An Adaptive Asymmetric Image Steganography Method and System Based on a Diffusion Model

Abstract

This invention discloses an adaptive asymmetric image steganography method and system based on a diffusion model, relating to the fields of artificial intelligence and information security. The invention calculates the corresponding cumulative distribution probability based on the noise to be embedded, then embeds secret information by slightly modifying the cumulative distribution probability. Finally, an inverse cumulative distribution function is used to obtain Gaussian noise with embedded information, maintaining the probability distribution of the embedded Gaussian noise unchanged. Before actual embedding, embedding is simulated in the noise to be embedded, completing simulated embedding +1 and -1 processes to remove pixels that cannot correctly extract information, and calculating the modification amount introduced by embedding +1 and -1 on the noise. Then, the asymmetric steganography embedding cost of each pixel is calculated based on the modification amount, and the secret information is embedded into the cumulative distribution of the Gaussian noise. Finally, the reverse process is completed to generate the steganographic image. This addresses the problems of insufficient anti-detection and imperceptibility in existing steganography methods.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of artificial intelligence and information security, and particularly relates to an adaptive asymmetric image steganography method and system based on a diffusion model. BACKGROUND

[0002] With the rapid development of the Internet, deep learning technology uses neural networks to realize the automatic extraction of features from shallow to deep semantics. Compared with traditional detection, classification and generation algorithms, deep learning technology has achieved better results, and has been widely studied in the fields of computer vision, natural language processing and other fields in recent years. Among them, the generation model based on deep learning can generate nearly real new sample data by learning the features of existing data, so it has been widely studied and applied in image and text generation tasks.

[0003] The most widely used deep generation model at present is the diffusion model, which is based on Markov chain. In the forward process, a neural network is used to learn to add noise to the original sample step by step, so that the sample data is finally close to Gaussian noise. Then in the reverse process, the noise is predicted and denoised by the neural network, and finally a new sample result is generated. Compared with variational autoencoder and generative adversarial network, the generated result by diffusion model is of better quality and the training process is more stable. Since the diffusion model can be adapted to generate various types of data, it has become one of the main research directions in the field of artificial intelligence.

[0004] Diffusion model is also suitable for application in generative image steganography, which can be used to protect the security of private information. Steganography hides secret information in the carrier by making minor changes to the carrier. Compared with traditional encryption technology, steganography not only can effectively protect the security of private information, but also can hide the existence of private information in a public network environment, realize the secret storage and covert transmission of private information, and thus reduce the risk of private information being attacked, intercepted or analyzed by attackers. Using diffusion model, image steganography can combine the reverse process of diffusion model to directly generate a stego image containing secret information, realizing the embedding of private information to protect the security of private information.

[0005] The generative image steganography based on diffusion model realizes the embedding of secret information by adding an embedding step of secret information in the reverse denoising process of diffusion model. This type of steganography can usually use multiple strategies to embed secret information, including embedding in prompt words, replacing initial noise with secret information and modifying final noise based on secret information. However, the existing diffusion model-based image steganography methods based on the above strategies have the following shortcomings:

[0006] (1) The existing generative image steganography method mostly uses a neural network to directly fuse the features of the carrier and the secret information, but the secret information cannot be accurately extracted and restored through the neural network, so the generative steganography method that modifies noise by fusing features has a certain loss of secret information embedding.

[0007] (2) The result generated by the reverse process of the diffusion model is a floating-point number, which needs to be truncated and converted into an integer when saved as a stego image, which brings great challenges to the accuracy of the secret information extraction of the diffusion model image steganography method. Truncating floating-point numbers may cause the pixel values of some pixel points to remain unchanged before and after embedding, resulting in loss of secret information and introducing embedding loss. If redundant information is added during embedding, such as using error correction coding, the actual embedding capacity of steganography will be greatly reduced.

[0008] (3) The steganography method based on the diffusion model usually directly modifies or replaces the data of the selected embedding points when embedding secret information, resulting in a large difference between the original image and the stego image generated under the same conditions, making it difficult for the stego image to resist detection by the steganalysis analyzer, that is, the anti-detection performance is insufficient. SUMMARY

[0009] In view of the deficiencies of the prior art, the present application provides an adaptive asymmetric image steganography method and system based on a diffusion model to solve the problems of insufficient anti-detection and imperceptibility of existing steganography methods.

[0010] The technical scheme of the present application is as follows:

[0011] On the one hand, the present application provides an adaptive asymmetric image steganography method based on a diffusion model, comprising the following steps:

[0012] Initialize the diffusion model and its parameter configuration, and perform the reverse diffusion process on the initialized initial sample iteratively, save the generated Gaussian noise, predicted denoising residual, predicted reverse diffusion sampling mean and denoising sample at each step, until the iteration is completed; the sample is an image;

[0013] Based on the generated Gaussian noise, predicted denoising residual, predicted reverse diffusion sampling mean and denoising sample, the modification amount and mask cost when embedding all +1 and -1 analog secret information are calculated respectively;

[0014] According to the modification amount and mask cost when embedding all +1 and -1 analog secret information, the embedding cost introduced by embedding +1 and -1 analog secret information at each pixel point is calculated, the original secret information is encoded based on the embedding cost using a steganography encoder, and the encoded secret information is embedded in the i-th step of the reverse diffusion process, and finally a stego image is generated;

[0015] The secret information is extracted from the stego image.

[0016] Further, the initialized diffusion model and its parameter configuration, the initialized initial sample is iteratively executed, and the generated Gaussian noise, the predicted denoising residual, the predicted reverse diffusion sampling mean and the denoised sample at each step are saved until the iteration is completed, specifically including the following steps:

[0017] A1: initialize the diffusion model, set the image resolution, set the total inference step number , and the step number of the information to be embedded , set the seed of the random number generator, load the weight of the predicted noise network in the diffusion model, and set the key of the steganographic encoder;

[0018] A2: based on the set seed, generate an initial sample using a random number generator , use the predicted noise network to perform a reverse diffusion process to gradually denoise the initial sample , for the step number , obtain the Gaussian noise , the predicted denoising residual , the predicted reverse diffusion sampling mean and the denoised sample at each step;

[0019] The reverse diffusion process is shown in equation (1):

[0020] (1);

[0021] wherein, is the denoised sample predicted by the t-th step of the reverse diffusion process; is the predicted reverse diffusion sampling mean, is the sample of the t-th step of the reverse diffusion process, is the denoising residual obtained by the predicted noise network, is the sampling standard deviation of the reverse diffusion process, is the predicted Gaussian noise, is the unit matrix, is the variance scheduling of the forward diffusion, , , and k is the index.

[0022] Further, based on the generated Gaussian noise, the predicted denoising residual, the predicted reverse diffusion sampling mean and the denoised sample, the modification amount and the mask cost when embedding all +1 and -1 simulated secret information are calculated respectively, including the following steps:

[0023] B1: based on the reverse diffusion process of A2, use the cumulative distribution function CDF to calculate the modification amount and the mask cost when embedding all +1 and -1 simulated secret information Gaussian noise generated Transformed into cumulative distribution ;

[0024] (2);

[0025] wherein, is a cumulative distribution function;

[0026] B2: without using steganographic encoder, directly generate secret information with set image resolution size , simulate embedding all +1 analog secret information, record the secret information as ;

[0027] B3: according to secret information , calculate the modification amount m of embedding secret information;

[0028] (3);

[0029] wherein, is the modification amount of embedding secret information, is the secret information, is the scaling coefficient; in the simulation of embedding all +1 analog secret information, the modification amount of embedding secret information , the secret information

[0030] B4: modify the cumulative distribution according to the modification amount m of embedding , and then transform it into a probability distribution through the inverse cumulative distribution function ICDF to obtain the modified Gaussian noise ;

[0031] (4);

[0032] wherein, is the inverse cumulative distribution function; in the simulation of embedding all +1 analog secret information, the Gaussian noise ;

[0033] B5: add the first step predicted reverse diffusion sampling mean value obtained by A2 and the modified Gaussian noise to obtain the embedding after denoising sample of the first step ;

[0034] The embedding after denoising sample is expressed as:

[0035] (5);

[0036] Among them, when simulating embedding simulated secret information where all values ​​are +1, the denoised samples after embedding ;

[0037] B6: Regarding the first Denoising samples after embedding Continue with the subsequent steps of the reverse diffusion process. Obtain the encrypted image sample ;

[0038] The back-diffusion process of the embedded denoised samples is shown in equation (6):

[0039] (6);

[0040] in, The denoised sample is the one predicted after embedding secret information in step t of the back diffusion process. For the sample that has embedded secret information in step t of the back diffusion process, The mean of backdiffusion sampling is calculated based on the denoised samples after embedding; the mean of backdiffusion sampling is calculated when simulating embedded secret information where all values ​​are +1. ;

[0041] B7: Sample the original image respectively and encrypted image samples Rounding down yields the original image. and encrypted images As shown in equation (7);

[0042] (7);

[0043] Where, round means rounding to the nearest integer; when simulating embedded secret information consisting entirely of +1, the encrypted image sample Confidential images ;

[0044] B8: Based on the predicted denoising residual and generated Gaussian noise during the backdiffusion process, the original image is respectively... With encrypted images Reverse diffusion process to the first Step by step, the restored original samples are obtained respectively. and dense samples ;

[0045] The method for reverse diffusion process is as follows:

[0046] (8);

[0047] in, To reverse the diffusion process in the first stage The reduced sample; when simulating embedding of the simulated secret information with all +1, the stego sample ;

[0048] B9: The original sample is reduced and the stego sample respectively, and the difference is obtained The original noise and the stego noise are converted into cumulative distribution and the difference is obtained and scaled to obtain the reduced embedding modification , and then the reduced embedding modification is rounded and truncated to the interval [-1, +1] to obtain the extracted secret information ;

[0049] (9);

[0050] (10);

[0051] wherein, The reduced embedding modification; when simulating embedding of the simulated secret information with all +1, the reduced embedding modification , the extracted secret information ;

[0052] B10: The original secret information and the extracted secret information are compared, wherein the pixel points with different secret information are wet points, and the mask cost when simulating embedding of the simulated secret information is calculated according to the determined wet points ;

[0053] (11);

[0054] wherein, The mask cost is a matrix, wherein the element corresponding to the wet point is , and the element corresponding to the non-wet point is ; when simulating embedding of the simulated secret information with all +1, the mask cost .

[0055] B11: According to the method of B2-B10, the embedding modification of the secret information when simulating embedding of the simulated secret information with all -1 is obtained , the wet point when simulating embedding of the simulated secret information with all -1 is determined, and the mask cost when simulating embedding of the simulated secret information with all -1 is calculated .

[0056] Further, the step of calculating the embedding cost of each pixel when embedding simulated secret information consisting entirely of +1 and -1, based on the modification amount and mask cost when embedding simulated secret information consisting entirely of +1 and -1, using a stegcoder to encode the original secret information based on the embedding cost, and embedding the encoded secret information in the i-th step of the back-diffusion process to finally generate a secret-carrying image, specifically includes the following steps:

[0057] C1: Modification amount based on simulated secret information where all elements are +1 and -1. and modification amount The mask cost when the simulated embedding consists entirely of simulated secret information consisting of +1 and -1 is combined. and Calculate the embedding cost introduced by each pixel when embedding simulated secret information of +1 and -1 respectively. and embedding cost ;

[0058] (12);

[0059] in, It is a tiny floating-point number;

[0060] C2: Generate a temporary carrier matrix n consisting entirely of zeros, based on the set image resolution.

[0061] C3: Use a stegcoder, based on embedding cost. and The original secret information g is embedded in the temporary carrier matrix n to obtain the encoded secret information s;

[0062] C4: Following the methods in B3 and B4, obtain the modified Gaussian noise based on the secret information s. ;

[0063] C5: Following the method in B5, the first... The mean of the backdiffusion sampling of the step prediction Compared with modified Gaussian noise Add them together to get the denoised samples after embedding. ;

[0064] C6: Following methods B6 and B7, denoise the embedded samples. The reverse diffusion process is completed, and finally, a high-resolution image is generated and saved. .

[0065] Furthermore, the extraction of secret information from the encrypted image includes the following steps:

[0066] D1: Using the same diffusion model parameters, including image resolution, random number generator seed, and weights of the prediction noise network, perform the backdiffusion process of A1 and A2, where the number of steps... Generate original image samples Then obtain the original image using method B7. ;

[0067] D2: Read the original images respectively and received encrypted images Following the methods of B8 and B9, the reverse diffusion process is traced back to the first... Step, calculate the amount of embedded modifications to be restored. And extract secret information. ;

[0068] D3: Based on the key of the steganography encoder, use the steganography encoder to decode the secret information s' and extract the transmitted secret information g'.

[0069] On the other hand, the present invention also provides an adaptive asymmetric image steganography system based on a diffusion model, for implementing an adaptive asymmetric image steganography method based on a diffusion model, comprising:

[0070] The data acquisition module is used to initialize the diffusion model and its parameter configuration, iteratively execute the back diffusion process on the initial sample obtained after initialization, and save the Gaussian noise generated at each step, the predicted denoised residual, the predicted back diffusion sampling mean and the denoised sample, until the iteration is completed;

[0071] An embedded simulation module is used to calculate the modification amount and mask cost when embedding simulated secret information that is all +1 and -1, based on the generated Gaussian noise, the predicted denoised residual, the predicted back-diffusion sampling mean, and the denoised sample, respectively.

[0072] The secret image generation module is used to calculate the embedding cost of each pixel when embedding simulated secret information of +1 and -1 based on the modification amount and mask cost when embedding simulated secret information of all +1 and -1. The module uses a steg encoder to encode the original secret information based on the embedding cost and embeds the encoded secret information in the i-th step of the back diffusion process to finally generate the secret image.

[0073] The secret information extraction module is used to extract secret information from images containing secret information.

[0074] Thirdly, this application proposes an electronic device, comprising: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the aforementioned adaptive asymmetric image steganography method based on a diffusion model.

[0075] Fourthly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the aforementioned adaptive asymmetric image steganography method based on a diffusion model.

[0076] Fifthly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the aforementioned adaptive asymmetric image steganography method based on a diffusion model.

[0077] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0078] 1. To address the embedding loss problem caused by directly fusing features of the carrier and secret information, this invention is based on adaptive steganography, that is, using a steganalytic encoder to encode the secret information to achieve embedding of the secret information. Since modern steganalytic encoders can achieve embedding and accurate extraction close to the upper limit of the optimal embedding theory, this invention can achieve efficient and accurate embedding of secret information, while not needing to consider the embedding loss caused by feature fusion.

[0079] 2. To address the embedding loss problem introduced by floating-point truncation in the diffusion model, this invention first simulates embedding information consisting entirely of +1 and -1 before embedding the secret information. Then, it compares the extracted information with the original simulated information to identify pixels where embedding fails due to truncation. Therefore, in actual embedding, this invention sets an infinitely large embedding cost for pixels that fail to embed, thus preventing the stegcoder from embedding information in them and avoiding the embedding loss caused by floating-point truncation.

[0080] 3. To address the issue of insufficient anti-detection performance of encrypted images caused by direct modification or replacement of data, this invention calculates the modification amount of embedding +1 and -1 simulated information to determine the embedding cost, and achieves optimal embedding based on adaptive steganography and a stegcoder. This invention modifies the cumulative distribution of embedded secret information, maintaining the probability distribution of Gaussian noise after embedding. Simultaneously, by adjusting the embedding cost, this invention causes the stegcoder to prioritize embedding secret information in regions with smaller embedding modifications, thereby improving the anti-detection performance of this invention and further optimizing the quality of encrypted images. Attached Figure Description

[0081] Figure 1 This is a flowchart of an adaptive asymmetric image steganography method based on a diffusion model in an embodiment of the present invention;

[0082] Figure 2 This is a flowchart illustrating the overall process of back-diffusion embedding of simulated secret information and finding wet points in an embodiment of the present invention.

[0083] Figure 3This is a flowchart illustrating the specific process of embedding simulated secret information in an embodiment of the present invention;

[0084] Figure 4 This is a flowchart illustrating the specific process of extracting simulated secret information in an embodiment of the present invention;

[0085] Figure 5 This is a flowchart illustrating the overall process of reverse diffusion and actual embedding of secret information in an embodiment of the present invention;

[0086] Figure 6 This is a flowchart illustrating the overall process of reverse engineering and actually extracting secret information in an embodiment of the present invention;

[0087] Figure 7 This is a flowchart illustrating the actual embedding of secret information in an embodiment of the present invention.

[0088] Figure 8 This is a flowchart illustrating the specific process of reverse engineering the actual extraction of secret information in an embodiment of the present invention;

[0089] Figure 9 The original image generated in the embodiments of the present invention and the simulated dense images with different embedding rates are shown.

[0090] Among them, (a) is the original image generated by loading CelebA-HQ weights; (b) is the original image generated by loading BED weights; (c) is the original image generated by loading Church weights; (d) is the simulated encrypted image with CelebA-HQ weights at an embedding rate of 1 bpp; (e) is the simulated encrypted image with BED weights at an embedding rate of 1 bpp; (f) is the simulated encrypted image with Church weights at an embedding rate of 1 bpp; (g) is the simulated encrypted image with CelebA-HQ weights at an embedding rate of 0.4 bpp; (h) is the simulated encrypted image with BED weights at an embedding rate of 0.4 bpp; (i) is the simulated encrypted image with Church weights at an embedding rate of 0.4 bpp; (j) is the simulated encrypted image with CelebA-HQ weights at an embedding rate of 0.2 bpp; (k) is the simulated encrypted image with BED weights at an embedding rate of 0.2 bpp; and (l) is the simulated encrypted image with Church weights at an embedding rate of 0.2 bpp.

[0091] Figure 10 The original image generated in the embodiments of the present invention and the actual embedded encrypted image;

[0092] Among them, (a) is the original image generated by loading CelebA-HQ weights; (b) is the encrypted image embedded using check lattice encoding at an embedding rate of 1 bpp with CelebA-HQ weights; (c) is the encrypted image embedded using check lattice encoding at an embedding rate of 0.4 bpp with CelebA-HQ weights; and (d) is the encrypted image embedded using check lattice encoding at an embedding rate of 0.2 bpp with CelebA-HQ weights. Detailed Implementation

[0093] To make the objectives, technical methods, and advantages of this invention more apparent, the following description is provided in conjunction with... Figures 1-8 The present invention will be further described in detail below with reference to specific embodiments. The specific embodiments described herein are for illustrative purposes only and are limited to the present invention. The present invention can also be applied through other specific implementation methods. Modifications or alterations can be made according to similar needs without departing from the spirit of the present invention. In this embodiment, bold letters represent matrices.

[0094] The purpose of this invention is to provide an adaptive asymmetric image steganography method and system based on a diffusion model. Taking the Denoising Diffusion Probabilistic Models (DDPM) as an example, this invention embeds secret information into one layer of Gaussian noise in the reverse process of the diffusion model, based on optimal embedding theory and adaptive steganography, ultimately generating a steganographic image. This invention uses a cumulative distribution function to calculate the corresponding cumulative distribution probability based on the Gaussian noise to be embedded. Then, it embeds the secret information by slightly modifying the cumulative distribution probability, and uses the inverse cumulative distribution function to obtain the Gaussian noise after embedding the information, thus maintaining the probability distribution of the embedded Gaussian noise unchanged. Before actually embedding the secret information, this invention first simulates embedding in the noise to be embedded, completing simulated embedding +1 and -1 processes respectively to remove pixels that cannot correctly extract information, and calculating the modification amount introduced by embedding +1 and -1 on the noise. Then, based on the modification amount, the asymmetric steganography embedding cost of each pixel is calculated, and the secret information is then embedded into the cumulative distribution of the Gaussian noise. Finally, the reverse process is completed to generate the steganographic image. In experimental verification, the performance of this invention was first tested using a steganalysis simulator, and then the embedding and extraction of secret information was achieved through a steganalysis encoder in practical applications.

[0095] Example 1:

[0096] An adaptive asymmetric image steganography method based on a diffusion model, such as Figure 1 As shown, it includes the following steps:

[0097] Step 1: Initialize the diffusion model and its parameter configuration, iteratively execute the backdiffusion process on the initial sample obtained after initialization, and save the Gaussian noise generated at each step, the predicted denoising residual, the predicted backdiffusion sampling mean, and the denoised sample until the iteration is completed; the sample is an image.

[0098] Specifically, the following steps are included:

[0099] Step 1.1: Initialize the diffusion model, set the image resolution, and set the total number of inference steps. and the number of steps for embedding information. Set the seed for the random number generator (PyTorch's randn method), load the weights of the prediction noise network (U-Net) in the diffusion model, and set the key for the steganography encoder.

[0100] Step 1.2: Based on the set seed, generate initial samples using a random number generator. The backdiffusion process is performed stepwise on the initial samples using a predictive noise network (U-Net). Denoising is performed for the number of steps. Gaussian noise generated at each step is obtained. Predicted denoising residual Predicted backdiffusion sampling mean and denoised samples This is to prepare for the subsequent embedding of secret information;

[0101] The reverse diffusion process is shown in equation (1):

[0102] (1);

[0103] in, The denoised sample is the prediction obtained in step t of the back diffusion process; The mean of the predicted backdiffusion sampling. For the sample at step t of the reverse diffusion process, To predict the denoised residual obtained from the noisy network, The sampling standard deviation of the reverse diffusion process. For the predicted Gaussian noise, It is the identity matrix. For variance scheduling of forward diffusion, , k is an index used to calculate the cumulative product;

[0104] Step 2: Based on the generated Gaussian noise, the predicted denoising residual, the predicted back-diffusion sampling mean, and the denoised sample, calculate the modification amount and mask cost when embedding simulated secret information that is all +1 and -1, respectively.

[0105] The process of embedding simulated secret information and finding wet spots in back diffusion is as follows: Figure 2 As shown, the specific processes for embedding and reverse-engineering the simulated secret information are as follows: Figure 3 and Figure 4 As shown, the specific steps include:

[0106] Step 2.1: Based on the backdiffusion process in Step 1.2, use the cumulative distribution function (CDF) to... Gaussian noise generated step by step Transform into cumulative distribution ;

[0107] (2);

[0108] in, It is the cumulative distribution function;

[0109] Step 2.2: Generate secret information directly at the set image resolution without using a stegcode encoder. When simulating embedding simulated secret information consisting entirely of +1, this secret information is denoted as... ;

[0110] Step 2.3: Based on the secret information Calculate the amount of modification m embedded with the secret information;

[0111] (3);

[0112] in, The amount of modification to embed secret information. For confidential information, This is the scaling factor; the amount of modification to the embedded secret information when simulating embedded secret information where all values ​​are +1. Secret information

[0113] Step 2.4: Modify the cumulative distribution based on the embedded modification amount m Then, the Gaussian noise is transformed into a probability distribution using the inverse cumulative distribution function ICDF to obtain the modified Gaussian noise. ;

[0114] (4);

[0115] in, It is the inverse cumulative distribution function; when simulating embedded simulated secret information where all values ​​are +1, Gaussian noise after embedding simulated secret information consisting entirely of +1;

[0116] Step 2.5: Take the first result obtained in step 1.2 and... The mean of the backdiffusion sampling of the step prediction With modified Gaussian noise Add them together to get the first one. Denoising samples after embedding ;

[0117] The embedded denoised samples Represented as:

[0118] (5);

[0119] In the case of simulating embedded secret information where all values ​​are +1, After embedding simulated secret information where all values ​​are +1, the first... Denoising samples after embedding;

[0120] Step 2.6: For the first Denoising samples after embedding Continue with the subsequent steps of the reverse diffusion process. Obtain the encrypted image sample ;

[0121] The back-diffusion process of the embedded denoised samples is shown in equation (6):

[0122] (6);

[0123] in, The denoised sample is the one predicted after embedding secret information in step t of the back diffusion process. For the sample that has embedded secret information in step t of the back diffusion process, The mean of the back-diffusion sampling is calculated based on the denoised samples after embedding. This is used when simulating the embedding of simulated secret information where all values ​​are +1. ;

[0124] Step 2.7: Sample the original image respectively and encrypted image samples Rounding down yields the original image. and encrypted images As shown in equation (7);

[0125] (7);

[0126] Where "round" represents rounding to the nearest integer. In simulating the embedding of simulated secret information consisting entirely of +1, the encrypted image sample... Confidential images ;

[0127] Step 2.8: Based on the predicted denoising residual and the generated Gaussian noise during the backdiffusion process, the original image is processed... With encrypted images Reverse diffusion process to the first Step by step, the restored original samples are obtained respectively. and dense samples ;

[0128] The method for reverse diffusion process is as follows:

[0129] (8);

[0130] in, To reverse the diffusion process in the first stage The sample restored step by step, when simulated by embedding simulated secret information consisting entirely of +1, yields the restored secret-carrying sample. ;

[0131] Step 2.9: Restore the original sample With dense sample Compared with the backdiffusion sampling mean respectively The difference between the two is used to obtain the original noise and the noise density, which are then converted into a cumulative distribution. The difference between the two is then calculated and scaled to obtain the restored embedding modification. Subsequently, the amount of embedded modification was restored. Rounding down and truncating to the interval [-1, +1] yields the extracted secret information. ;

[0132] (9);

[0133] (10);

[0134] in, The amount of embedded modification to be restored is the amount of embedded modification restored when simulating simulated secret information where all embedded values ​​are +1. Extracted secret information ;

[0135] Step 2.10: Compare the original secret information and extracted secret information Pixels with unequal secret information are called wet pixels, and the mask cost for simulating the embedding of simulated secret information is calculated based on the determined wet pixels. ;

[0136] (11);

[0137] in, The mask cost is a matrix, where the elements corresponding to the wet points are... The non-wet point is When simulating embedded simulated secret information consisting entirely of +1s, the masking cost is... ;

[0138] Step 2.11: Based on the methods in steps 2.2-2.10, determine the wet point when simulating embedding simulated secret information consisting entirely of -1, and calculate the mask cost when simulating embedding simulated secret information consisting entirely of -1. ;

[0139] In this embodiment, simulated coded secret information consisting entirely of -1s is directly generated. The modification amount of embedding -1 is obtained. After embedding Gaussian noise, the result is Finally, the reverse diffusion process is completed to generate a simulated high-density image. , restored to And extract secret information Find the wet points embedded with -1 and save the mask cost of the wet points. ;

[0140] Step 3: Based on the modification amount and mask cost when embedding simulated secret information that is all +1 and -1, calculate the embedding cost that each pixel will introduce when embedding simulated secret information of +1 and -1. Use a steg encoder to encode the original secret information based on the embedding cost, and embed the encoded secret information in step i during the back diffusion process to finally generate a secret image.

[0141] The process of back-diffusion actually embedding secret information is as follows: Figure 5 As shown, the specific process of actually embedding secret information is as follows: Figure 6 As shown, the specific steps include:

[0142] Step 3.1: Modification amount based on the simulated secret information where all values ​​are +1 and -1. and modification amount The mask cost when simulating embedding simulated secret information consisting entirely of +1 and -1, obtained in step 2. and Calculate the embedding cost introduced by each pixel when embedding simulated secret information of +1 and -1 respectively. and embedding cost ;

[0143] (12);

[0144] in, To be a tiny floating-point number, to avoid ;

[0145] Step 3.2: Generate a temporary carrier matrix n consisting entirely of zeros, based on the set image resolution.

[0146] Step 3.3: Use a stegcoder, based on the embedding cost and The original secret information g is embedded in the temporary carrier matrix n to obtain the encoded secret information s;

[0147] Step 3.4: Following the methods in steps 2.3 and 2.4, obtain the modified Gaussian noise based on the secret information s. ;

[0148] Step 3.5: Following the method in Step 2.5, the first... The mean of the backdiffusion sampling of the step prediction Compared with modified Gaussian noise Add them together to get the denoised samples after embedding. ;

[0149] Step 3.6: Following the methods in steps 2.6 and 2.7, denoise the embedded samples. The reverse diffusion process is completed, and finally, a high-resolution image is generated and saved. ;

[0150] Step 4: Extract the secret information from the encrypted image at the receiving end;

[0151] The process of reverse engineering and actually extracting secret information is as follows: Figure 7 As shown, the specific process for actually extracting secret information is as follows: Figure 8 As shown, the specific steps include:

[0152] Step 4.1: At the receiving end, perform the back-diffusion process of steps 1.1 and 1.2 with the same diffusion model parameters (image resolution, random number generator seed, prediction noise network weights), where the number of steps... Generate original image samples Then, obtain the original image using the method in step 2.7. ;

[0153] Step 4.2: Read the original images respectively and received encrypted images Following steps 2.8 and 2.9, the reverse diffusion process is traced back to the first... Step, calculate the amount of embedded modifications to be restored. And extract secret information. ;

[0154] Step 4.3: Based on the key of the steganography encoder (which is consistent with the key of the sender), use the steganography encoder to decode the secret information s' and extract the transmitted secret information g'.

[0155] Comparison of steganographic embedding results with experimental results:

[0156] Generative steganography methods based on diffusion models should not only generate high-quality images but also achieve secure and efficient steganography. The generated steganographic images should possess strong resistance to detection, making them difficult for steganalysts to detect and attack. Simultaneously, the generated steganographic images should also have good imperceptibility, possessing image quality close to that of the directly generated original images. Detailed experimental analysis is conducted on the proposed method regarding imperceptibility, resistance to steganalysis, and practical application performance, verifying the advancement and effectiveness of the invention.

[0157] The platform used in this invention is: Intel(R) Core(TM) i7-9700K CPU @ 4.80GHz; memory: 64GB; external storage: 1TB solid-state drive; operating system: CentOS Linux 9 64-bit; implementation language: Python and C++; implementation framework: PyTorch 2.7.0.

[0158] In experimental verification, this invention uses the diffusion model DDPM as an example, setting the resolution of the generated image to 256×256 pixels, the batch size to 8, and the number of diffusion steps to... = 50, Steps for embedding secret information = 3, scaling factor The seed for the random number generator is randomly set. In step 3.3, a steganalysis simulator is used to perform random simulated embeddings to verify the performance of this invention, generating a total of 6400 images. Of these, 5000 images are used to train the steganalysis analyzer, and 1600 images are used for testing. In verifying actual embeddings, the stegcoder used is a check lattice code (STC), and the same random number generator seed is used to generate 6400 steganalysis images.

[0159] (1) Imperceptibility;

[0160] The result of embedding secret information in this invention is as follows: Figure 9 As shown in the figure. Among them, (a)-(c), (d)-(f), (g)-(i), and (j)-(l) are the original image generated by loading CelebA-HQ, bed, and church weights into the denoising network, the simulated denoised image with an embedding rate of 1 bpp generated by the embedding simulator, the simulated denoised image with an embedding rate of 0.4 bpp generated by the embedding simulator, and the simulated denoised image with an embedding rate of 0.2 bpp generated by the embedding simulator, respectively.

[0161] As the results above show, the images generated by the original diffusion model and the dense images generated by this invention are extremely similar, and cannot be directly distinguished by the human eye. Therefore, this invention has good imperceptibility.

[0162] By calculating the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) between the generated original image and the steganalytic image, the differences between the two sets of images are evaluated to quantitatively assess the image quality of the steganalytic image, and to further objectively evaluate the imperceptibility of the steganography method. PSNR assesses image distortion by calculating the ratio of the maximum power of the signal to the noise power, thus evaluating image quality. SSIM, based on human visual perception, compares the similarity between two images in terms of brightness, contrast, and structure to measure image quality loss. Higher PSNR and SSIM results indicate higher image quality. Specifically, two identical images have an SSIM value of 1.

[0163] To verify the imperceptibility of this invention, images were generated using CelebA-HQ weights as an example, and the PSNR and SSIM values ​​of this invention and existing diffusion-based steganography methods were tested respectively. In the experimental tests, all images used for training and testing underwent image quality testing, and the final average value was taken. As shown in Table 1, the PSNR and SSIM values ​​of this invention are higher than those of existing steganography methods, and the SSIM value is close to 1, indicating that the original image embedding the secret information is almost identical to the image carrying the secret information, which proves that this invention has good imperceptibility.

[0164] Table 1. PSNR and SSIM results of the encrypted images generated by this invention;

[0165]

[0166] (2) Resistance to detection;

[0167] Generative steganography also needs to have good anti-detection properties to resist steganalysis detection and thus protect the security of embedded secret information. With the widespread application of deep learning, steganalysis based on deep neural networks has gradually become the main threat to steganography. Neural network-based steganalysts can use neural networks to automatically extract feature information of images and classify images to determine whether an image is a secret image. In order to objectively verify the accuracy of the detection results of steganalysts, the false alarm rate and false negative rate of steganalysts are usually calculated to measure the detection error rate, as shown in Equation (13):

[0168] (13);

[0169] in, To detect the error rate, False alarm rate This represents the false negative rate. Therefore, a steganography method with better anti-detection performance should have a higher false positive rate after being detected by a steganalysis, proving that it can more effectively deceive the steganalysis.

[0170] To verify the anti-detection performance of this invention, XuNet, SRNet, and YeNet were used as steganalyzers to attack and detect the original and encrypted images generated by this invention and existing diffusion-based embedding methods, respectively. The average detection error rate was calculated, and the experimental results are shown in Table 2. It can be seen that this invention has the highest detection error rate, i.e., it has good anti-steganalysis detection performance.

[0171] Table 2. Detection error rate of steganalysis for raw and stegated images;

[0172]

[0173] (3) Practical application testing;

[0174] Adaptive steganography, by generating embedding probabilities, can achieve secret information embedding close to the theoretical upper limit using a steganalytic encoder, thus possessing significant practical application value. To verify the performance of this invention in practical applications, the secret information is first encoded using STC, and then the encoded secret information is embedded into Gaussian noise.

[0175] STC-encoded encrypted images, such as Figure 10 As shown in the figure. Among them, (a), (b), (c) and (d) are the original image generated by loading CelebA-HQ weights into the denoising network, the encrypted image with an embedding rate of 1 bpp generated by the STC encoder, the encrypted image with an embedding rate of 0.4 bpp generated by the STC encoder, and the encrypted image with an embedding rate of 0.2 bpp generated by the STC encoder, respectively.

[0176] In terms of imperceptibility, such as Figure 10 It is evident that the human eye still cannot directly distinguish between the original and encrypted images. Table 3 shows the PSNR and SSIM results of the encrypted image generated through STC encoding. As can be seen from the above results, using the STC encoder introduces only a slight loss of image quality, demonstrating the good imperceptibility of this invention in practical applications.

[0177] Table 3. PSNR and SSIM results of the encrypted images generated by this invention;

[0178]

[0179] Regarding resistance to detection, a steganalysis attack was used to detect the encrypted image generated by STC encoding, and the results are shown in Table 4. As the results show, the present invention still has good resistance to detection when using a steganalysis encoder, making it very suitable for applications in covert transmission and storage scenarios, and thus possessing good practical application value.

[0180] Table 4. Detection error rate of steganalysis for raw and stegated images;

[0181]

[0182] Example 2:

[0183] An adaptive asymmetric image steganography system based on a diffusion model, used to implement an adaptive asymmetric image steganography method based on a diffusion model, includes:

[0184] The data acquisition module is used to initialize the diffusion model and its parameter configuration, iteratively execute the back diffusion process on the initial sample obtained after initialization, and save the Gaussian noise generated at each step, the predicted denoised residual, the predicted back diffusion sampling mean and the denoised sample, until the iteration is completed;

[0185] An embedded simulation module is used to calculate the modification amount and mask cost when embedding simulated secret information that is all +1 and -1, based on the generated Gaussian noise, the predicted denoised residual, the predicted back-diffusion sampling mean, and the denoised sample, respectively.

[0186] The secret image generation module is used to calculate the embedding cost of each pixel when embedding simulated secret information of +1 and -1 based on the modification amount and mask cost when embedding simulated secret information of all +1 and -1. The module uses a steg encoder to encode the original secret information based on the embedding cost and embeds the encoded secret information in the i-th step of the back diffusion process to finally generate the secret image.

[0187] The secret information extraction module is used to extract secret information from images containing secret information.

[0188] Example 3:

[0189] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the aforementioned adaptive asymmetric image steganography method based on a diffusion model.

[0190] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements an adaptive asymmetric image steganography method based on a diffusion model as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and communication components.

[0191] The processor is used to execute all or part of the steps in the adaptive asymmetric image steganography method based on a diffusion model as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0192] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the adaptive asymmetric image steganography method based on a diffusion model described in the above embodiments.

[0193] Example 4:

[0194] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0195] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the adaptive asymmetric image steganography method based on a diffusion model as described in the various embodiments of this application.

[0196] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) application stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned diffusion-based adaptive asymmetric image steganography method.

[0197] Example 5:

[0198] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned adaptive asymmetric image steganography method based on a diffusion model.

[0199] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0200] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0201] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.

Claims

1. An adaptive asymmetric image steganography method based on diffusion model, characterized in that, The method comprises the following steps: initializing a diffusion model and its parameter configuration, performing an inverse diffusion process on an initial sample obtained after initialization in iterations, saving generated Gaussian noise, predicted denoising residuals, predicted inverse diffusion sampling mean and denoised samples at each step until the iteration is completed, and specifically comprising A1 and A2; the sample is an image; A1: initialize the diffusion model, set the image resolution, set the total number of inference steps , and the number of steps of information to be embedded , set the seed of the random number generator, load the weights of the prediction noise network in the diffusion model, and set the key of the steganographic encoder; A2: generating an initial sample using a random number generator based on a set seed performing a denoising process on the initial sample using a predictive noise network for a number of steps obtaining a Gaussian noise generated for each step a predicted denoising residual a predicted reverse diffusion sampling mean and a denoised sample ; Based on the generated Gaussian noise, the predicted denoised residual, the predicted back-diffusion sampling mean, and the denoised samples, the calculations for the first... The modification amount and masking cost when embedding simulated secret information consisting entirely of +1 and -1 are given. The masking cost is a matrix, where the elements corresponding to the wet points are... The element corresponding to the non-wet point is Pixels whose extracted secret information differs from the embedded secret information during the simulation process are considered wet pixels. According to the The modification amount and mask cost when embedding simulated secret information consisting entirely of +1 and -1 are calculated for each pixel at the 1st step. The embedding cost introduced when embedding the simulated secret information of +1 and -1 is used to encode the original secret information based on the embedding cost using a stegcode encoder, and the encoded secret information is embedded in the i-th step of the back diffusion process to finally generate a secret image. extracting secret information from the stego image.

2. The adaptive asymmetric image steganography method based on diffusion model according to claim 1, wherein, The inverse diffusion process is shown in formula (1): (1)； wherein, denoised sample predicted for the t-th step of the reverse diffusion process; predicted reverse diffusion sampling mean, sample of the t-th step of the reverse diffusion process, denoised residual obtained from the predicted noise network, sampling standard deviation of the reverse diffusion process, predicted Gaussian noise, identity matrix, variance schedule for the forward diffusion, , , k is an index.

3. The adaptive asymmetric image steganography method based on diffusion model according to claim 2, characterized in that, The generated Gaussian noise, the predicted de-noising residual, the predicted inverse diffusion sampling mean and the de-noised sample are calculated at the first The modification amount and the mask cost when embedding the analog secret information all of which are +1 and -1 include the following steps: B1 : Reverse diffusion process based on A2 using cumulative distribution function CDF to transform the Gaussian noise generated in step ;​​ (2)； wherein is the cumulative distribution function; B2: without using steganographic encoder, directly generate secret information with set image resolution size , when simulating embedding of analog secret information all being +1, record the secret information as ; B3: calculating a modification amount m embedding the secret information , calculating a modification amount m embedding the secret information (3)； wherein is a modification quantity for embedding the secret information, is the secret information, is a scaling factor; in the case of embedding a simulated secret information of all +1, the modification quantity for embedding the secret information , the secret information ; B4: modifying the cumulative distribution according to the embedded modification amount m , and then converting the modified Gaussian noise into a probability distribution through an inverse cumulative distribution function (ICDF) ; (4)； wherein is the inverse cumulative distribution function; in the simulation of the embedding of the simulated secret information all +1, Gaussian noise ; B5: The result obtained from A2 The mean of the backdiffusion sampling of the step prediction With modified Gaussian noise Add them together to get the first one. Denoising samples after embedding ; the embedded post denoised sample is represented as: (5)； wherein, in the simulation of embedding all +1's of the simulation secret information, the embedded de-noised sample ; B6: to the embedding of the samples of the first step post-embedding denoising samples the number of subsequent steps of the back diffusion process is continued , obtaining the latent image samples ; The inverse diffusion process of the denoised sample after embedding is shown in formula (6): (6)； wherein, is the predicted denoised sample after embedding the secret information in the reverse diffusion process in the tth step, is the sample in the tth step of the reverse diffusion process after embedding the secret information, is the reverse diffusion sampling mean value calculated based on the denoised sample after embedding; in the simulation of embedding the simulation secret information all as +1, the reverse diffusion sampling mean value ; B7: rounding the original image sample and the stego image sample respectively, to obtain the original image and the stego image as shown in equation (7); (7)； wherein round is a rounding function; in simulating embedding all +1s of the analog secret information, the stego image sample , stego image ; B8: based on the predicted denoised residual and generated Gaussian noise in the reverse diffusion process, respectively, the original image and the stego image are obtained. The reverse diffusion process is reversed to the first step, respectively, to obtain the restored original sample and the stego sample . The method for inverse diffusion is: (8)； wherein, is the inverse of the forward diffusion process in the first step; the stego sample ; B9: The original sample to be restored With dense sample Compared with the backdiffusion sampling mean respectively The difference between the two is used to obtain the original noise and the noise density, which are then converted into a cumulative distribution. The difference between the two is then calculated and scaled to obtain the restored embedding modification. Subsequently, the amount of embedded modification was restored. Rounding down and truncating to the interval [-1, +1] yields the extracted secret information. ; (9)； (10)； wherein is the reduced embedding modification amount; the reduced embedding modification amount when simulating the simulated secret information with an embedding of all +1 , the extracted secret information ; B10: comparing the original secret information and the extracted secret information wherein the pixel points with unequal secret information are wet points, and a mask cost in embedding the simulated secret information is calculated according to the determined wet points ; (11)； wherein, is a mask cost; in simulating embedding of analog secret information all +1, the mask cost ; B11: The modification amount of the embedding secret information when the analog secret information in which all of the analog embedding is -1 is obtained according to the method of B2 to B10 , the wet point when the analog secret information in which all of the analog embedding is -1 is determined, and the mask cost when the analog secret information in which all of the analog embedding is -1 is calculated .

4. The adaptive asymmetric image steganography method based on diffusion model according to claim 3, characterized in that, The modification amount of the step of embedding the analog secret information all of which are +1 and -1 and the mask cost are calculated. The modification amount of the step of embedding the analog secret information all of which are +1 and -1 and the mask cost are calculated. The embedding cost introduced when embedding the analog secret information of +1 and -1 in the i-th step is calculated, the original secret information is encoded by using a steganographic encoder based on the embedding cost, and the encoded secret information is embedded in the i-th step in the reverse diffusion process, and finally a stego image is generated, specifically including the following steps: C1: modification amount when embedding the analog secret information with all +1 and -1 based on simulation and the modification amount , combine the obtained mask cost when embedding the analog secret information with all +1 and -1 based on simulation and , respectively calculate the embedding cost that will be introduced by embedding +1 and -1 analog secret information at each pixel point and the embedding cost ; (12)； wherein is a tiny float; C2: generating a temporary carrier matrix n with all 0s in a set image resolution size; C3: using a steganographic encoder, embedding the original secret information g in the temporary carrier matrix n to obtain the encoded secret information s; and embedding the original secret information g in the temporary carrier matrix n to obtain the encoded secret information s; C4: Modified Gaussian noise according to secret information s is obtained according to the methods of B3 and B4 ; C5: Following the method of B5, the first inverse diffusion sample mean predicted by step plus the modified Gaussian noise to obtain the embedded de-noised sample ; C6: Denoising the embedded sample according to the method of B6 and B7 The reverse diffusion process is completed, and finally the stego image is generated and saved .

5. The adaptive asymmetric image steganography method based on diffusion model according to claim 3, characterized in that, The secret information extraction from the stego image comprises the following steps: D1 : Perform the backward diffusion process of A1 and A2 with the same diffusion model parameters, including image resolution, seed of random number generator, weights of the prediction noise network, where the step number , to generate the original image sample , and then get the original image according to the method of B7 ; D2: Read the original images respectively and received encrypted images Following the methods of B8 and B9, the reverse diffusion process is traced back to the first... Step, calculate the amount of embedded modifications to be restored. And extract secret information. ; D3: decoding the secret information s' using the steganographic encoder according to the key of the steganographic encoder to extract the transmitted secret information g'.

6. An adaptive asymmetric image steganography system based on diffusion model, for implementing the adaptive asymmetric image steganography method based on diffusion model of any one of claims 1-5, characterized in that, The method comprises: a data acquisition module configured to initialize a diffusion model and its parameter configuration, perform an inverse diffusion process on an initial sample obtained after initialization in iterations, and save generated Gaussian noise, predicted denoising residuals, predicted inverse diffusion sampling mean and denoised samples at each step until the iteration is completed; Specifically: initialize the diffusion model, set the image resolution, set the total number of reasoning steps , and the number of steps of the information to be embedded , set the seed of the random number generator, load the weights of the prediction noise network in the diffusion model, and set the key of the steganographic encoder; based on the set seed, generate an initial sample using the random number generator , and gradually denoise the initial sample using the prediction noise network to perform a reverse diffusion process , for a number of steps , to obtain the Gaussian noise generated at each step , the predicted denoising residual , the predicted reverse diffusion sampling mean , and the denoised sample ; An embedding simulation module is used to calculate the modification amount and the mask cost when embedding the simulation secret information all of which are +1 and -1, the mask cost is a matrix, the element corresponding to the wet point is , the element corresponding to the non-wet point is 0, the pixel point of the secret information extracted in the simulation process which is different from the embedded secret information is the wet point. ​ The load image generation module is configured to calculate the modification amount of each pixel point in the first step when embedding the analog secret information all of which are +1 and -1 and the mask cost, and to calculate the embedding cost introduced when embedding the analog secret information of +1 and -1 in the i th step. The load image generation module is configured to calculate the modification amount of each pixel point in the first step when embedding the analog secret information all of which are +1 and -1 and the mask cost, and to calculate the embedding cost introduced when embedding the analog secret information of +1 and -1 in the i th step. The load image generation module is configured to calculate the modification amount of each pixel point in the first step when embedding the analog secret information all of which are +1 and -1 and the mask cost, and to calculate the embedding cost introduced when embedding the analog secret information of +1 and -1 in the i th step. a secret information extraction module configured to extract secret information from the stego image.

7. An electronic device, comprising: The method comprises: one or more processors, and a memory configured to store instructions, which, when executed by the one or more processors, cause the one or more processors to perform the diffusion model-based adaptive asymmetric image steganography method of any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer program product has executable instructions stored therein, which, when executed, cause a processor to perform the diffusion model-based adaptive asymmetric image steganography method of any one of claims 1-5.

9. A computer program product, characterised in that, The computer program product has executable instructions stored therein, which, when executed, cause a processor to perform the diffusion model-based adaptive asymmetric image steganography method of any one of claims 1-5.

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