Optical asymmetric encryption and decryption method and system based on synchronous compression wavelet transform
By using an optical asymmetric encryption algorithm based on synchronous compressed wavelet transform, the problem that existing technologies are difficult to resist known plaintext and special attacks is solved, achieving higher security image encryption, which is also applicable to audio asymmetric encryption.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TIANJIN NORMAL UNIVERSITY
- Filing Date
- 2025-12-24
- Publication Date
- 2026-04-21
AI Technical Summary
Existing DRPE-based systems are vulnerable to known-plaintext and chosen-plaintext attacks, while phase-truncation-based asymmetric encryption systems are not resistant to special attacks.
An optical asymmetric encryption algorithm based on synchronous compressed wavelet transform (SWT) is adopted. By multiplying the image to be encrypted with a random phase mask, double random phase encoding is performed in the fractional Fourier transform domain. After encryption, the image is decomposed into sub-blocks of different frequencies using one-dimensional Haar synchronous compressed wavelet transform. The high-frequency coefficients are saved as the final encryption result, and the low-frequency and high-frequency coefficients are used as decryption keys.
This method can effectively resist shearing attacks, noise attacks, known-plaintext attacks, chosen-plaintext attacks, and special attacks, and has higher security and attack resistance compared with existing technologies.
Smart Images
Figure CN121397157B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of optical encryption technology and information security technology, specifically relating to an optical asymmetric encryption and decryption method and system based on synchronous compressed wavelet transform. Background Technology
[0002] As a primary means of protecting image information security, image encryption technology has been extensively studied in recent years and has become one of the research hotspots in the field of image information security. Image encryption involves scrambling the pixel positions or sizes of an image to encode meaningful image information into meaningless gibberish, thereby protecting the image's information security. Based on the technical means employed, image encryption methods can be divided into digital image encryption methods and optical image encryption methods. Among them, optical image encryption has advantages such as high speed, large capacity, parallelism, and the ability to quickly perform convolution and correlation operations. Optical image encryption methods are generally classified as symmetric and asymmetric. In symmetric encryption systems, the encryption system is vulnerable to attacks such as chosen plaintext and known plaintext attacks due to its linearity or symmetry.
[0003] To improve the security of encryption systems, researchers have proposed introducing nonlinear operations or constructing asymmetric encryption systems. Phase truncation, as one of the most representative techniques in the field of asymmetric encryption, has been extensively studied in image encryption in recent years. The main advantage of phase-truncation-based asymmetric encryption systems is their resistance to chosen-plaintext attacks, but they are not resistant to special attacks. Therefore, the development, design, and research of asymmetric image encryption systems have become a focus and important research direction in the field of information security. Proposing a secure and effective asymmetric optical encryption algorithm will have a positive and significant impact on promoting the progress of image encryption research. Summary of the Invention
[0004] This invention provides an optical asymmetric encryption and decryption method and system based on synchronous compressed wavelet transform. Addressing the problems of existing DRPE (Dual Random Phase Coding) systems' inability to resist known-plaintext and chosen-plaintext attacks, and the inability of phase-truncation-based asymmetric encryption systems to resist special attacks, this invention designs an optical asymmetric encryption algorithm based on synchronous compressed wavelet transform (SWT). This encryption algorithm can encrypt images while effectively resisting cropping attacks, noise attacks, known-plaintext attacks, chosen-plaintext attacks, and special attacks.
[0005] To achieve the above objectives, the present invention provides the following solution:
[0006] Optical asymmetric encryption and decryption methods based on synchronous compressed wavelet transform include:
[0007] The image to be encrypted is multiplied by the first random phase mask to obtain the first modulated image. The first modulated image is then encrypted in the fractional Fourier transform domain using double random phase coding technology to obtain a preliminary encryption result.
[0008] The preliminary encryption result is multiplied by the second random phase mask to obtain the second modulated image. The second modulated image is then encrypted in the fractional Fourier transform domain using a double random phase coding technique to obtain an intermediate encryption result.
[0009] The intermediate encryption result is decomposed into sub-blocks of different frequencies by one-dimensional Haar synchronous compressed wavelet transform to obtain low-frequency coefficient CA, high-frequency coefficient CH in the horizontal direction, high-frequency coefficient CV in the vertical direction, and high-frequency coefficient CD in the diagonal direction.
[0010] The high-frequency coefficient CH in the horizontal direction is saved as the final encryption result to complete the encryption of the image to be encrypted; the low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction are saved as decryption keys to decrypt the final encryption result.
[0011] Preferably, the calculation formula for obtaining the preliminary encryption result is as follows:
[0012] ,
[0013] in, The image to be encrypted is an M×N pixel image. This represents the initial encryption result. Represents the first random phase mask. , Represents the fractional Fourier transform. and Here are the parameters for the fractional Fourier transform, where i represents the imaginary unit. Represents a random function.
[0014] Preferably, the calculation formula for obtaining the intermediate encryption result is as follows:
[0015] ,
[0016] in, This represents the intermediate encryption result. , and represents the parameters of the fractional Fourier transform.
[0017] Preferably, the method for decrypting the final encryption result includes:
[0018] The final encryption result and the decryption key are subjected to an inverse synchronous compressed wavelet transform to obtain a preliminary decryption result.
[0019] The preliminary decryption result is multiplied by the conjugate plate of the second random phase mask after undergoing an inverse fractional Fourier transform to obtain an intermediate decryption result;
[0020] The intermediate decryption result is multiplied by the conjugate plate of the first random phase mask after undergoing an inverse fractional Fourier transform to obtain the final decryption result.
[0021] The preferred formula for obtaining the preliminary decryption result is as follows:
[0022] ,
[0023] in, This represents the preliminary declassification results. Represents the inverse fractional Fourier transform. Represents the low-frequency coefficient. Represents the final encryption result. High-frequency coefficients in the vertical direction High-frequency coefficients in the diagonal direction This represents the wavelet transform basis.
[0024] The preferred formula for calculating the intermediate decryption result is as follows:
[0025] ,
[0026] in, This represents the intermediate decryption result. The conjugate plate representing the second random phase mask, .
[0027] The preferred formula for calculating the final decryption result is as follows:
[0028] ,
[0029] in, This represents the final decryption result. The conjugate plate representing the first random phase mask, .
[0030] This invention also provides an optical asymmetric encryption / decryption system based on synchronous compressed wavelet transform for implementing the method, comprising:
[0031] The preliminary encryption module is used to multiply the image to be encrypted with the first random phase mask to obtain the first modulated image, and to encrypt the first modulated image in the fractional Fourier transform domain using double random phase coding technology to obtain the preliminary encryption result.
[0032] An intermediate encryption module is used to multiply the preliminary encryption result with a second random phase mask to obtain a second modulated image, and to encrypt the second modulated image in the fractional Fourier transform domain using a double random phase coding technique to obtain an intermediate encryption result.
[0033] The wavelet transform module is used to decompose the intermediate encryption result into sub-blocks of different frequencies through one-dimensional Haar synchronous compressed wavelet transform 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.
[0034] The key generation module is used to save the high-frequency coefficient CH in the horizontal direction as the final encryption result to complete the encryption of the image to be encrypted; and to 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 decryption keys to decrypt the final encryption result.
[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: Compared with the proposed double random phase coding encryption algorithm and the phase truncation-based asymmetric encryption algorithm, the present invention mainly focuses on the security of resisting noise attacks, shearing attacks, chosen plaintext, known plaintext attacks and special attacks. By proposing an encryption module composed of an asymmetric optical encryption system, an optical asymmetric image encryption and decryption method based on SWT is designed. Its advantages are: (1) This method can resist shearing attacks and noise attacks to a certain extent; (2) Compared with the symmetric system based on double random phase coding, the method proposed in the present invention can resist attacks such as chosen plaintext and known plaintext; (3) Compared with the widely used phase truncation-based asymmetric encryption system, the method proposed in the present invention can resist special attacks; (4) The optical asymmetric image encryption and decryption method based on SWT proposed in the present invention can be extended to audio asymmetric encryption. Attached Figure Description
[0036] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0037] Figure 1 A schematic diagram of the encryption principle provided by this invention;
[0038] Figure 2 A schematic diagram illustrating the decryption principle provided by this invention;
[0039] Figure 3 Here is a sample of the original grayscale image to be encrypted, the encrypted result, and the decrypted result: Figure 3 (a) is the original grayscale image; Figure 3 (b) is the encrypted result; Figure 3 (c) represents the decrypted result;
[0040] Figure 4 Histogram distribution of the original and encrypted images; Figure 4 In the middle (a), the histogram distribution of the original image is shown. Figure 4 (b) shows the histogram distribution of the encrypted image;
[0041] Figure 5 For different key cases from Figure 3 The image decrypted in (b); 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;
[0042] 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);
[0043] 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.
[0044] 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;
[0045] 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.
[0046] Figure 10 This is a schematic diagram of the optical path according to an embodiment of the present invention. Detailed Implementation
[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0048] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0049] Example 1:
[0050] like Figure 1 As shown, the optical asymmetric encryption and decryption method based on synchronous compressed wavelet transform includes:
[0051] S1: Multiply the image to be encrypted (i.e., the original image) with the first random phase mask to obtain the first modulated image. Then, use double random phase coding technology to encrypt the first modulated image in the fractional Fourier transform domain to obtain a preliminary encryption result. For example... Figure 1 As shown. A further implementation method involves calculating the preliminary encryption result using the following formula:
[0052] ,
[0053] in, The image to be encrypted is an M×N pixel image (grayscale image). This represents the initial encryption result. Represents the first random phase mask. , Represents the fractional Fourier transform. and The parameters are those of the fractional Fourier transform, and all can serve as additional keys to enhance the security of the encryption system. Furthermore, any optical transform can be used instead of the fractional Fourier transform for encryption. 'i' represents the imaginary unit. Represents a random function. Figure 1 In Representing optical transformation, the fractional Fourier transform is used in this invention. .
[0054] S2: Multiply the preliminary encryption result by the second random phase mask to obtain the second modulated image. Then, encrypt the second modulated image in the fractional Fourier transform domain using a double random phase coding technique to obtain an intermediate encryption result. A further implementation method is as follows: The formula for calculating the intermediate encryption result is as follows:
[0055] ,
[0056] in, This represents the intermediate encryption result. , and represents the parameters of the fractional Fourier transform.
[0057] S3: The intermediate encryption result is decomposed into sub-blocks of different frequencies using a one-dimensional Haar synchronous compressed wavelet transform, yielding 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. The expressions are as follows:
[0058] .
[0059] SWT stands for Synchronous Compressed Wavelet Transform.
[0060] S4: Save the high-frequency coefficient CH in the horizontal direction as the final encryption result. The encryption of the image to be encrypted is completed; the low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction are saved as the decryption key. This is used to decrypt the final encrypted result.
[0061] ,
[0062] ,
[0063] Two random phase masks were used in the encryption process. and Parameters of fractional Fourier transform , , , The three square matrices generated during the encryption process Both are used as decryption keys to decrypt the image. The decryption process is as follows: Figure 2 As shown. Figure 2In this context, ISWT represents a one-dimensional Haar synchronous compressed inverse wavelet transform; Representing inverse optical transformation, the inverse fractional Fourier transform is used in this invention; This represents the preliminary decryption results; represent RPM 2 The conjugate plate, ; Represents preliminary decryption results The decryption result obtained through the second inverse fractional Fourier transform; represent RPM 1 The conjugate plate, ; This represents the final decrypted image.
[0064] A further implementation method includes a method for decrypting the final encrypted result, comprising:
[0065] The final encrypted result With decryption key Perform inverse synchronous compressed wavelet transform to obtain preliminary decryption results. A further implementation method involves using the following formula to calculate the preliminary decryption result:
[0066] ,
[0067] in, This represents the preliminary declassification results. Represents the inverse fractional Fourier transform. Represents the low-frequency coefficient. Represents the final encryption result. High-frequency coefficients in the vertical direction High-frequency coefficients in the diagonal direction This represents the wavelet transform basis.
[0068] Preliminary decryption results After inverse fractional Fourier transform, the conjugate plate with the second random phase mask RPM2 Multiply to obtain the intermediate decryption result. A further implementation method involves using the following formula to calculate the intermediate decryption result:
[0069] ,
[0070] in, This represents the intermediate decryption result. The conjugate plate representing the second random phase mask, .
[0071] intermediate decryption results After inverse fractional Fourier transform, the conjugate plate with the first random phase mask RPM1 Multiply by each product to obtain the final decryption result. .
[0072] A further implementation method involves obtaining the final decryption result. The calculation formula is as follows:
[0073] ,
[0074] in, This represents the final decryption result. The conjugate plate representing the first random phase mask, .
[0075] This invention uses a random phase mask and Parameters of fractional Fourier transform , , , Encryption is performed using a private key. The ciphertext is decrypted because the keys used for encryption and decryption are different, thus achieving asymmetric encryption.
[0076] 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.
[0077] 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.
[0078] 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.
[0079] 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.
[0080] 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.
[0081] 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.
[0082] 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 8As 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.
[0083] 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.
[0084] Figure 10 This is a schematic diagram of the optical path according to an embodiment of the present invention. The original image is first modulated with the first phase plate and then subjected to a first optical transformation to obtain a preliminary encryption result; then the preliminary encryption result is modulated with the second phase plate and subjected to a second optical transformation to obtain an intermediate encryption result; finally, a one-dimensional Haar synchronous compressed wavelet transform is performed on the intermediate encryption result, 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 decryption key pairs, which are used to decrypt the final ciphertext.
[0085] Example 2:
[0086] This invention also provides an optical asymmetric encryption / decryption system based on synchronous compressed wavelet transform, used to implement the optical asymmetric encryption / decryption method described in Embodiment 1, including:
[0087] The preliminary encryption module is used to multiply the image to be encrypted with a first random phase mask to obtain a first modulated image, and to encrypt the first modulated image in the fractional Fourier transform domain using a double random phase coding technique to obtain a preliminary encryption result.
[0088] The intermediate encryption module is used to multiply the preliminary encryption result with the second random phase mask to obtain the second modulated image. The second modulated image is then encrypted in the fractional Fourier transform domain using double random phase coding technology to obtain the intermediate encryption result.
[0089] The wavelet transform module is used to decompose the intermediate encryption result into sub-blocks of different frequencies through one-dimensional Haar synchronous compressed wavelet transform, 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.
[0090] The key generation module is used to save the high-frequency coefficient CH in the horizontal direction as the final encryption result to complete the encryption of the image to be encrypted; and to 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 decryption keys to decrypt the final encryption result.
[0091] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. An optical asymmetric encryption / decryption method based on synchronous compressed wavelet transform, characterized in that, include: The image to be encrypted is multiplied by the first random phase mask to obtain the first modulated image. The first modulated image is then encrypted in the fractional Fourier transform domain using double random phase coding technology to obtain a preliminary encryption result. The preliminary encryption result is multiplied by the second random phase mask to obtain the second modulated image. The second modulated image is then encrypted in the fractional Fourier transform domain using a double random phase coding technique to obtain an intermediate encryption result. The intermediate encryption result is decomposed into sub-blocks of different frequencies by one-dimensional Haar synchronous compressed wavelet transform to obtain low-frequency coefficient CA, high-frequency coefficient CH in the horizontal direction, high-frequency coefficient CV in the vertical direction, and high-frequency coefficient CD in the diagonal direction. The high-frequency coefficient CH in the horizontal direction is saved as the final encryption result, thus completing the encryption of the image to be encrypted; The low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction are saved as decryption keys, which are used to decrypt the final encryption result. The formula for obtaining the initial encryption result is as follows: ， in, The image to be encrypted is an M×N pixel image. This represents the initial encryption result. Represents the first random phase mask. , Represents the fractional Fourier transform. and Here are the parameters for the fractional Fourier transform, where i represents the imaginary unit. Represents a random function; The formula for calculating the intermediate encryption result is as follows: ， in, This represents the intermediate encryption result. , and These are the parameters of the fractional Fourier transform; The methods for decrypting the final encrypted result include: The final encryption result and the decryption key are subjected to an inverse synchronous compressed wavelet transform to obtain a preliminary decryption result. The preliminary decryption result is multiplied by the conjugate plate of the second random phase mask after undergoing an inverse fractional Fourier transform to obtain an intermediate decryption result; The intermediate decryption result is multiplied by the conjugate plate of the first random phase mask after undergoing an inverse fractional Fourier transform to obtain the final decryption result; The formula for obtaining the preliminary decryption result is as follows: ， in, This represents the preliminary declassification results. Represents the inverse fractional Fourier transform. Represents the low-frequency coefficient. Represents the final encryption result. High-frequency coefficients in the vertical direction High-frequency coefficients in the diagonal direction Represents the wavelet transform basis; The formula for calculating the intermediate decryption result is as follows: ， in, This represents the intermediate decryption result. The conjugate plate representing the second random phase mask, , and These are the parameters of the inverse fractional Fourier transform; The formula for calculating the final decryption result is as follows: ， in, This represents the final decryption result. The conjugate plate representing the first random phase mask, , and These are the parameters of the inverse fractional Fourier transform.
2. An optical asymmetric encryption / decryption system based on synchronous compressed wavelet transform, used to implement the method described in claim 1, characterized in that, include: The preliminary encryption module is used to multiply the image to be encrypted with the first random phase mask to obtain the first modulated image, and to encrypt the first modulated image in the fractional Fourier transform domain using double random phase coding technology to obtain the preliminary encryption result. An intermediate encryption module is used to multiply the preliminary encryption result with a second random phase mask to obtain a second modulated image, and to encrypt the second modulated image in the fractional Fourier transform domain using a double random phase coding technique to obtain an intermediate encryption result. The wavelet transform module is used to decompose the intermediate encryption result into sub-blocks of different frequencies through one-dimensional Haar synchronous compressed wavelet transform 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. The key generation module is used to save the high-frequency coefficients CH in the horizontal direction as the final encryption result, thereby completing the encryption of the image to be encrypted. The low-frequency coefficient CA, the high-frequency coefficient CV in the vertical direction, and the high-frequency coefficient CD in the diagonal direction are saved as decryption keys, which are used to decrypt the final encryption result.