JPEG image batch steganography method and system based on experience security

Abstract

The invention discloses a JPEG image batch steganography method and system based on experience security, and belongs to the technical field of information security. The method comprises the following steps: screening batch steganography carriers from a candidate JPEG image set based on experience security; calculating a non-zero DCT coefficient feature and a cost response curve D-alpha of each batch of steganography carriers; and calculating the optimal load rate of each batch of steganography carriers based on the non-zero DCT coefficient characteristics, the cost response curve D-alpha and the length of the load message, and executing steganography of the load message according to the optimal load rate. According to the method, the security of large-batch image steganography communication under an adaptive steganography algorithm can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of information security, and in particular relates to a JPEG image batch steganography method and system based on empirical security. Background Art

[0002] Steganography is an information hiding technology that uses special encoding methods to embed secret information in digital media such as images, audio, video, and text, ensuring that the impact of the embedded information on the media is difficult to detect. Compared with watermarking technology, steganography emphasizes the imperceptibility of hidden information. Even if an outsider analyzes the steganographic multimedia file, the existence of the secret information is difficult to detect. Unlike encryption technology, steganography does not change the content of the message. Instead, it hides the message in other media for transmission to achieve the purpose of protecting secret information and even communication behavior. This allows confidential messages to be transmitted more securely and covertly on the Internet. The design of steganography algorithms generally needs to consider the following factors:

[0003] (1) Imperceptibility: The steganographic carrier should be indistinguishable from the natural carrier in terms of sensory perception, so that humans cannot determine whether it has been steganographic through vision or hearing.

[0004] (2) Security: Steganographic security generally refers to the ability of the steganographic carrier to resist steganalysis. Even if the attacker has prior knowledge of the steganographic algorithm, the existing steganalysis methods are still unable to detect or decipher the steganographic information with a sufficiently high accuracy.

[0005] (3) Embedding capacity: While ensuring the security of steganography, the amount of secret information that can be embedded in the carrier should be increased as much as possible.

[0006] (4) Embedding efficiency: When the amount of embedded information is constant, the modification of the carrier should be minimized to reduce the impact on the original data.

[0007] (5) Computational complexity: While ensuring the security of steganography, the computational complexity of the algorithm should be reduced as much as possible and the running speed should be increased to meet the actual application needs.

[0008] Steganography has evolved over the years, from traditional non-adaptive to adaptive. Traditional non-adaptive steganography methods treat all embeddable locations equally when embedding information, regardless of the content. The most classic algorithm is the Least Significant Bit Replacement (LSBR), which directly modifies the least significant bit of an image pixel. While simple to implement and highly efficient, it destroys the statistical characteristics of the image, making it susceptible to detection by steganalysis. To enhance steganalysis security, researchers have proposed steganalysis methods based on preserving statistical features. These algorithms, such as the F3 and F4 algorithms, adjust the embedding method to maintain the symmetry and monotonicity of the discrete cosine transform (DCT) coefficients of JPEG (Joint Photographic Experts Group) images. The OutGuess algorithm, on the other hand, restores the statistical distribution by reserving a compensation region, thereby better preserving first-order statistical characteristics and improving detection resistance. However, with the application of machine learning and deep learning technologies in steganalysis, non-adaptive steganography methods have exposed significant security risks, and high-dimensional feature analysis can easily detect steganographic images.

[0009] To enhance the anti-analysis capabilities of steganography methods, adaptive steganography has been proposed. The core of adaptive steganography lies in stegocost calculation and stegocoding. By measuring the impact of embedding on the image and selecting low-impact areas for information hiding through stegocoding, this significantly improves stegosecurity. STC (Syndrome-Trellis Codes) encoding has become widely used due to its excellent performance and has become the most mainstream stegocoding method. Over the past 20 years, research on stegocost functions has become relatively mature. Cost functions such as HUGO, WOW, and S-UNIWARD have been developed for spatial-domain images. However, because JPEG images are more common in practical applications and their encoding characteristics make steganography algorithms generally more secure than spatial-domain steganography at the same embedding rate, frequency-domain stegocosts, particularly those for JPEG images, have received more attention. J-UNIWARD, currently the most secure JPEG stegocost, demonstrates excellent anti-detection capabilities. UERD, while maintaining high stegosecurity, is computationally efficient and suitable for applications requiring high computational resources.

[0010] With the improvement of the confidentiality and security of steganographic communication, the application of steganographic technology is becoming more and more widespread, and the demand for steganographic communication capacity is also growing. However, since the size of images shared and circulated in daily life is usually relatively fixed, the steganographic capacity of a single image is limited. Therefore, multiple images are generally used to carry messages to meet the needs of steganographic communication with a large message volume. In the framework of adaptive steganography, stego-embedding can only minimize the embedding cost of a single image, but cannot minimize the overall steganographic cost of multiple images. Therefore, batch steganography technology has been proposed to improve the security of multi-image steganographic communication tasks. The main contents of batch steganography technology research are as follows:

[0011] (1) Carrier selection: The law revealed by adaptive steganography technology is that images with high texture complexity have higher steganographic security. Different images generally have different security. Therefore, the carrier selection method selects images with higher security as carriers to carry messages to improve the security of steganographic communication.

[0012] (2) Load rate distribution: The secure steganographic capacity of different images is inconsistent. In order to obtain the best security performance in the steganographic embedding process of multiple images, it is necessary to allocate load lengths to different images to improve the security of steganographic covert communication.

[0013] Currently, there are various methods for carrier selection and load rate distribution. However, existing batch steganography methods primarily rely on analyzing image features to indirectly measure the carrier's steganographic security. Effective methods for directly measuring the carrier's resistance to steganalysis have yet to be developed. Furthermore, current batch steganography methods primarily focus on spatial domain images, while existing algorithms have limited support for the widely used JPEG images. This hinders the practical application of steganography technology. Summary of the Invention

[0014] The present invention provides a JPEG image batch steganography method and system based on empirical security, which can improve the security of large-scale image steganography communication under an adaptive steganography algorithm.

[0015] To achieve the above objectives, the technical solution of the present invention includes the following contents.

[0016] A JPEG image batch steganography method based on empirical security, the method comprising:

[0017] Based on empirical security, a batch of steganalysis carriers is selected from a set of candidate JPEG images;

[0018] Calculate the non-zero DCT coefficient characteristics and cost response curve D-α for each batch of stego carriers; where D represents the stego distortion and α represents the load rate;

[0019] Based on the non-zero DCT coefficient characteristics, the cost response curve D-α and the length of the payload message, the optimal payload ratio of each batch of steganographic carriers is calculated, and the payload message is steganographically executed according to the optimal payload ratio.

[0020] Furthermore, the method of screening out a batch of steganographic carriers from a set of candidate JPEG images based on empirical security includes:

[0021] Calculate the non-zero DCT coefficient features and security response curve P of the candidate JPEG image E -α, P E represents the steganalysis error rate;

[0022] Based on the non-zero DCT coefficient characteristics and the security response curve P E -α, calculate the security metric of the candidate JPEG image;

[0023] Based on the security metrics of each candidate JPEG image, candidate JPEG images are selected as batch steganographic carriers.

[0024] Furthermore, the non-zero DCT coefficient features of the candidate JPEG image are calculated, including:

[0025] Count each 8×8 block of the candidate JPEG image and calculate the non-zero coefficients except the position (0,0);

[0026] The number of all non-zero coefficients of the entire candidate JPEG image is summed to obtain the non-zero DCT coefficient feature of the candidate JPEG image.

[0027] Furthermore, the security response curve P of the candidate JPEG image is calculated E -α, including:

[0028] Obtain the steganalysis error rate P by experimental fitting E Relationship with steganalytic distortion D E -D;

[0029] Perform two steganographic simulation embeddings on the candidate JPEG image at load rates α1 and α2 respectively, and record the corresponding steganographic costs D1 and D2;

[0030] Calculate the scaling factor m and the exponent n based on the load ratio α1, the load ratio α2, the steganographic cost D1, and the steganographic cost D2;

[0031] According to the scaling factor m and the exponent n, the relationship D-α between the steganographic distortion D and the load rate α of the candidate JPEG image is obtained;

[0032] According to the relationship P E-D and the relationship D-α to obtain the security response curve P of the candidate JPEG image E -α.

[0033] Further, based on the non-zero DCT coefficient feature and the security response curve P E -α, obtain the security metric of the candidate JPEG image, including:

[0034] Calculate the maximum descent rate of the security response curve P<000001o>-α;

[0035] Divide the maximum descent rate by the non-zero DCT coefficient feature of the candidate JPEG image to obtain the security metric of the candidate JPEG image.

[0036] Further, based on the non-zero DCT coefficient feature, the security response curve P E -α and the length of the payload message, calculate the optimal payload rate of each batch of stego carriers, including:

[0037] Initialize the lower bound λ of the Lagrange multiplier λ floor and the upper bound λ ceiling ;

[0038] According to the lower bound λ floor and the upper bound λ ceiling , calculate the midpoint λ of the upper and lower bounds of the Lagrange multiplier λ middle ;

[0039] Calculate the payload rate of the i-th batch of stego carriers where ω i is the non-zero DCT coefficient feature of the i-th batch of stego carriers, m i and n i are the scaling coefficient and exponent in the relationship D-α between the steganographic distortion D and the payload rate α corresponding to the i-th batch of stego carriers respectively;

[0040] According to the payload rate α i and the non-zero DCT coefficient feature ω i , obtain the capacity M of the i-th batch of stego carriers i ;

[0041] Sum the capacities M of the batch of stego carriers i to obtain the total capacity M0 of all batches of stego carriers;

[0042] Compare the total capacity M0 with the length M of the payload message;

[0043] In the case of M0 < M, let the lower bound λ floor = λ middle , and re-execute the above-mentioned according to the lower bound λ floorand upper bound λ ceiling , calculate the midpoint λ between the upper and lower bounds of the Lagrange multiplier λ middle ;

[0044] In the case of M0>M+Δm, let the upper bound λ ceiling =λ middle , and re-execute the lower bound λ floor and upper bound λ ceiling , calculate the midpoint λ between the upper and lower bounds of the Lagrange multiplier λ middle ; Where ΔM represents the redundancy factor;

[0045] In the case of M≤M0≤M+ΔM, the load factor α i as the optimal load ratio of the i-th batch of steganalytic carriers.

[0046] Furthermore, when initializing the Lagrange multiplier λ, the lower bound λ floor =0, the upper bound λ ceiling =max(m i n i / ω i ).

[0047] A JPEG image batch steganography system based on empirical security, the system comprising:

[0048] A carrier selection module is used to select a batch of steganographic carriers from a set of candidate JPEG images based on empirical security;

[0049] A calculation module is used to calculate the non-zero DCT coefficient characteristics and cost response curve D-α of each batch of stego carriers; where D represents the stego distortion and α represents the load rate;

[0050] The load rate allocation module is used to calculate the optimal load rate of each batch of steganographic carriers based on the non-zero DCT coefficient characteristics, the cost response curve D-α and the length of the load message, and perform steganography of the load message according to the optimal load rate.

[0051] An electronic device, characterized in that the electronic device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements any of the above-mentioned empirical security-based JPEG image batch steganography methods.

[0052] A computer-readable storage medium, characterized in that computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are executed by a processor, any of the above-mentioned empirical security-based JPEG image batch steganography methods is implemented.

[0053] Compared with the prior art, the present invention has at least the following beneficial effects.

[0054] (1) Improved the security of steganographic communication. This method introduces a security response curve to achieve quantitative security evaluation of images at different load rates, and adopts an optimal load rate allocation strategy to allocate load rates based on the security capacity of different images, thereby reducing the risk of detection in steganographic communication. Compared with traditional average load rate embedding methods or empirical methods, the method of the present invention can effectively improve steganographic security and enhance the overall security of steganographic communication;

[0055] (2) It has high computational efficiency. This method improves the computational efficiency of batch steganography tasks while optimizing the security of batch steganography. Compared with the traditional random selection and average embedding methods, this method significantly improves the security of steganography. Compared with the existing optimal batch steganography method IMS, this method quickly iterates and approaches the optimal solution through binary search, avoiding the large amount of computational overhead caused by exhaustive search, and has high computational efficiency;

[0056] (3) Improved the diversity of carrier selection strategies. This method directly measures the security of the carrier from the perspective of empirical security for the first time. By calculating the rate of decline of the security response curve, it can screen out images with stronger resistance to steganalysis. Compared with traditional indirect measurements of carrier security such as image texture complexity, non-zero DCT coefficient distribution and other statistical features, this method is more direct and can better reflect the performance of the image in actual steganalysis. The new carrier selection method based on empirical security designed in this invention further enriches the diversity of carrier selection strategies and provides more options for actual batch steganography research and steganalysis covert communication users. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the JPEG image batch steganography method based on empirical security of the present invention.

[0058] Figure 2 It is a flow chart of the batch steganographic carrier screening of the present invention.

[0059] Figure 3 Schematic diagram of the load rate distribution method of the present invention DETAILED DESCRIPTION

[0060] The modulation method of the present invention is further described below through specific embodiments so that those skilled in the art can have a more thorough understanding of the features and advantages of the present invention.

[0061] The present invention's JPEG image batch steganography method based on empirical security is as follows: Figure 1 As shown, the following steps 1 to 3 are included.

[0062] Step 1: Based on empirical security, a batch of steganalysis carriers is screened from the candidate JPEG image set.

[0063] The vector selection process of the present invention is as follows Figure 2 As shown, the following steps are included from step 1.1 to step 1.4.

[0064] Step 1.1: Extract the non-zero DCT coefficient features of all images separately.

[0065] The present invention counts each 8×8 block of a JPEG image, calculates the number of non-zero coefficients except the (0,0) position, and sums all the non-zero AC coefficients of the entire image to obtain the non-zero DCT coefficient feature of the image, which is used to measure the image's ability to carry steganographic information.

[0066] Step 1.2: Calculate the safety response curves for all images separately.

[0067] The safety response curve P of the present invention E -α can characterize the security trend of the image under different load rates, which is the relationship between the analyzer error rate and the steganographic distortion P E -D and the relationship between steganographic distortion and load ratio D-α are derived.

[0068] Among them, P E The relationship between P and D is obtained by experimental fitting. E is the steganalysis error rate of each group of samples, D is the average steganalysis cost of each group of samples, and the experiment shows that the relationship is P E =ae bD +c. The above relationship is related to the dataset, image quality factor, steganalysis cost and steganalyzer. Table 1 shows the P of different variable combinations. E -D relationship curve parameters, after generalization experiments, the above factors have little impact on the safety of the selection results, and the generalization ability of the experimental parameters is strong. E -D relationship parameters use the highest security group: a = 0.47, b = 0.02, c = 0.04, that is, P E =0.47e 0.02D +0.04.

[0069] Table 1P E -D relationship curve parameters

[0070]

[0071] The D-α relationship of each image is quickly calculated as follows:

[0072] Sample generation: Perform two steganographic simulation embeddings on the image at different load rates, and record the corresponding load rates and steganographic costs (α1, D1) and (α2, D2);

[0073] Parameter calculation: Substituting the above sample points into the following formula can quickly calculate the D-α relationship of the image D = mα n , where m is the scaling factor and n is the exponent.

[0074]

[0075] Therefore, P E The relationship between -D and the relationship between D-α gives P E -α relational expression:

[0076] Step 1.3: Calculate all image steganographic security metrics separately.

[0077] The present invention adopts the method of optimizing the number of non-zero AC coefficients of the image E The lowest point of the first-order derivative of the -α relationship measures image security, and the calculation expression is:

[0078]

[0079] Where ω is the number of non-zero AC coefficients for each image, and its metric is calculated for each candidate image.

[0080] Step 1.4: Sort by metric value in descending order and select the first k images as carriers.

[0081] The present invention sorts images in descending order according to their security metrics, prioritizing images with larger metrics as steganalysis carriers. These images experience a slower rate of security degradation under steganalysis, which can more effectively improve steganalysis security.

[0082] Step 2: Calculate the non-zero DCT coefficient features and cost response curve D-α of each batch of stego carriers.

[0083] The batch steganography process for JPEG images involves the non-zero DCT coefficient characteristics and cost response curve D-α of the batch steganographic carrier. The calculation methods of the non-zero DCT coefficient characteristics and cost response curve D-α are described in steps 1.1 and 1.2, respectively.

[0084] Step 3: Based on the non-zero DCT coefficient characteristics, the cost response curve D-α and the length of the payload message, the optimal payload ratio of each batch of steganographic carriers is calculated, and the payload message is steganographically executed according to the optimal payload ratio.

[0085] This step provides a fast load rate allocation method based on minimizing the total distortion cost of batch steganography for JPEG images. The principle is to minimize the overall steganographic distortion under the premise of satisfying the message embedding length constraint. The specific mathematical expression is as follows: The embedded message length is equal to the sum of all image payload messages.

[0086] The steganalytic distortion of each image can be described by the D-α curve of the image. The optimal load rate distribution method is solved by the Lagrange multiplier method. The cost load response curve of each image is D=mα n The first-order derivative of is equal to the number of its non-zero DCT coefficients, that is:

[0087]

[0088] The overall steganographic cost can be minimized, expressed as λ = mnα n-1 / ω. Where λ is the Lagrange multiplier and ω is the number of non-zero DCT coefficients of the image. Therefore, the steganographic embedding load rate of each image is α i The relationship with λ is: (i=1,2,…,k), the load rate vector α of k images can be searched by enumerating the value of λ.

[0089] Specifically, if Figure 3 As shown, the load rate distribution process includes the following steps 3.1 to 3.3.

[0090] Step 3.1: Initialize the lower bound of the binary search: Initialize the lower bound of the Lagrange multiplier λ to λ floor =0, the upper bound is the maximum value of (mn) / ω for all images: λ ceiling =max(m i n i / ω i ).

[0091] Step 3.2: Calculate the midpoint value: The midpoint value is the midpoint of the upper and lower bounds: λ = (λ floor +λ ceiling ) / 2.

[0092] Step 3.3: Load ratio distribution: For each image, substitute λ into the formula The load rate of the image can be calculated.

[0093] (1) Calculate the current capacity: multiply the load rate of each image calculated in step 3.3 by the image non-zero AC coefficient eigenvalue extracted in step 2 to obtain the current capacity of each image. The sum of the two values ​​can be used to obtain the total capacity M0 of all images under the current allocation strategy.

[0094] (2) Capacity discrimination: Compare the current total capacity M0 with the expected load message length M to determine whether the optimal allocation result is found. To control the number of iterations of the algorithm, a redundancy factor ΔM is set. If the current total capacity is greater than M and less than M + ΔM, it is considered that the optimal solution is found and the loop is terminated prematurely. By setting the value of ΔM, the running speed of the algorithm can be controlled. Generally, ΔM is set to the number of images k of the load rate to be allocated, that is, at most 1 bit of message can be embedded in each image on average. The following describes the possible situations in discrimination and the corresponding processing methods:

[0095] (2.1) M0 < M: It means that the message capacity is insufficient. Let λ floor = λ, and return to step 3.2;

[0096] (2.2) M ≤ M0 ≤ M + ΔM: It means that the message capacity is sufficient and the optimal allocation scheme is found. End the loop and output the allocation load rate of each current image;

[0097] (2.3) M0 > M + ΔM: It means that the message capacity is too large and it is not the optimal solution. Let λ ceiling = λ, and return to step 3.2.

[0098] In summary, the carrier selection method of the present invention mathematically models the relationship between the steganalysis detector error rate and the image load rate, and uses this mathematical model to directly measure the security level of the image to select images with high security. The load rate allocation method mathematically models the relationship between steganographic distortion and the image load rate, and provides a fast load rate allocation calculation method based on this model. This batch steganography method can be applied to the adaptive steganography algorithm of various JPEG images, and can effectively improve the security of the batch steganography task. Compared with other carrier selection methods, the present invention first constructs a carrier selection method for the direct measurement of the image anti-steganalysis ability, and selects images with a slower decline rate of the steganalysis detector error rate as the carrier as the load rate increases according to the relationship model between the steganalysis detector rate and the image load rate. Compared with other load rate allocation methods, the present invention can quickly calculate the steganographic distortion-load rate relationship curve of each image, and optimize the search efficiency of the load rate allocation method by the bisection method, with high security and calculation efficiency.

[0099] This paper mathematically models the relationship between steganalyzer error rate and steganalyzer distortion, image load ratio, and steganalyzer error rate. Furthermore, based on the relationships between steganalyzer error rate and steganalyzer distortion, and steganalyzer distortion and load ratio, a relational expression for the steganalyzer error rate and steganalyzer load ratio is derived. Based on this, a steganalyzer security metric is proposed, and a quantitative security-based JPEG image carrier selection method is constructed based on this. Furthermore, based on the mathematical relationship between steganalyzer distortion and embedding ratio, the batch steganalysis security problem is transformed into a batch steganalysis embedding distortion cost minimization problem under the constraint of total payload message length. This problem is solved using the Lagrange multiplier method, and an analytical expression for the optimal batch steganalysis is derived. Furthermore, the monotonic relationship between the Lagrange multiplier and the steganalyzer capacity of a batch of images is analyzed. A binary search solution for the optimal load ratio allocation scheme is then constructed. The number of iterations of the binary search algorithm can be adjusted by setting a redundancy factor, enabling adjustments to the computational speed and the algorithm's security against steganalysis, enhancing the algorithm's application flexibility.

[0100] The above examples are only used to illustrate the technical solutions of the present invention rather than to limit the same. Those skilled in the art may modify or make equivalent substitutions for the technical solutions of the present invention without departing from the spirit and scope of the present invention. The scope of protection of the present invention shall be based on the claims.

Claims

1. A JPEG image batch steganography method based on empirical security, characterized in that: The method comprises: Based on empirical security, a batch of steganalysis carriers is selected from a set of candidate JPEG images; Calculate the non-zero DCT coefficient characteristics and cost response curve D-α for each batch of stego carriers; where D represents the stego distortion and α represents the load rate; Based on the non-zero DCT coefficient characteristics, the cost response curve D-α and the length of the payload message, the optimal payload ratio of each batch of steganographic carriers is calculated, and the payload message is steganographically executed according to the optimal payload ratio.

2. The method according to claim 1, characterized in that The method of screening out a batch of steganographic carriers from a set of candidate JPEG images based on empirical security includes: Calculate the non-zero DCT coefficient features and security response curve P of the candidate JPEG image E -α, P E represents the steganalysis error rate; Based on the non-zero DCT coefficient characteristics and the security response curve P E -α, calculate the security metric of the candidate JPEG image; Based on the security metrics of each candidate JPEG image, candidate JPEG images are selected as batch steganographic carriers.

3. The method according to claim 2, characterized in that Calculate the non-zero DCT coefficient features of the candidate JPEG image, including: Count each 8×8 block of the candidate JPEG image and calculate the non-zero coefficients except the position (0,0); The number of all non-zero coefficients of the entire candidate JPEG image is summed to obtain the non-zero DCT coefficient feature of the candidate JPEG image.

4. The method according to claim 2, characterized in that Calculate the security response curve P of the candidate JPEG image E -α, including: Obtain the steganalysis error rate P by experimental fitting E Relationship with steganalytic distortion D E -D; Perform two steganographic simulation embeddings on the candidate JPEG image at load rates α1 and α2 respectively, and record the corresponding steganographic costs D1 and D2; Calculate the scaling factor m and the exponent n based on the load ratio α1, the load ratio α2, the steganographic cost D1, and the steganographic cost D2; According to the scaling factor m and the exponent n, the relationship D-α between the steganographic distortion D and the load rate α of the candidate JPEG image is obtained; According to the relationship P E -D and the relationship D-α, the security response curve P of the candidate JPEG image is obtained E -α.

5. The method according to claim 2, characterized in that Based on the non-zero DCT coefficient characteristics and the security response curve P E -α, obtain the security metrics of the candidate JPEG image, including: Calculate the safety response curve P E -The maximum rate of descent of α; The maximum degradation rate is divided by the non-zero DCT coefficient feature of the candidate JPEG image to obtain a security metric of the candidate JPEG image.

6. The method according to claim 1, characterized in that Based on the non-zero DCT coefficient characteristics, the security response curve P E -α and the length of the payload message, calculate the optimal payload rate for each batch of steganographic carriers, including: Initialize the lower bound λ of the Lagrange multiplier λ floor and upper bound λ ceiling ; According to the lower bound λ floor and upper bound λ ceiling , calculate the midpoint λ between the upper and lower bounds of the Lagrange multiplier λ middle ; Calculate the load rate of the i-th batch of steganographic carriers Among them, ω i is the non-zero DCT coefficient feature of the i-th batch of steganographic carriers, m i and n i are the scaling coefficient and exponent in the relationship D-α between the steganalysis distortion D and the load rate α corresponding to the i-th batch of steganalysis carriers; According to the load rate α i and the non-zero DCT coefficient characteristic ω i , get the capacity M of the i-th batch of steganographic carriers i ; The capacity M of the batch stegoscopy carrier i Sum up and get the total capacity M0 of all batches of steganographic carriers; Comparing the total capacity M0 with the length M of the load message; When M0 < M, let the lower bound be λ floor = λ middle , and re - execute the calculation of the mid - point λ floor of the upper and lower bounds of the Lagrange multiplier λ based on the lower bound λ ceiling and the upper bound λ middle ; In the case of M0>M+ΔM, let the upper bound λ ceiling =λ middle , and re-execute the lower bound λ floor and upper bound λ ceiling , calculate the midpoint λ between the upper and lower bounds of the Lagrange multiplier λ middle ; Where ΔM represents the redundancy factor; In the case of M≤M0≤M+ΔM, the load factor α i as the optimal load ratio of the i-th batch of steganalytic carriers.

7. The method according to claim 6, characterized in that When initializing the Lagrange multiplier λ, the lower bound λ floor =0, the upper bound λ ceiling =max(m i n i / ω i ).

8. A JPEG image batch steganography system based on empirical security, characterized in that: The system comprises: A carrier selection module is used to select a batch of steganographic carriers from a set of candidate JPEG images based on empirical security; A calculation module is used to calculate the non-zero DCT coefficient characteristics and cost response curve D-α of each batch of stego carriers; where D represents the stego distortion and α represents the load rate; The load rate allocation module is used to calculate the optimal load rate of each batch of steganographic carriers based on the non-zero DCT coefficient characteristics, the cost response curve D-α and the length of the load message, and perform steganography of the load message according to the optimal load rate.

9. An electronic device, characterized in that: The electronic device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, the JPEG image batch steganography method based on empirical security according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer program instructions, which, when executed by a processor, implement the JPEG image batch steganography method based on empirical security according to any one of claims 1 to 7.

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