High-performance deep learning attack method for asymmetric cryptographic system with few sample data

Abstract

The invention discloses a high-performance deep learning attack method for an asymmetric cryptographic system. The high-performance deep learning attack method comprises the following steps of: 1, encrypting an image by using a PTFT-based cryptographic system and an EMD-based cryptographic system respectively; 2, establishing plaintext-ciphertext pair data sets, and dividing each data set into a training set, a verification set and a test set which respectively comprise 600 pairs of plaintext-ciphertext data pairs, 200 pairs of plaintext-ciphertext data pairs and 200 pairs of plaintext-ciphertext data pairs; and a third step of designing a high-performance deep learning attack network RRU-NetPP, and training and debugging the network by using the established very small data set. And 4, attacking the ciphertext encrypted by the PTFT cryptosystem and the EMD cryptosystem by the established RRU-NetPP model, and retrieving the plaintext in real time with high quality. According to the method, the requirements on known plaintext-ciphertext data pairs can be remarkably reduced, the method has a few-sample learning capability, plaintexts can be retrieved from complex ciphertexts encrypted by different asymmetric cryptographic systems in real time in a high-quality manner, and the method has a strong attack capability.

Description

Technical Field

[0001] The present invention relates to the field of optical encryption and decryption, and in particular to a high-performance deep learning attack method for an asymmetric cryptographic system. Background Art

[0002] The encryption and authentication technology based on optical information processing theory is considered to be a new generation of information security technology. Its main advantages are: multi-dimensional (amplitude, phase and wavelength, etc.), large capacity and parallel data processing capabilities. Since Javidi et al. proposed an optical image encryption system based on "double random phase encoding" (DRPE) in 1995, many scholars have devoted themselves to the design and development of DRPE system tasks applied to different transformation fields, and have achieved a series of preliminary results. In addition, if the encrypted information based on the DRPE method is recorded by traditional optical methods, it is difficult to transmit the encrypted information through the network. Therefore, digitizing the encrypted information and methods is extremely beneficial to the preservation and transmission of information, and can even achieve the purpose of real-time transmission and remote display through the Internet.

[0003] However, early optical cryptographic systems are vulnerable to different types of attacks due to their inherent linear and symmetric properties. The symmetric property means that the encryption key and the decryption key are the same, which easily leads to security issues such as information leakage. The emergence of asymmetric cryptographic systems, such as the Phase Truncated Fourier Transform (PTFT) and Equimodular Decomposition (EMD) asymmetric cryptographic systems, reduces the risk of key leakage to a certain extent by designing a one-way trapdoor function. In addition, for asymmetric optical cryptographic systems, each user only needs to use a decryption key (private key) that is completely different from the encryption key (public key) to recover the original text, which is conducive to key management and transmission.

[0004] However, this cannot completely solve the problem of key management and transmission security. Some iteration-based attack methods have shown that these two asymmetric cryptographic systems are not completely secure. Existing attack methods basically rely on iterative phase or amplitude retrieval algorithms based on public keys and ciphertexts. However, they either use complex operations or suffer from serious degradation of attack results. With the continuous advancement of deep learning technology, more and more neural network models are being applied to attacks on asymmetric optical cryptographic systems. However, existing deep learning attack methods generally rely on large-scale data to drive neural networks to learn the mapping relationship between ciphertext and plaintext, thereby achieving password cracking. There are two main problems with these methods. First, current deep learning methods are highly dependent on large-scale data sets, which not only limits their application in data-scarce scenarios, but also consumes a lot of computing resources and time, further raising the threshold for their practical application. Second, existing attack methods mostly focus on simple data sets (such as Fashion-MNIST), and fail to give full play to the advantages of deep learning in complex feature extraction, resulting in its limitations in dealing with more complex attack scenarios.

[0005] The present invention proposes an attack method driven by a deep learning model - RRU-Net PP for two typical OACs, PTFT and EMD. Based on different data sets, a model that can be used to attack complex and small sample data is implemented, breaking the constraint that previous learning-based attack methods only target simple data, and realizing high-quality attacks on complex data. The present invention does not require a large amount of training data as the driving basis of the model, and can extract effective features from a small amount of samples, reducing the demand for data volume, effectively saving model training resources and time, and showing efficient learning ability. It can obtain high-quality prediction results under limited training sample conditions and show strong robustness. Summary of the invention

[0006] In view of this, the present invention provides a high-performance deep learning attack method for asymmetric cryptographic systems. The neural network proposed in the present invention is an end-to-end model designed and trained based on plaintext-ciphertext data pairs. After training driven by a small amount of sample data, the converged RRU-Net PP can directly retrieve high-quality plaintexts that are extremely similar to the real plaintexts from the test ciphertexts in real time. The data results prove the effectiveness of this method.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A high-performance deep learning attack method for an asymmetric cryptographic system, comprising the following steps:

[0009] Step 1: Use the PTFT and EMD based image encryption algorithms to encrypt a small number of images from the Fashion-MNIST, LFW-People and Animal Picture Set databases to obtain ciphertext-plaintext data pairs.

[0010] Step 2: Create a new database, including the six data sets generated in the above steps. Each data set is divided into a training set, a validation set, and a test set, which include 600 pairs, 200 pairs, and 200 pairs of plaintext-ciphertext data pairs respectively;

[0011] Step 3: Design a high-performance deep learning attack network RRU-NetPP and use the above different datasets to train and optimize the network.

[0012] Step 4: The established RRU-NetPP model attacks the ciphertext encrypted by the PTFT cryptosystem and the EMD cryptosystem, and can retrieve the plaintext in real time and with high quality.

[0013] Preferably, the training process is:

[0014] F(x)=Minloss(C i ,P i ) (1)

[0015] Among them, F(x), C i , P i They represent the trained and optimized model, ciphertext, and plaintext respectively; Minloss() represents the minimization of the loss function.

[0016] Preferably, the loss function is a mean square error loss function, which can be expressed as:

[0017]

[0018] Among them, n represents the number of samples, that is, the number of ciphertext-plaintext data pairs; x i is the true (plaintext) value of the ith sample, y i is the predicted value of the i-th sample; MSE represents the performance of the model; the smaller the MSE value, the smaller the difference between the predicted value and the true value of the model, and the better the performance of the model; when the MSE value no longer decreases, save the model file, and use the model file to attack the test ciphertext during the test reasoning process to decrypt the ciphertext.

[0019] Preferably, the model comprises 5 encoding modules (Recurrent Residual block), 10 decoding modules (VGG block) and a dense skip connection structure; in the encoding module, each block is constructed by residual propagation and residual feedback with two feature extraction layers, each of which is composed of a standard convolution layer with a convolution kernel size of 3×3, a stride of 1, and a padding of 1, as well as a Batch Normalization layer and a Rectified Linear Unit activation function. In the decoding module, each block is constructed by two feature extraction layers, each of which is composed of a standard convolution layer with a convolution kernel size of 3×3, a stride of 1, and a padding of 1, as well as a Batch Normalization layer and a Rectified Linear Unit activation function.

[0020] Through the above operations, it can be used to learn the nonlinear feature mapping from ciphertext to plaintext.

[0021] Preferably, the residual propagation consists of a standard convolution layer with a convolution kernel of 1×1, a Batch Normalization layer and a Rectified Linear Unit activation function;

[0022] The residual feedback consists of a standard convolutional layer with a 1×1 kernel;

[0023] In the whole module, residual propagation is performed twice and residual feedback is performed once.

[0024] Preferably, the first residual propagation process is:

[0025] y1=F(x)+x (3)

[0026] Among them, y1 represents the output after two feature extraction layers, x represents the input, and F() represents the feature map to be learned.

[0027] Preferably, the residual feedback process is:

[0028] y2=(F s (G(y1))+1)x (4)

[0029] Where x represents the input, G() represents a linear mapping, y1 is the output in formula (3), and F s represents the sigmoid activation function, and y2 represents the output after feedback.

[0030] Through the above operations, it can be used to change the dimension of y1;

[0031] The sigmoid activation function is used to drive the overall feedback learning to distinguish the nonlinear effect between the ciphertext mapping and the plaintext feature communication, avoid the diffusion of feature information, and shield the information interference between ciphertexts, so that the model can retrieve different plaintexts with high quality from multiple extremely similar ciphertexts.

[0032] Preferably, the second residual propagation process:

[0033] y3=F(y2)+x (5)

[0034] Where y2 is the output in formula (4), F() is the feature map, x represents the input, and y3 represents the output of the second residual propagation.

[0035] Preferably, the model further includes a downsampling operation and an upsampling operation, the downsampling operation is used for the encoder part, and the upsampling process is used for the decoder part; the Max-Pooling layer used for downsampling represents a maximum pooling layer with a convolution kernel size of 2×2, which filters out redundant features through downsampling and retains key information of the feature map;

[0036] Among them, a single-channel ciphertext image of size 256×256 is transformed into a 16×16 1024-channel feature map after passing through the encoder;

[0037] The transposed-convolution layer used for upsampling represents a transposed convolution layer with a convolution kernel size of 4×4, a stride of 2, and a padding of 1; upsampling amplifies the extracted feature map.

[0038] Through the above operations, the downsampling operation can halve the height and width of the feature map, reduce the amount of calculation, prevent overfitting, and do not change the communication dimension of the feature map.

[0039] Preferably, after the feature map passes through the decoder, it outputs a 256×256 single-channel map, passes through a standard convolution layer with a convolution kernel size of 1×1, and generates predicted plaintext after the sigmoid activation function.

[0040] Compared with the prior art, the present invention has achieved the following technical effects:

[0041] 1. The present invention does not require a large amount of data as a driving support, and can efficiently learn mapping features with less training data, maintain its strong attack capability, and has a wide range of scene applications.

[0042] 2. The method provided by the present invention can retrieve high-quality plaintext in real time for both simple and complex images, and is feasible and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is an overview diagram of a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0044] Figure 2 This is a basic module structure diagram of the RR(R2)U-Net PP of a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0045] Figure 3 A model attack result diagram corresponding to PTFT-basedOAC of a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0046] Figure 4 A model attack result diagram corresponding to EMD-basedOAC of a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0047] (I) Attack results on Fashion-MNIST, (II) Attack results on Animal Picture Set, (III) Attack results on LFW-People; (a) Ciphertext in the test set, (b) real plaintext, (c) predicted plaintext;

[0048] Figure 5 This is a data loss attack result diagram based on the PTFT cryptographic system of a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0049] (I) Attack results on Fashion-MNIST, (II) Attack results on Animal Picture Set, (III) Attack results on LFW-People; (a) Real plaintext, (b), (c), (d) The corresponding attack results of ciphertexts with zero pixels accounting for 5%, 10%, and 15% of the total pixels in the image, respectively;

[0050] Figure 6 A data loss attack result diagram based on an EMD cryptographic system of a high-performance deep learning attack method for an asymmetric cryptographic system according to the present invention;

[0051] (I) Attack results on Fashion-MNIST, (II) Attack results on Animal Picture Set, (III) Attack results on LFW-People; (a) Real plaintext, (b), (c), (d) The corresponding attack results of ciphertexts with zero pixels accounting for 5%, 10%, and 15% of the total pixels in the image, respectively;

[0052] Figure 7A diagram showing the noise resistance attack results of a PTFT cryptographic system based on a high-performance deep learning attack method for an asymmetric cryptographic system according to the present invention;

[0053] (I) Attack results of Fashion-MNIST test noisy ciphertext, (II) Attack results of Animal Picture Set test noisy ciphertext, (III) Attack results of LFW-People test noisy ciphertext; (a) The real plaintext, (b) and (c) are the corresponding attack results of ciphertext with Gaussian noise variance of 0.01 and 0.02 respectively;

[0054] Figure 8 A noise resistance attack result diagram of an EMD cryptographic system based on a high-performance deep learning attack method for an asymmetric cryptographic system according to the present invention;

[0055] (I) Attack results of Fashion-MNIST test noisy ciphertext, (II) Attack results of Animal Picture Set test noisy ciphertext, (III) Attack results of LFW-People test noisy ciphertext; (a) The real plaintext, (b) and (c) are the corresponding attack results of ciphertext with Gaussian noise variance of 0.01 and 0.02 respectively;

[0056] Fig. 9 A comparison chart of attack results of the RU-Net PP model and the GAN model on the PTFT-based cryptographic system according to a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0057] (I) Attack results of Fashion-MNIST, (II) Attack results of Animal Picture Set, (III) Attack results of LFW-People; (a) Real plaintext, (b) Attack results of RU-Net PP model, (C) Attack results of GAN model;

[0058] Fig.10 A comparison chart of attack results of the RU-Net PP model and the GAN model on the EMD-based cryptographic system according to a high-performance deep learning attack method for an asymmetric cryptographic system of the present invention;

[0059] (I) Attack results of Fashion-MNIST, (II) Attack results of Animal Picture Set, (III) Attack results of LFW-People; (a) Real plaintext, (b) Attack results of RU-Net PP model, (C) Attack results of GAN model.

[0060] Fig.11A comparison chart of decryption results of different models of a high-performance deep learning attack method for an asymmetric cryptographic system on EMD OAC; (I)Fashion-MNIST, (II)Animal Picture Set (III)LFW-People. (a) Groundtruth, (b) RRU-NetPP, (c) GAN. DETAILED DESCRIPTION

[0061] 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.

[0062] like Figure 1 As shown, the present invention discloses a high-performance deep learning attack method for an asymmetric cryptographic system, comprising the following steps:

[0063] Step 1: Use the PTFT and EMD-based image encryption algorithms to encrypt a small amount of image data from the Fashion-MINST, LFW-People and Animal Picture set databases respectively to generate ciphertext-plaintext data pairs.

[0064] Step 2: Create a new database, including the six data sets generated in the above steps. Each data set is divided into a training set, a validation set, and a test set, which include 600 pairs, 200 pairs, and 200 pairs of plaintext-ciphertext data pairs respectively;

[0065] Step 3: Design a high-performance deep learning attack network RRU-NetPP and use the above different datasets to train and optimize the network.

[0066] Step 4: The established RRU-NetPP model attacks the ciphertext encrypted by the PTFT cryptosystem and the EMD cryptosystem, and can retrieve the plaintext in real time and with high quality. The training process is:

[0067] F(x)=Minloss(C i ,P i ) (1)

[0068] Among them, F(x), C i , P i They represent the trained and optimized model, ciphertext, and plaintext respectively; Minloss() represents the minimization of the loss function.

[0069] The loss function is the mean square error loss function, which can be expressed as:

[0070]

[0071] Among them, n represents the number of samples, that is, the number of ciphertext-plaintext data pairs; x i is the true (plaintext) value of the ith sample, y i is the predicted value of the i-th sample; MSE represents the performance of the model; the smaller the MSE value, the smaller the difference between the predicted value and the true value of the model, and the better the performance of the model; when the MSE value no longer decreases, save the model file, and use the model file to attack the test ciphertext during the test reasoning process to decrypt the ciphertext.

[0072] like Figure 2 As shown in the figure, the model contains 5 encoding modules, 10 decoding modules and a dense skip connection structure; it is used to learn the nonlinear feature mapping from ciphertext to plaintext; in the encoding module and the decoding module, each block is constructed with two feature extraction layers through residual propagation and residual feedback, and each feature extraction layer consists of a standard convolution layer with a convolution kernel size of 3×3, a stride of 1, and a padding of 1, as well as a Batch Normalization layer and a Rectified LinearUnit activation function.

[0073] The residual propagation consists of a standard convolution layer with a convolution kernel of 1×1, a Batch Normalization layer, and a RectifiedLinear Unit activation function;

[0074] The residual feedback consists of a standard convolutional layer with a 1×1 kernel;

[0075] In the whole module, residual propagation is performed twice and residual feedback is performed once.

[0076] The first residual propagation process is:

[0077] y1=F(x)+x (3)

[0078] Among them, y1 represents the output after two feature extraction layers, x represents the input, and F() represents the feature map to be learned.

[0079] The residual feedback process is:

[0080] y2=(F s (G(y1))+1)x (4)

[0081] Where x represents the input, G() represents a linear mapping used to change the dimension of y1, y1 is the output in formula (3), and F srepresents the sigmoid activation function, and y2 represents the output after feedback.

[0082] The sigmoid activation function is used to drive the overall feedback learning to distinguish the nonlinear effect between the ciphertext mapping and the plaintext feature communication, avoid the diffusion of feature information, and shield the information interference between ciphertexts, so that the model can retrieve different plaintexts with high quality from multiple extremely similar ciphertexts.

[0083] The second residual propagation process:

[0084] y3=F(y2)+x (5)

[0085] Where y2 is the output in formula (4), F() is the feature map, x represents the input, and y3 represents the output of the second residual propagation.

[0086] The model also includes downsampling and upsampling operations. The downsampling operation is used in the encoder part, and the upsampling process is used in the decoder part. The Max-Pooling layer used for downsampling represents the maximum pooling layer with a convolution kernel size of 2×2. The purpose is to halve the height and width of the feature map, reduce the amount of calculation, prevent overfitting, and do not change the communication dimension of the feature map. Redundant features are filtered out by downsampling to retain the key information of the feature map.

[0087] Among them, a single-channel ciphertext image of size 256×256 is transformed into a 16×16 1024-channel feature map after passing through the encoder;

[0088] The transposed-convolution layer used for upsampling represents a transposed convolution layer with a convolution kernel size of 4×4, a stride of 2, and a padding of 1; upsampling enlarges the extracted feature map.

[0089] After the feature map passes through the decoder, it outputs a 256×256 single-channel map, passes through a standard convolution layer with a convolution kernel size of 1×1, and generates the predicted plaintext after the sigmoid activation function.

[0090] After training, the RRU-NetPP model can be used to decipher any ciphertext in the test set.

[0091] Embodiment 1:

[0092] In order to verify the effectiveness of the proposed deep learning model for asymmetric optical cryptography, the reference light wavelength introduced in the optical encryption part is 532nm, and all experimental images are grayscale images of 256×256 pixels. The optical encryption part is implemented by MATLAB 2021b, and the deep learning numerical simulation is implemented on Pytorch 2.0. The RRU-Net PP model is trained using a computing platform (CUDA) of four graphics processing units (GPUs) (NVIDIA TITAN XP). During training, the model is optimized using the AdamW optimizer with a learning rate of 0.0001.

[0093] Since the ciphertext generated by EMD-based OAC is a complex image, it is impossible to directly save the image into a folder. Therefore, the amplitude part of the EMD-based OAC ciphertext is used as the input of the model in the present invention, which can effectively save time and facilitate network training.

[0094] The model training for different cryptographic systems and different data sets is completed and saved. In order to verify the feasibility of the proposed RRU-Net PP model, three test sets encrypted by PTFT-based OAC and EMD-based OAC are input into the corresponding trained models. The attack results of the model corresponding to PTFT-based OAC are shown in Figure 2. Figure 3 As shown in Figure 2, the model attack results corresponding to EMD-based OAC are as follows: Figure 4 Obviously, the visualization result of the predicted plaintext is very similar to the real plaintext, and it is difficult to detect the difference between the predicted plaintext and the real plaintext, which shows that the present invention successfully attacks the two OACs, and the attack results are very clear.

[0095] Embodiment 2:

[0096] In addition, in order to quantitatively analyze the reliability of the learning-based attack method proposed in this invention, the cross-correlation coefficient (CC), peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) image evaluation indicators are introduced to quantitatively analyze the quality of the predicted plaintext and the similarity with the real plaintext. The CC, PSNR, and SSIM between the real plaintext X and the predicted plaintext Y are defined as:

[0097]

[0098] In formula (6) and represents the average value of X(i,j) and Y(i,j), and n represents the number of predicted plaintexts. lg() in formula (7) represents log 10 (), M, N represent the pixel size of the image. X(i,j) and μY(i,j) represents the mean of X(i,j) and Y(i,j), σ X(i,j) and σ Y(i,j) represents the covariance of X(i,j) and Y(i,j), C1=(K1L) 2 , C2=(K2L) 2 Represents two constants, K1 and K2 default to 0.01 and 0.03 respectively, and L represents the range of image pixel values, which is 255.

[0099] The maximum values ​​of CC and SSIM are both 1. The higher the value, the better the image quality and the higher the similarity with the real plaintext. A PSNR value lower than 20dB indicates that the image quality is extremely poor, a PSNR value higher than 30dB indicates that the image quality is good, and a PSNR value between 20-30dB indicates that the image quality is poor but acceptable.

[0100] We calculated the average CC, PSNR and SSIM values ​​of the real plaintext and predicted plaintext of the three datasets using two different methods, and the results are shown in Tables 1 and 2.

[0101] Table 1:

[0102]

[0103] Table 2:

[0104]

[0105] For PTFT-based OAC, the average CC values ​​of the real plaintext and predicted plaintext of Fashion-MNIST, Animal Picture Set and LFW-People are 0.987, 0.993 and 0.993 respectively; the average PSNR values ​​are 25.339dB, 31.454dB and 30.242dB respectively; the average SSIM values ​​are 0.803, 0.891 and 0.895 respectively.

[0106] For EMD-based OAC, the average CC values ​​of the real plaintext and predicted plaintext of Fashion-MNIST, Animal Picture Set and LFW-People are 0.976, 0.992 and 0.991 respectively; the average PSNR values ​​are 22.327dB, 30.231dB and 31.556dB respectively; the average SSIM values ​​are 0.790, 0.878 and 0.887 respectively.

[0107] In the process of ciphertext transmission and communication, part of the ciphertext data may be lost. Therefore, the present invention randomly sets the pixel values ​​of a part of the test ciphertext to 0 to test the robustness of the model. Specifically, the present invention randomly selects a group of test ciphertexts and replaces the pixels corresponding to the coordinates (i, j) of the ciphertext images with 0. For PTFT, the corresponding visualization results are as follows Figure 5 As shown; for EMD, the corresponding visualization results are as follows Figure 6 As shown in the figure, as the proportion of zero pixels in the ciphertext increases, the predicted ciphertext becomes increasingly difficult to identify, and more and more information is lost. In addition, we also calculated the average CC, PSNR, and SSIM values ​​of the attack results of different test sets for different cryptographic systems. The results are shown in Tables 3 and 4.

[0108] Table 3:

[0109]

[0110] Table 4:

[0111]

[0112]

[0113] Embodiment 3:

[0114] The present invention also studies the robustness of this method to noise. We add Gaussian noise with variance of 0.01 and 0.02 and mean of 0 to different test set ciphertext images, and use the noisy ciphertext to test the model's robustness to noise. The corresponding visualization results are shown in Figure 2. Figure 7 and 8 The average CC, PSNR and SSIM values ​​of the attack results are shown in Tables 5 and 6. As shown in the results, this method has strong anti-noise robustness.

[0115] Table 5:

[0116]

[0117] Table 6:

[0118]

[0119]

[0120] Embodiment 4:

[0121] In order to highlight the excellent attack capability of the RU-Net PP model of the present invention, the present invention compares and analyzes the retrieval capabilities of the GAN model and the RU-Net PP model proposed by previous scholars. Experimental results show that the use of the RU-Net PP model avoids the problem of retrieving some ambiguous results to a great extent. We use the same training set to train the RU-Net PP model and the GAN model respectively. In order to ensure the accuracy of the experimental results, the two models are trained to the optimal state (minimization of the loss function), and other experimental parameters (such as the number of iterations, learning rate, loss function, optimizer) remain consistent with those described in the paper. The experimental results based on the PTFT cryptographic system and the EMD cryptographic system are shown in Figure 2. Fig. 9 and Fig.10 shown.

[0122] Obviously, the attack results of the RU-Net PP model for any data have more high-frequency features than the GAN model, and the visualization results are clearer, and there is no problem of being unable to identify the attack. This is because the dense feature extraction module and jump connection module of the RU-Net PP model give it a strong perception of information, allowing the learning method to achieve high-quality attack restoration for complex ciphertexts. We further quantitatively calculated the average CC, PSNR, and SSIM values ​​of the real plaintext and the attack results of the two models, and the results are shown in Tables 7 and 8.

[0123] Table 7:

[0124]

[0125]

[0126] Table 8:

[0127]

[0128] The above description is only a preferred embodiment of the present invention and does not limit the technical scope of the present invention. Therefore, any slight modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A high-performance deep learning attack method for asymmetric cryptographic systems, characterized in that: The following steps are involved: Step 1: Use PTFT-based and EMD-based image encryption algorithms to encrypt a small amount of image data from Fashion-MNIST, LFW-People and Anima Picture Set databases respectively, so as to obtain the corresponding ciphertext and plaintext data pairs; Step 2: Create a new database, including the six data sets generated in the above steps. Each data set is divided into a training set, a validation set, and a test set, which include 600 pairs, 200 pairs, and 200 pairs of plaintext-ciphertext data pairs respectively; Step 3: Design a high-performance deep learning attack network RRU-NetPP and use the above different datasets to train and optimize the network; Step 4: The established RRU-NetPP model attacks the ciphertext encrypted by the PTFT cryptosystem and the EMD cryptosystem, and can retrieve the plaintext in real time and with high quality.

2. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 1, characterized in that: The training process is: F(x)=Minloss(C i ,P i ) (1) Among them, F(x), C i , P i They represent the trained and optimized model, ciphertext, and plaintext respectively; Minloss() represents the minimization of the loss function.

3. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 2, characterized in that: The loss function is a mean square error loss function, which can be expressed as: Among them, n represents the number of samples, that is, the number of ciphertext-plaintext data pairs; x i is the true (plaintext) value of the ith sample, y i is the predicted value of the i-th sample; MSE represents the performance of the model; the smaller the MSE value, the smaller the difference between the predicted value and the true value of the model, and the better the performance of the model; when the MSE value no longer decreases, save the model file, and use the model file to attack the test ciphertext during the test reasoning process to decrypt the ciphertext.

4. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 1, characterized in that: The model includes 5 encoding modules (Recurrent Residualblock), 10 decoding modules (VGGblock) and a dense skip connection structure; in the encoding module, each block is constructed with two feature extraction layers through residual propagation and residual feedback, each of which is composed of a standard convolution layer with a convolution kernel size of 3×3, a stride of 1, and a padding of 1, as well as a Batch Normalization layer and a Rectified Linear Unit activation function; in the decoding module, each block is constructed with two feature extraction layers, each of which is composed of a standard convolution layer with a convolution kernel size of 3×3, a stride of 1, and a padding of 1, as well as a Batch Normalization layer and a Rectified Linear Unit activation function.

5. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 4, characterized in that: The residual propagation consists of a standard convolution layer with a convolution kernel of 1×1, a Batch Normalization layer, and a Rectified Linear Unit activation function; The residual feedback consists of a standard convolutional layer with a 1×1 kernel; In the whole module, residual propagation is performed twice and residual feedback is performed once.

6. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 5, characterized in that: The first residual propagation process is: y1=F(x)+x (3) Among them, y1 represents the output after two feature extraction layers, x represents the input, and F() represents the feature map to be learned.

7. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 5, characterized in that: The residual feedback process is: y2=(F s (G(y1))+1)x (4) Where x represents the input, G() represents a linear mapping, y1 is the output in formula (3), and F s represents the sigmoid activation function, and y2 represents the output after feedback.

8. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 5, characterized in that: The second residual propagation process: y3=F(y2)+x (5) Where y2 is the output in formula (4), F() is the feature map, x represents the input, and y3 represents the output of the second residual propagation.

9. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 1, characterized in that: The model also includes a downsampling operation and an upsampling operation, the downsampling operation is used in the encoder part, and the upsampling process is used in the decoder part; the Max-Pooling layer used for downsampling represents a maximum pooling layer with a convolution kernel size of 2×2, which filters out redundant features through downsampling and retains key information of the feature map; Among them, a single-channel ciphertext image of size 256×256 is transformed into a 16×16 1024-channel feature map after passing through the encoder; The transposed-convolution layer used for upsampling represents a transposed convolution layer with a convolution kernel size of 4×4, a stride of 2, and a padding of 1; upsampling enlarges the extracted feature map.

10. A high-performance deep learning attack method for an asymmetric cryptographic system according to claim 9, characterized in that: After the feature map passes through the decoder, it outputs a 256×256 single-channel map, passes through a standard convolution layer with a convolution kernel size of 1×1, and generates predicted plaintext after the sigmoid activation function.

11. A high-performance deep learning attack method for an asymmetric cryptographic system with few sample data according to claim 1, characterized in that: The deep learning attack method shown can extract effective features from a small number of samples and achieve high-quality attack effects, significantly reducing the limitations of its application scenarios. Its efficient learning characteristics can significantly shorten the training time and reduce the consumption of resources and time.

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