A Fresnel domain algorithm and multiplexing and multi-image encryption method for correlation imaging

Abstract

The present invention discloses a multiplexing and multi-image encryption method of Fresnel domain algorithm and associated imaging, including: performing the Fresnel domain Gerchberg-Saxton algorithm on a single image to obtain a pure phase function; performing the above operation on each image to be encrypted to obtain multiple pure phase functions; superimposing and normalizing multiple phase functions to obtain a combined phase function; using the combined phase function as a plaintext for secondary encryption, i.e., associated imaging encryption; a series of random speckle modulated light is irradiated onto the imaging image, and the light field intensity information is collected and recorded by a bucket detector to complete the secondary encryption. The method first implements "one code, one key" through distance multiplexing of Fresnel diffraction. According to the present invention, it not only has good security but also can resist attacks such as noise and cropping, but also has good encryption capacity, solving the potential risks of sharing public keys.

Description

Technical Field

[0001] The invention relates to the technical field of optical image encryption, and in particular to a Fresnel domain algorithm and a multiplexing and multi-image encryption method of associated imaging. Background Art

[0002] With the development of global economy and informatization, information exchange is becoming more and more frequent, and people's demand for information transmission and processing in daily life is constantly increasing. In order to ensure the security, authenticity and integrity of information, information security technology has been continuously expanded and deepened with the development of information technology, and has played an indispensable role in personal information security, enterprise development, national security and social stability. Traditional information security technology mainly relies on means such as computers or digital signal processors, but these means are limited by processing speed, so there is an urgent need for a fast and safe means as a supplement and alternative. Optical information security technology, as an emerging technical means in recent years, has received widespread attention. Optical information security technology uses light as the carrier of information, has the characteristics of high speed and parallelism, and the wavelength of light is short, the information capacity is large, and it can hide information in multiple dimensions (such as wavelength, amplitude, phase, orbital angular momentum, etc.). These advantages fully demonstrate that optical information security technology has unique advantages in information transmission and protection compared with traditional technologies.

[0003] As an information carrier, images have the advantages of transmitting large amounts of information, being specific and vivid, while time-varying signals can show the volatility of information over time. Both amplitude and frequency can represent different contents. Compared with images, they are more real-time. They are both important forms of optical information security technology. As people's requirements for information security gradually increase, optical information security technology is favored by researchers due to its advantages such as fast speed and large capacity. Exploring and developing optical information security technology and ensuring the security of images and time-varying signals have extremely high scientific research value and practical value. Summary of the invention

[0004] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a multiplexing and multi-image encryption method of a Fresnel domain algorithm and associated imaging, which not only has good security but also can resist attacks such as noise and cropping, and also has good encryption capacity, solving the potential risks of sharing public keys. In order to achieve the above-mentioned purpose and other advantages according to the present invention, a multiplexing and multi-image encryption method of a Fresnel domain algorithm and associated imaging is provided, comprising:

[0005] S1, using the Fresnel domain Gerchberg–Saxton algorithm to perform initial encryption on a single plaintext image;

[0006] S2, repeat the above operation for each plaintext image to obtain multiple pure phase functions;

[0007] S3, performing phase superposition on multiple pure phase functions and normalizing them to obtain a combined phase function;

[0008] S4, using the combined phase function as a plaintext image encrypted by correlation imaging;

[0009] S5, modulating the light field using a series of random illumination speckles, and irradiating the modulated light onto the target image;

[0010] S6. Use the bucket detector to collect and record the light field intensity information to complete the final encryption.

[0011] Preferably, in step S1, different Fresnel diffraction distances are selected according to image features, and the Gerchberg–Saxton algorithm is used to perform Fresnel diffraction at different distances on each plaintext image. For different image features, a more optimal iterative phase map can be obtained, and “one code, one key” is achieved through distance multiplexing of Fresnel diffraction.

[0012] Preferably, filtering is performed as the number of superimposed images increases, and then the filtered phase images are superimposed. In this way, as the number of superimposed phase images increases, a certain amount of information can still be maintained, thereby suppressing the loss of image information to a certain extent.

[0013] Preferably, the iterated phase map is multiplied by a coefficient matrix during superposition to adjust the grayscale value of the phase map so that the information amount of each phase map is maintained during the subsequent superposition process and the superimposed image does not exceed the threshold overflow.

[0014] Preferably, each image includes a primary public key and an auxiliary private key, and different keys are sent to different authorized users.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] (1) Using the Fresnel domain Gerchberg–Saxton algorithm, we can first obtain a better iterative phase map for different image features, and then achieve “one code, one key” through distance multiplexing of Fresnel diffraction.

[0017] (2) Secondly, as the number of superimposed images increases, the filtered phase images are superimposed through a specific filtering method. In this way, as the number of superimposed phase images increases, a certain amount of information can still be maintained, thus suppressing the loss of image information to a certain extent.

[0018] (3) When the phase image is superimposed, it is multiplied by a coefficient matrix to adjust the gray value of the phase image so that the information of each phase image can be maintained in the subsequent superposition process and the superimposed image will not exceed the threshold. At the same time, the amount of ciphertext transmission is reduced and the image transmission efficiency is improved.

[0019] (4) Each image has a primary public key and an auxiliary private key, which solves the potential risks of sharing public keys and ensures the security, authenticity and integrity of image information. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flowchart of the Gerchberg–Saxton algorithm of the Fresnel domain algorithm and the multiplexing and multi-image encryption method of the associated imaging according to the present invention;

[0021] Figure 2 A schematic diagram of a calculation ghost image encryption system according to the Fresnel domain algorithm and the multiplexing and multi-image encryption method of the associated imaging of the present invention;

[0022] Figure 3 A multi-image encryption flow chart of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and the associated imaging of the present invention;

[0023] Figure 4 A multi-image decryption flow chart of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and associated imaging of the present invention;

[0024] Figure 5 It is a feasibility analysis diagram of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and the associated imaging of the present invention;

[0025] Figure 6 A statistical graph showing the CC value and SSIM value of the decrypted image and the original image as a function of the sampling rate according to the Fresnel domain algorithm and the multiplexing and multi-image encryption method of the associated imaging of the present invention;

[0026] Figure 7 A key security analysis diagram of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and associated imaging of the present invention;

[0027] Figure 8 The diffraction distance sensitivity analysis diagram of the multiplexing and multi-image encryption method of the Fresnel domain algorithm and the associated imaging according to the present invention, wherein (a) and (c) are line graphs of the relationship between the diffraction distance error and CC and SSIM, and (b) and (d) are partial enlarged diagrams of (a) and (c), respectively;

[0028] Fig. 9The ciphertext cropping ratio and the decrypted image CC and SSIM statistical graphs of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and associated imaging of the present invention;

[0029] Fig.10 The figure is a relationship diagram between CC, SSIM, PSNR and noise intensity of the decrypted image of the multiplexing and multi-image encryption method according to the Fresnel domain algorithm and associated imaging of the present invention. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] In this encryption system, the amplitude function generated by the Fresnel transform of the plaintext image is used as the target function distribution of the iterative approximation, and the original image to be encrypted is used as the initial value of the iterative calculation. The phase generated during the iterative encryption process is used as the key for decryption. At the same time, the algorithm is based on the GS algorithm in the Fresnel transform domain, so the Fresnel transform parameters can be used as the additional key of the encryption scheme. At the same time, the combined phase function is used as the last key when performing associated imaging encryption.

[0032] Reference Figure 1-10 ,A multiplexing and multi-image encryption method of Fresnel domain algorithm and associated imaging, comprising: S1, initially encrypting a single plaintext image using a Fresnel domain Gerchberg–Saxton algorithm;

[0033] S2, repeat the above operation for each plaintext image to obtain multiple pure phase functions;

[0034] S3, performing phase superposition on multiple pure phase functions and normalizing them to obtain a combined phase function;

[0035] S4. The combined phase function is used as the plaintext image for correlation imaging encryption. A series of random illumination speckles are used to modulate the light field. The modulated light is irradiated onto the target image. The bucket detector is used to collect and record the light field intensity information to complete the final encryption. This further improves the security of the entire encryption system.

[0036] S5, modulating the light field using a series of random illumination speckles, and irradiating the modulated light onto the target image;

[0037] S6. Use the bucket detector to collect and record the light field intensity information to complete the final encryption.

[0038] Multi-image encryption has large encryption capacity, high transmission efficiency and rich information. This method proposes a multi-image encryption method based on phase iteration and correlation imaging. In this encryption system, the transmission amount of ciphertext is reduced and the security of the encryption system is guaranteed. First, through the distance multiplexing of Fresnel diffraction, "one code and one key" is realized; secondly, the phase superposition and normalization method is used to reduce the transmission amount of ciphertext; finally, the correlation imaging algorithm is used to further improve the security of the entire encryption system. This method is verified from three aspects: feasibility, security and robustness through simulation experiments. The experimental results show that the proposed method is safe, effective and has good encryption performance.

[0039] Furthermore, in step S1, different Fresnel diffraction distances are selected according to image features, and the Fresnel diffraction at different distances is performed on each plaintext image by using the Gerchberg–Saxton algorithm.

[0040] Furthermore, filtering is performed according to the increase in the number of superimposed images, and then the filtered phase images are superimposed.

[0041] Furthermore, the iterated phase images are multiplied by a coefficient matrix during superposition to adjust the grayscale value of the phase images so that the information content of each phase image is maintained during the subsequent superposition process.

[0042] Furthermore, each image includes a primary public key and an auxiliary private key, and different keys are sent to different authorized users.

[0043] Encryption process:

[0044] Step S1: For each secret image, an initial random phase is arbitrarily given ,in , then the known amplitude function (Assume that the amplitude value in the spatial domain is 1) to form a new function as input, and the expression is: , the distance of the input function is The Fresnel transform of ,in is the frequency domain coordinate, is the spatial coordinate, and the distance of the Fresnel transformation here is set by the user and can be used as a key. The phase and amplitude expected on the output plane To form a new complex function, its expression is Then Performing the inverse Fresnel transform, we get the wave function as .Will The phase is multiplied by the preset output amplitude to form a new complex amplitude function again, thus forming the input function required for the next iteration. Repeat the above iterative steps. As the number of iterations accumulates, the output image gradually converges to the desired image. The iteration stop is controlled by a preset threshold. The diffraction distance of each image is the most appropriate image diffraction distance selected for different image features. In this way, a better iterative phase map can be obtained. Through the distance reuse of Fresnel diffraction, "one code, one key" is realized.

[0045] Step S2: The above phase iteration operation is performed on each image (the Fresnel transform distances are , then The phase functions of the images are summed and normalized to obtain a combined phase function. In the process of superimposing and normalizing the phase functions, the filtered phase images are superimposed through a specific filtering according to the increase in the number of superimposed images. In this way, as the number of superimposed phase images increases, a certain amount of information can still be maintained, which suppresses the loss of image information to a certain extent. The subsequent phase image is multiplied by a coefficient matrix during superposition to adjust the grayscale value of the phase image so that the information of each phase image can be maintained in the subsequent superposition process, and the superimposed image will not exceed the threshold overflow.

[0046] Step S3: Combine the normalized ciphertext As the plaintext image encrypted by association imaging, the association calculation is performed on it to obtain a series of bucket detector values ​​as the final ciphertext , the second encryption is completed. The encryptor transmits the ciphertext and key to the receiver through the public channel and the private channel respectively, thus completing the whole encryption process.

[0047] Decryption process:

[0048] Step S1: The decryptor needs to first decrypt the ciphertext according to formula 1 Perform correlation calculation to reconstruct the combined phase function after phase superposition , as shown in formula 1;

[0049] (1)

[0050] Step S2: for the reconstructed combined phase function, the distances are By taking the inverse Fresnel transform of the image and cutting off its amplitude part, a single secret image can be obtained.

[0051] In summary, in the encryption system, the amount of ciphertext transmission is reduced and the security of the encryption system is guaranteed. First, according to different image features, the appropriate image diffraction distance is selected, so that a better iterative phase map can be obtained. Through the distance reuse of Fresnel diffraction, "one code and one key" is realized; secondly, according to the increase in the number of superimposed images, the filtered phase map is superimposed through a specific filtering, so that as the number of superimposed phase images increases, a certain amount of information can still be maintained, which suppresses the loss of image information to a certain extent. When the sub-phase image is superimposed, it is multiplied by a coefficient matrix to adjust the grayscale value of the phase image, so that the information of each phase image can be maintained in the subsequent superposition process, and the superimposed image will not exceed the threshold overflow. At the same time, the amount of ciphertext transmission is reduced and the image transmission efficiency is improved; finally, the security of the entire encryption system is further improved through the association imaging algorithm. The present invention has been verified from three aspects of feasibility, security and robustness through simulation experiments. The experimental results show that the proposed encryption system not only has good security but also can resist attacks such as noise and cropping. It also has good encryption capacity. More importantly, in the method proposed in this paper, each image has a primary public key and an auxiliary private key, which solves the potential risks of sharing public keys. The security, authenticity and integrity of image information are guaranteed.

[0052] Feasibility analysis:

[0053] In order to prove the feasibility of this encryption system, the CC value and SSIM value between the decrypted image and the original image are statistically analyzed with the sampling rate, and a line graph is drawn as shown in the figure. Figure 6 As shown. For the convenience of statistics, during the overlay process, no matter how many pictures are overlaid, the picture "lena" must exist. When drawing the line chart, among the different overlay samples, the picture "lena" is fixedly selected as the statistical sample. Figure 5-6 The results are shown in the table below: (1) As the number of superimposed images increases, the decryption results of the image will decrease overall; (2) As the sampling rate increases, the quality of the decrypted image continues to increase; (3) At the same time, under the condition of full image sampling, the CC values ​​of the decrypted images are all above 0.6, and the SSIM values ​​are all above 0.65, indicating that the system has excellent multi-image encryption performance and good feasibility.

[0054] Security Analysis:

[0055] Key security: In the multi-image encryption system based on phase iteration and correlation imaging, it is necessary to first perform phase iteration encryption on the image, and then superimpose and normalize the obtained phase functions to obtain a combined phase function. The coherent light passes through the spatial light modulator, and the modulated light beam is irradiated onto the phase function for secondary encryption. Finally, the light beam information is collected by the bucket detector to obtain the final ciphertext. In this process, each image corresponds to two keys, and only when the correct key is used can the decryptor reconstruct the encrypted image. In order to verify the security of the encryption system, taking 4 images as an example, four different grayscale images are selected here, and the correct key, primary key and secondary key are used to reconstruct the information of the original image. The results are shown as follows. Figure 7 Results analysis: (1) The encryption system that combines the phase iteration algorithm with the correlation imaging algorithm in this paper has good image decryption quality. Figure 7 (a) and Figure 7 (b) The initial image and the reconstructed image using the correct ciphertext and key. It can be seen that only when the cracker has the correct key and ciphertext can the encrypted image be reconstructed; (2) Figure 7 (c) It can be seen that when the cracker only has the primary key, even if he knows the decryption algorithm, the information he obtains is wrong information; (3) Figure 7 (d) shows that when the cracker only uses the secondary key to decrypt the encryption system, he cannot obtain any information of the encrypted image. The encryption algorithm in this paper first implements "one code, one key" through distance multiplexing, then superimposes and normalizes the phase function to reduce the amount of transmitted data, and finally performs secondary encryption through joint imaging, which improves the security of the entire system.

[0056] On this basis, the sensitivity of the primary key diffraction distance is analyzed. According to the decryption results when the diffraction distance deviates by 0.1m, 0.01m, 0.001m, 0.0001m, 0.00001m, 0.000001m, 0.000001m, and 0.0000001m, the sensitivity of the key is analyzed, and then the security of the key is analyzed. From the decryption results when the diffraction distance deviates to different degrees, it can be seen that the decrypted image is extremely sensitive to the diffraction distance. Due to the addition of the amplitude modulation template, the amplitude of the light field in the Fresnel domain is randomly disturbed, making the decryption result extremely sensitive to the deviation of the diffraction distance, thereby enhancing the security of the system. The line graphs of the diffraction distance error-image CC value and the diffraction distance error-image SSIM value are shown in the figure. Figure 8 As shown. Figure 8 (a) shows the variation curve of the correlation coefficient CC of "starfish", "pepper", "house" and "lena" with the diffraction distance deviation. Figure 8(c) shows the variation curve of the correlation coefficient SSIM of "starfish", "pepper", "house", and "lena" with the diffraction distance deviation. Figure 8 (b) and Figure 8 (d) Figure 8 (a) and Figure 8 (c) A partial enlarged view.

[0057] Depend on Figure 8 It can be seen that: (1) As the diffraction distance error increases, the CC value and SSIM value between the reconstructed image and the original image gradually increase. The lower the clarity of the reconstructed image, the more difficult it is to distinguish the information of the original image; (2) When the diffraction distance error reaches, the CC value of the reconstructed image and the original image is below 0.5, and the SSIM value is below 0.32. The reconstructed image contains only very little effective information, and the original image cannot be clearly distinguished, and the reconstruction effect is poor. (3) When the diffraction distance error is controlled within, the CC value of the reconstructed image and the original image is above 0.75, and the SSIM value is above 0.55. Most of the information of the original image can be distinguished, and some detailed information is lost to a certain extent. The above results confirm that the decryption result is extremely sensitive to the diffraction distance deviation, and the security of the system is guaranteed.

[0058] Robustness analysis:

[0059] Depend on Fig. 9 It can be seen that (1) as the key cropping area increases, the NC value between the reconstructed image and the original image gradually decreases. The lower the clarity of the reconstructed image, the more difficult it is to distinguish the information of the original image; (2) when the cropping ratio is 30%, the CC value of the reconstructed image and the original image is above 0.85, and the SSIM value is above 0.65, which can clearly distinguish the information of the original image, and the reconstruction effect is good; (3) when the key cropping ratio is 50%, the CC value of the reconstructed image and the original image is greater than 0.65, and the SSIM value is greater than 0.55, which can still distinguish part of the encrypted image information, indicating that this method can resist cropping attacks well. In summary, it can be concluded that the encryption system proposed in this paper not only shows good robustness to noise attacks, but also can resist cropping attacks, indicating that the encryption system has good robustness.

[0060] In order to further prove the robustness of the encryption system, after obtaining the decrypted images of different noise types and different noise intensities, a line graph of the decrypted image CC, SSIM, and PSNR with the noise embedding strength is drawn, as shown in Fig.10 As shown. Fig.10It can be seen that (1) the three indicators simultaneously show that for the same embedding strength, Gaussian noise has the greatest impact on image quality; (2) when the embedding strength of multiplicative noise and salt and pepper noise is 5%, the CC value of the image can still reach above 0.57, the SSIM can still reach above 0.75, and the PSNR can still reach about 17, with strong noise resistance; (3) the decryption quality of the image decreases with the increase of noise embedding strength, but for noise of general strength, the encryption system has good decryption quality and strong robustness, which further proves the good robustness performance of the encryption system.

[0061] In summary, it can be concluded that the encryption system proposed in this paper shows good robustness against noise attacks. Although the decryption result of the image has a certain degree of loss as the degree of noise attack increases, the image decryption quality is good when resisting noise attacks of general intensity. At the same time, the encryption system can resist a certain degree of cropping attack. When the cropping information reaches 50%, the image can still observe its contour information, while the detail information is seriously damaged. This shows that the encryption system has good robustness.

[0062] In summary: The present invention proposes a multi-image encryption method based on phase iteration and correlation imaging. On the basis of phase-iterative optical image encryption, Fresnel diffraction distance multiplexing is used to superimpose the phase function obtained by phase superposition of a single secret image and normalize it, thereby realizing diffraction distance multiplexing, greatly improving the compression of encrypted multi-image information, and solving the problem of large ciphertext transmission volume of multi-image encryption. Finally, correlation imaging is combined with phase iteration to improve the security and accuracy of the encryption system. Since phase-iterative optical image encryption is very sensitive to distance keys, the information of the encrypted image can only be reconstructed when the key is completely correct or produces very small errors. The encryption system is simple, easy to transmit and record, and has better practicality than double random phase encoding. In addition, this method can send different keys to different authorized users, and has a broader application prospect.

[0063] The number of devices and processing scales described here are used to simplify the description of the present invention, and the application, modification and variation of the present invention will be obvious to those skilled in the art.

[0064] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A multiplexing and multi-image encryption method of Fresnel domain algorithm and associated imaging, characterized in that: The following steps are involved: S1, use the Fresnel domain Gerchberg–Saxton algorithm to perform initial encryption on a single plaintext image; S2, repeat the above operation for each plaintext image to obtain multiple pure phase functions; S3, performing phase superposition on multiple pure phase functions and normalizing them to obtain a combined phase function; S4, using the combined phase function as a plaintext image encrypted by correlation imaging; S5, modulating the light field using a series of random illumination speckles, and irradiating the modulated light onto the target image; S6. Use the bucket detector to collect and record the light field intensity information to complete the final encryption.

2. A Fresnel domain algorithm and multiplexing and multi-image encryption method for associated imaging as claimed in claim 1, characterized in that: In the step S1, different Fresnel diffraction distances are selected according to image features, and the Fresnel diffraction at different distances is performed on each plaintext image by using the Gerchberg-Saxton algorithm.

3. A Fresnel domain algorithm and multiplexing and multi-image encryption method for associated imaging as claimed in claim 1, characterized in that: According to the increase in the number of superimposed images, filtering processing is performed, and then the filtered phase images are superimposed.

4. A Fresnel domain algorithm and multiplexing and multi-image encryption method for associated imaging as claimed in claim 1, characterized in that: The iterated phase images are multiplied by a coefficient matrix when being superimposed, which is used to adjust the grayscale value of the phase images so that the information content of each phase image is maintained in the subsequent superposition process.

5. A Fresnel domain algorithm and multiplexing and multi-image encryption method for associated imaging as claimed in claim 1, characterized in that: Each image includes a primary public key and a secondary private key, and different keys are sent to different authorized users.

Images