fractional Fourier transform.

[0032] Figure 6 (a) is the ciphertext cut by 1 / 16. Figure 6 Image (b) is the corresponding decrypted image. Figure 6 (c) is the ciphertext cut by 1 / 4. Figure 6 (d) is the corresponding decrypted image. For ease of observation, the cut-out area has been marked. It can be seen from the decrypted image that some noise appears after the cut-out attack, but the main information of the image can still be discerned. Calculations show that the correlation coefficients between the decrypted image and the attacked original image are 0.9748 and 0.9078, respectively. Therefore, the encryption method proposed in this invention can resist cut-out attacks.

[0033] Figure 7 Images decrypted under speckle random noise interference at different noise intensity coefficients.Figure 7 (a) Figure 7 (b) Figure 7 (c) Figure 7 Figure (d) shows the decrypted images with noise intensity coefficients of 0.01, 0.05, 0.1, and 0.2, respectively. It can be seen from the decrypted images that the stronger the noise, the more severe the interference to the decrypted image. However, the main information of the original image can still be discerned. Calculations show that the correlation coefficients between the decrypted images and the attacked original images are 0.8172, 0.7909, 0.7760, and 0.7565, respectively, thus proving that the encryption method proposed in this invention can resist noise attacks.

[0034] Therefore, even if the encrypted image is heavily contaminated by noise or some information is missing, the present invention can still decrypt the original image that can be identified, verifying the feasibility of the system and meeting various needs in practical applications.

[0035] Figure 8 This section presents a pseudo-plaintext image and the decrypted image under a chosen-plaintext attack. Assuming the attacker already knows the ciphertext and the entire encryption process, the attacker encrypts the pseudo-plaintext. Figure 8 (a) Obtaining a fake key. The attacker then uses the fake key to decrypt the ciphertext. Figure 3 (b) The decrypted image is as follows Figure 8 As shown in (b), the decrypted image does not contain the original image that was attacked. Figure 3 (a) contains no information. By calculation, the correlation coefficient between the decrypted image and the attacked original image is 0.1667, proving that the encryption method can resist chosen-plaintext attacks.

[0036] Figure 9 This is the result of a special attack against the encryption method designed in this invention. A special attack with 100 iterations was performed on the encryption method proposed in this invention. Figure 9 Image (a) is the image recovered after a special attack. Figure 9 Figure (b) shows the curve of the correlation coefficient between the decrypted image recovered by the special attack and the original image as a function of the number of iterations. It can be observed that the image recovered after 100 iterations does not contain any information related to the original image. According to Figure (b), the correlation coefficient converges and stabilizes at 0.0031. A correlation coefficient of 0.0031 indicates that the correlation between the recovered image and the original image is extremely low; the convergence and stabilization of the correlation coefficient indicates that the correlation coefficient does not change with the number of iterations, meaning that even with many more iterations, it is impossible to recover more relevant information from the original image. Therefore, it can be proven that the encryption method proposed in this invention can resist special attacks based on iterative recovery.

[0037] Figure 10 The optical path schematic diagram of the embodiment of the present application is shown in the figure. The original image is firstly modulated by the first phase plate and then the preliminary encryption result is obtained through the first optical transformation; then the preliminary encryption result is modulated by the second phase plate and then the intermediate encryption result is obtained through the second optical transformation; finally, the intermediate encryption result is subjected to one-dimensional Haar synchronous compression wavelet transformation, the high frequency coefficients in the horizontal direction are saved as the final ciphertext, and the low frequency coefficients, the high frequency coefficients in the vertical direction and the high frequency coefficients in the diagonal direction are saved as the decryption key pair for decrypting the final ciphertext.

[0038] Embodiment two: The present application also provides an optical asymmetric encryption and decryption system based on synchronous compression wavelet transformation, which is used for realizing the optical asymmetric encryption and decryption method of the embodiment one, and comprises: A preliminary encryption module is used for multiplying the image to be encrypted with the first random phase mask to obtain a first modulated image, and encrypting the first modulated image in the fractional Fourier transform domain by using the double random phase encoding technology to obtain a preliminary encryption result.

[0039] An intermediate encryption module is used for multiplying the preliminary encryption result with the second random phase mask to obtain a second modulated image, and encrypting the second modulated image in the fractional Fourier transform domain by using the double random phase encoding technology to obtain an intermediate encryption result.

[0040] A wavelet transformation module is used for decomposing the intermediate encryption result into sub-blocks of different frequencies through one-dimensional Haar synchronous compression wavelet transformation to obtain low frequency coefficients CA, high frequency coefficients CH in the horizontal direction, high frequency coefficients CV in the vertical direction and high frequency coefficients CD in the diagonal direction.

[0041] A key generation module is used for saving the high frequency coefficients CH in the horizontal direction as the final encryption result to complete the encryption of the image to be encrypted, and saving the low frequency coefficients CA, the high frequency coefficients CV in the vertical direction and the high frequency coefficients CD in the diagonal direction as the decryption key for decrypting the final encryption result.

[0042] The above-described embodiments are only used for describing the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements of the technical solutions of the present application made by those skilled in the art shall fall into the protection scope determined by the claims of the present application.

Claims

1. An optical asymmetric encryption and decryption method based on synchronous compressive wavelet transform, characterized in that, The method comprises the steps of: multiplying the image to be encrypted with a first random phase mask to obtain a first modulated image, and encrypting the first modulated image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain a preliminary encryption result; multiplying the preliminary encryption result with a second random phase mask to obtain a second modulated image, and encrypting the second modulated image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain an intermediate encryption result; decomposing the intermediate encryption result into sub-blocks of different frequencies by one-dimensional Haar synchronous compression wavelet transform to obtain a low-frequency coefficient CA, a high-frequency coefficient CH in a horizontal direction, a high-frequency coefficient CV in a vertical direction, and a high-frequency coefficient CD in a diagonal direction; saving the high-frequency coefficient CH in the horizontal direction as a final encryption result to complete the encryption of the image to be encrypted; and saving the low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction as a decryption key for decrypting the final encryption result.

2. The method of claim 1, wherein, The calculation formula for obtaining the preliminary encryption result is as follows: ， wherein, an image to be encrypted of MxN pixels, representing a preliminary encryption result, representing a first random phase mask, , representing a fractional Fourier transform, and is a parameter of the fractional Fourier transform, i represents the imaginary unit, representing a random function.

3. The method of claim 2, wherein, The calculation formula for obtaining the intermediate encryption result is as follows: ， wherein represents an intermediate encryption result, , and are parameters of a fractional Fourier transform.

4. The method of claim 1, wherein, The method for decrypting the final encryption result comprises the steps of: performing inverse synchronous compression wavelet transform on the final encryption result and the decryption key to obtain a preliminary decryption result; multiplying the preliminary decryption result after inverse fractional Fourier transform with a conjugate plate of the second random phase mask to obtain an intermediate decryption result; multiplying the intermediate decryption result after inverse fractional Fourier transform with a conjugate plate of the first random phase mask to obtain a final decryption result.

5. The method of claim 1, wherein, The calculation formula for obtaining the preliminary decryption result is as follows: ， wherein, represents a preliminary decryption result, represents an inverse fractional Fourier transform, represents a low frequency coefficient, represents a final encryption result, high frequency coefficients in a vertical direction, high frequency coefficients in a diagonal direction, represents a wavelet transform base.

6. The method of claim 5, wherein, The calculation formula for obtaining the intermediate decryption result is as follows: ， wherein representing an intermediate decryption result, representing a conjugate plate of the second random phase mask, , and are parameters of an inverse fractional Fourier transform.

7. The method of claim 5, wherein, The calculation formula for obtaining the final decryption result is as follows: ， wherein represents the final decryption result, represents a conjugate plate of the first random phase mask, , and are parameters of the inverse fractional Fourier transform.

8. An optical asymmetric encryption / decryption system based on synchronized compressive wavelet transform for implementing the method of any one of claims 1 to 7, characterized in that, The method comprises: a preliminary encryption module, configured to multiply an image to be encrypted with a first random phase mask to obtain a first modulated image, and encrypt the first modulated image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain a preliminary encryption result; an intermediate encryption module, configured to multiply the preliminary encryption result with a second random phase mask to obtain a second modulated image, and encrypt the second modulated image in a fractional Fourier transform domain by using a double random phase encoding technique to obtain an intermediate encryption result; a wavelet transform module, configured to decompose the intermediate encryption result into sub-blocks of different frequencies by one-dimensional Haar synchronous compression wavelet transform to obtain a low-frequency coefficient CA, a high-frequency coefficient CH in a horizontal direction, a high-frequency coefficient CV in a vertical direction, and a high-frequency coefficient CD in a diagonal direction; a key generation module, configured to save the high-frequency coefficient CH in the horizontal direction as a final encryption result to complete the encryption of the image to be encrypted; save the low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction as a decryption key for decrypting the final encryption result.

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