A pixel cost reassignment algorithm based on artificial immune system

Abstract

This invention discloses a pixel cost redistribution algorithm based on an artificial immune system for digital image information hiding. Under a model minimizing additive distortion, the algorithm adjusts the pixel modification probability distribution obtained from a given cost function and constructs an immune information hiding model to dynamically optimize the adjustment method of the pixel modification probability distribution, thereby rationally redistributing the modification cost. This concentrates modified pixels in areas of the carrier image that are difficult to detect. The method is applicable to various advanced cost functions, overcomes the problem that existing heuristic adaptive steganography algorithms, which rely heavily on empirical design, struggle to achieve optimal security, and can improve the security of state-of-the-art spatial image steganography algorithms, demonstrating practical value.

Description

Technical Field

[0001] This invention relates to the field of digital image information hiding technology, and in particular to an image adaptive steganography algorithm based on a minimal distortion steganography framework, which minimizes overall distortion while embedding secret information, thereby ensuring the undetectability of the coded image on the carrier. Background Technology

[0002] With the development of computer science and technology, digital multimedia technology has become increasingly mature. While bringing convenience to life, it also presents various security risks, such as the illegal alteration and theft of information. Therefore, ensuring the security of information transmission in communication channels is currently a hot research topic in the field of network security. Steganography, an important branch of information hiding, is of great significance to network security. Image adaptive steganography, as the most secure steganography scheme currently available, can be described as a source coding problem that minimizes embedding distortion. Considering the simplicity of cost function design, current research is usually based on a simplified additive distortion model.

[0003] Current adaptive steganography research can be divided into three categories: distortion minimization steganography schemes, model-based steganography schemes, and neural network-based steganography schemes. Among them, adaptive steganography algorithms based on distortion minimization steganography select appropriate pixels for modification by defining the modification cost of a single carrier element, as illustrated in references: 1. "Universal distortion function for steganography in an arbitrary domain", EURASIP J.Inf.Secur., vol. 2014, no. 1, pp. 1-13, Jan. 2014; 2. "Designing steganographic distortion using directional filters", in Proc. 4th IEEE Int. Workshop Inf. ForensicsSecurity, Costa Adeje, ESP, 2012, pp. 234-239; 3. "A new cost function for spatial image steganography", in Proc. IEEE Int.Conf.Image. Process. (ICIP), Paris, FR, 2014, pp. 4206-4210. Most of these algorithms are heuristic, heavily reliant on empirical design and thus lacking optimal security. Model-based steganography algorithms utilize mathematical models to model the carrier and the steganographic image, transforming steganography into a mathematical optimization problem, such as in reference 4, "Content-adaptive steganography by minimizing statistical detectability," IEEE Trans. Inf. Forensics Security, vol. 11, no. 2, pp. 221-234, Feb. 2016. The security of these algorithms depends on the rationality of the established mathematical model; however, natural images are often difficult to characterize with precise mathematical models, thus limiting the security of these algorithms. Neural network-based steganography algorithms typically have high security, such as in reference 5, "An embedding cost learning framework using GAN," IEEE Trans. Inf. Forensics. Security, vol.15, no.99, pp.839-851, Jun.2020. However, the security of such steganography algorithms largely depends on the training set and generally lacks generalization ability. Furthermore, the black-box structure of neural networks makes them uninterpretable. Therefore, such algorithms still have certain limitations.Artificial immune system is an intelligent method that mimics biological immune mechanisms and has self-learning, self-organizing, and adaptive characteristics. This invention proposes a pixel cost redistribution algorithm based on artificial immune system to further improve the security of the basic steganography algorithm. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned limitations and provide a pixel cost redistribution algorithm based on an artificial immune system. This algorithm can adjust the modification probability distribution obtained by the basic steganography algorithm to redistribute the modification cost of each pixel, and dynamically optimize the adjustment method of the modification probability distribution based on the immune information hiding model, so that the modification points are more concentrated in the hard-to-detect areas of the carrier image, thereby further improving the security of the basic steganography algorithm.

[0005] The technical solution for achieving the objective of this invention is as follows:

[0006] A pixel cost redistribution algorithm based on an artificial immune system is proposed for digital image information hiding processing. It searches for ways to adjust the pixel modification probability distribution obtained from the basic steganography algorithm based on the artificial immune system, thereby redistributing the modification cost of each pixel and further improving the security of the steganography algorithm. The steganography process includes: firstly, processing the carrier image... The modified cost matrix of the carrier image is obtained based on the cost function to be optimized. ρ ij ∈[0,+∞), x ij Let ∈{0,1,...,255} represent pixel values, n1 and n2 be the length and width of the image, respectively, and obtain the modification probability matrix of the carrier image X under optimal embedding simulation. A new modified probability distribution is obtained by transforming P based on the optimal antibody. Then flip it back into a cost matrix. Based on the cost matrix ρ', secret information is embedded into the carrier image X under optimal embedding simulation to obtain a target secret image with high security.

[0007] (1) The specific transformation form of the modified probability matrix P is as follows:

[0008] first step

[0009]

[0010] Step 2

[0011]

[0012] Where, p ij For pixels x ij The original modification probability, p', obtained under a specific basic steganography algorithm.ij and p” ij The original modification probability p ij The modification probability p obtained after the first and second steps of transformation ij ,p' ij ,p” ij ∈[0,1], max(·) represents taking the maximum value;

[0013] (2) Parameter α Ab_opt ,β Ab_opt γ Ab_opt δ Ab_opt Combination (α) Ab_opt ,β Ab_opt ,γ Ab_opt ,δ Ab_opt α represents the specific value of the optimal antibody, obtained through dynamic search based on the artificial immune system. Ab_opt ∈[0,1], β Ab_opt ∈[0,10], γ Ab_opt ∈[0,10], δ Ab_opt ∈[0,1 / 3]; The process of immune dynamic optimization is as follows: first, initialize the antibody population Population={Ab ∈[0,1 / 3] according to the set antibody size. i |i=0,1,...,Pop_scale}, where Pop_scale is the antibody size, Ab i =(α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Let be the i-th antibody in the antibody population; initialize the antibody population (Population); then calculate the fitness of each antibody, antibody Ab. i Fitness is calculated as follows:

[0014]

[0015] in, Num represents the fitness of the i-th antibody. cov X represents the number of carrier images. k For the k-th carrier image, For carrier image X k Based on antibody Ab i The resulting corresponding encrypted image, where the modification probability matrix is ​​based on antibody Ab. i The transformation form is:

[0016]

[0017]

[0018] and These are the carrier image X k and encrypted images The SPAM feature matrix is ​​calculated as follows:

[0019]

[0020] Here, SPAM(·) represents extracting SPAM features from the image; the antibody with the highest fitness is selected for cloning based on both the number of antibody selections and the number of antibody clones; then, for each selected antibody, a random mutation method is used to search for better antibodies in its surrounding clonal antibody set, and the antibody with the best fitness from each derived clonal antibody set is selected to add to the new antibody group to achieve the search and retention of the optimal embedding mode; finally, the remaining antibodies are randomly generated and added to the new antibody group to form a new generation of antibody group; and the subsequent iteration process is performed sequentially. When the maximum number of iterations is reached and the optimal antibody is obtained, the search process terminates; the optimal antibody (α) Ab_opt ,β Ab_opt ,γ Ab_opt ,δ Ab_opt The original modified probability distribution P is transformed using the final parameter value in the two-step transformation.

[0021] This invention adjusts the modification probabilities obtained from the basic steganography algorithm within a two-step transformation framework, and dynamically optimizes the adjustment method of the modification probability distribution based on an artificial immune system to achieve pixel cost redistribution. Compared with existing image adaptive steganography algorithms, the gain effect of this invention is that it can improve the performance of the basic steganography algorithm against various steganalysis methods without depending on the dataset, and it is applicable to various existing cost functions, thus having strong practicality. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the basic steganography process in an embodiment of the present invention.

[0023] Figure 2 This is a flowchart illustrating the optimal antibody search process in an embodiment of the present invention.

[0024] Figure 3 This is a flowchart illustrating the antibody fitness calculation process in an embodiment of the present invention.

[0025] Figure 4 This is a histogram showing the probability of modification by the steganography algorithm in an embodiment of the present invention.

[0026] Figure 4 (a) A carrier image selected for an embodiment of the present invention.

[0027] Figure 4(b) is the histogram of modification probabilities obtained by the HILL algorithm at an embedding rate of 0.4 bpp.

[0028] Figure 4 (c) is the histogram of the modified probabilities obtained after the first step of the transformation from the original modified probabilities.

[0029] Figure 4 (d) is the histogram of the modified probabilities obtained after the second step of transformation of the original modified probabilities.

[0030] Figure 5 This is an illustration of the embedding effect in an embodiment of the present invention.

[0031] Figure 5 (a) is the final modification probability map of the carrier image based on the embodiments of the present invention with an embedding rate of 0.4 bpp.

[0032] Figure 5 (b) is a modified pixel map of the carrier image obtained based on the embodiments of the present invention.

[0033] Figure 5 (c) is the final encrypted image obtained in the embodiment of the present invention.

[0034] Figure 6 This section compares the experimental results of the embodiments of the present invention with those of existing methods under SRM and SPAM detection.

[0035] Figure 7 This section compares the experimental results of the embodiments of the present invention with those of existing methods under Zhu-Net detection. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0037] Combined with the appendix representing the main process of this invention Figure 1 As can be seen, firstly, the modification cost matrix ρ of the carrier image X is obtained based on the cost function to be optimized, and then the modification probability matrix P of the carrier image X is obtained under optimal embedding simulation. After transforming P based on the optimal antibody, a new modification probability distribution P' is obtained. Then, it is flipped back to the cost matrix ρ'. Based on the cost matrix ρ', secret information is embedded into the carrier image X under optimal embedding simulation to obtain a highly secure secret image Y. The specific transformation form of the modification probability matrix P is as follows:

[0038]

[0039]

[0040] Where, p ij For pixels x ij The original modification probability, p', obtained under a specific basic steganography algorithm.ij and p” ij The original modification probability p ij The modification probability obtained after the first and second steps of transformation, max(·) represents taking the maximum value, and the parameter α Ab_opt ,β Ab_opt γ Ab_opt δ Ab_opt Combination (α) Ab_opt ,β Ab_opt ,γ Ab_opt ,δ Ab_opt The optimal antibody is the key parameter in the transformation process. Different values ​​of the parameter will lead to different transformation effects, thus determining the security of the steganography algorithm.

[0041] The first step is a linear transformation, the purpose of which is to compress the original modification probability interval [0, max(P)] into a smaller range [0, δ]. Ab_opt Within this range, to ensure that the total number of modified pixels in the carrier image does not increase significantly after subsequent transformation steps. The second transformation is a piecewise gamma transform, the core idea of ​​which is to transform the carrier image... Each pixel is divided into a set A = {x} based on its modification probability value, with pixels having a lower modification probability value. ij |p ij ≤δ Ab_opt ·α Ab_opt} and the set of pixels B = {x} with a larger probability of modification. ij |p ij >δ Ab_opt ·α Ab_opt Let A∪B=X. Two gamma transforms are applied to the modification probabilities of pixels in sets A and B respectively, thereby decreasing the modification probability of pixels in set A and increasing the modification probability of pixels in set B. The four parameters involved in the two-step transform each have their own role and influence each other. Among them, parameter δ... Ab_opt The parameter α determines the degree to which the interval of the modification probability is compressed after the first linear transformation. Ab_opt The parameter β determines the boundary point between pixel sets A and B in the second step of the gamma transform. Ab_opt The parameter γ determines the degree to which the modification probability value of each pixel in set A decreases. Ab_opt This determines the extent to which the modification probability value of each pixel in set B increases.

[0042] This invention utilizes the optimal antibody in the transformation process of the modified probability matrix P, and dynamically searches for the specific value of the optimal antibody based on the artificial immune system. Through... Figure 2 The main process of immune dynamic optimization can be seen. First, the antibody population Population = {Ab} is initialized according to the set antibody size. i|i=0,1,...,Pop_scale}, where Pop_scale is the antibody size, Ab i =(α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Let be the i-th antibody in the antibody population. Initializing the antibody population (Population) involves initializing the antibodies within it. i The method is to respectively treat α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Take a random value. Then calculate the fitness of each antibody. i Fitness is calculated as follows:

[0043]

[0044] in, Num represents the fitness of the i-th antibody. cov X represents the number of carrier images. k For the k-th carrier image, For carrier image X k Based on antibody Ab i The resulting corresponding encrypted image, where the modification probability matrix is ​​based on antibody Ab. i The transformation form is:

[0045]

[0046]

[0047] and These are the carrier image X k and encrypted images The SPAM (Subtractive Pixel Adjacency Matrix) feature matrix is ​​calculated as follows:

[0048]

[0049] Here, SPAM(·) represents the extraction of SPAM features from the image. Higher antibody fitness indicates a closer similarity between the vector and the corresponding SPAM features of the embedded image, resulting in higher security of the steganography algorithm and a superior antibody. To retain antibodies with high security corresponding to the embedded image, the antibodies with the highest fitness are selected and cloned based on both the number of antibodies chosen and the number of antibody clones. Then, for each selected antibody, a random mutation method is used to search for better antibodies in its surrounding area. The antibody with the best fitness from each derived clone is selected and added to the new antibody group to achieve the search and retention of the optimal embedding method. Finally, the remaining antibodies are randomly generated and added to the new antibody group, forming a new generation of antibody groups, thus ensuring the richness of the antibody group. Subsequent iterations are then performed sequentially. The search process terminates when the maximum number of iterations is reached, thus achieving heuristic searching for better antibodies in the correct direction and around the better antibodies. The optimal antibody (α) obtained through artificial immunization is... Ab_opt ,β Ab_opt ,γ Ab_opt ,δ Ab_opt The original modified probability distribution P will be transformed using the final parameter values ​​in the two-step transformation.

[0050] This invention performs a two-step transformation on the modification probability obtained from the basic steganography algorithm to optimize its distribution. Based on the correlation between the artificial immune system and the steganography problem, the adjustment method of the modification probability is used as an antibody, and the steganography algorithm security corresponding to the antibody is used as the antibody fitness. By constructing an immune information hiding model, a better antibody is searched in the correct direction and around the better antibody, so as to dynamically optimize the pixel modification probability distribution and thus improve the security of the steganography algorithm.

[0051] Example

[0052] Combination Figure 1 Figure 2 Figure 3 This embodiment includes the following steps:

[0053] S1: The basic steganography process in this example is as follows: Figure 1 As shown, the modification cost matrix ρ of the carrier image X is obtained based on the cost function to be optimized (taking the HILL algorithm as an example), and the modification probability matrix P of the carrier image X is obtained under optimal embedding simulation.

[0054] S2: Based on the following two-step transformation framework, the modification probability matrix of the carrier image X is transformed to obtain a new probability matrix P”:

[0055]

[0056]

[0057] Where, p ij For pixels x ij The original modification probability, p', obtained under a specific basic steganography algorithm. ij and p” ij The original modification probability p ij The modification probability obtained after the first and second steps of transformation, max(·) represents taking the maximum value. Figure 4 This illustrates the pixel modification probability histogram obtained after the above two transformations in this embodiment. Parameter α Ab_opt ,β Ab_opt γ Ab_opt δ Ab_opt Combination (α) Ab_opt ,β Ab_opt ,γ Ab_opt ,σ Ab_opt The optimal antibody is the key parameter in the transformation process. This invention constructs an immune information hiding model and searches for its value. The search process is as follows: Figure 2 As shown, the specific steps to obtain its value are as follows:

[0058] S2.1: Construct an artificial immune model and initialize various parameters, including antibody size, number of antibody selections, number of antibody clones, and maximum number of iterations. The antibody size is the total number of antibodies in the initial antibody swarm. The number of antibody selections determines the number of antibodies with the highest fitness retained in each round of the search. The number of antibody clones determines the number of clones to be created for each selected antibody.

[0059] S2.2: First, initialize the antibody population Population = {Ab} according to the set antibody size. i |i=0,1,...,Pop_scale}, where Pop_scale is the antibody size, Ab i =(α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Let be the i-th antibody in the antibody population. Initializing the antibody population (Population) involves initializing the antibodies within it. i The method is to respectively treat α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Get a random value.

[0060] S2.3: Calculate the fitness of each antibody Abi The calculation process is as follows: Figure 3 As shown, the specific calculation steps are as follows:

[0061] S2.3.1: Randomly select Num from the BOSSbase ver.1.01 dataset. cov Image carrier

[0062] S2.3.2: For the selected carrier images The cost matrix of each carrier image was calculated based on the HILL steganography algorithm under the embedding rate ER.

[0063] S2.3.3: Utilizing the optimal embedding simulator and the image cost matrix of each carrier The modification probability matrix of each carrier image was calculated.

[0064] S2.3.4: Based on antibody Ab i The modification probability matrices of each carrier image are subjected to linear and gamma transformations respectively to obtain the transformed modification probability matrices. Based on antibody Ab i The transformation form of the modified probability matrix is ​​as follows:

[0065]

[0066]

[0067] S2.3.5: Modify the probability matrix Re-flip it to the cost matrix in the following way To achieve pixel modification cost redistribution:

[0068]

[0069] S2.3.6: Based on the image cost matrix of each carrier The corresponding encrypted image obtained under optimal embedding simulation

[0070] S2.3.7: Extract the X images of each carrier separately. k and corresponding encrypted images SPAM characteristics and And calculate the Euclidean distance between the two, antibody Ab i =(α Ab_i ,β Ab_i ,γ Ab_i ,δ Ab_i Fitness is calculated as follows:

[0071]

[0072] S2.4: Select several antibodies with the highest fitness based on the number of antibody selections and clone them.

[0073] S2.5: Clone the selected antibodies according to the number of antibody clones to obtain a collection of cloned antibodies.

[0074] S2.6: For each set of cloned antibodies derived from the selected antibody, use random mutation to search for more antibody values ​​around its value.

[0075] S2.7: Calculate the fitness of the clonal antibodies and select the antibody with the best fitness from each derived clonal antibody set to add to the new antibody group.

[0076] S2.8: Randomly generate the remaining number of antibodies and add them to the new antibody population to form a new generation of antibodies. The search process terminates after reaching the maximum number of iterations, and the optimal antibody (α) obtained through the artificial immune system is output. Ab_opt ,β Ab_opt ,γ Ab_opt ,σ Ab_opt This is the optimal way to adjust and modify the probability distribution.

[0077] S3: Based on the optimal antibody (α) Ab_opt ,β Ab_opt ,γ Ab_opt ,σ Ab_opt The obtained probability matrix P” is flipped back into a cost matrix ρ'. Based on the cost matrix ρ', secret information is embedded into the carrier image under optimal embedding simulation to obtain the secret-carrying image Y. The modified probability map, modified pixel map, and secret-carrying image obtained in this embodiment are as follows: Figure 5 As shown.

[0078] In this embodiment, the antibody size is set to 50, the number of selected antibodies is set to 25, the number of antibody clones is set to 10, the maximum number of iterations is set to 100, and the number of vector images is Num. cov Set it to 10, and the embedding rate ER is set to 0.4.

[0079] This embodiment employs three steganalysis methods to verify security: one based on a 34641-dimensional feature set SRM (Spatial Rich Models), another based on a 686-dimensional feature set SPAM, and a neural network-based steganalysis network, Zhu-Net. This embodiment uses steganalysis to detect the error rate (P0.05). E () as an evaluation indicator for safety.

[0080] Figure 6 The present invention and existing methods show the detection error rates under SRM and SPAM detection. Figure 7 The error rate of this invention and existing methods under Zhu-Net detection is given. Figure 6 and Figure 7 This paper demonstrates the detection error rates of the neural network-based steganography algorithm UT-GAN, the heuristic steganography algorithms S-UNIWARD, WOW, and HILL, and the model-based steganography algorithm MiPOD, along with their corresponding optimized steganography algorithms, against various steganalysis algorithms. Figure 6 and Figure 7 It is evident that, for various steganography algorithms, the steganography algorithm optimized by this invention can improve the security of the basic steganography algorithm against SPAM, SRM and Zhu-Net algorithms, and can improve the security of some classic steganography algorithms (such as S-UNIWARD) to a level comparable to that of neural network-based steganography algorithms, overcoming their limitations of weak security.

Claims

1. A pixel cost redistribution algorithm based on an artificial immune system for digital image information hiding processing. The algorithm searches for adjustment methods of the pixel modification probability distribution obtained by the basic steganography algorithm based on the artificial immune system to redistribute the modification cost of each pixel, thereby further improving the security of the steganography algorithm. Its steganography process includes: First, examine the carrier image. The modified cost matrix of the carrier image is obtained based on the cost function to be optimized. , , For pixel values, and The length and width of the image are given respectively, and the carrier image is obtained under optimal embedding simulation. Modification probability matrix , ,Will A new modified probability distribution is obtained after performing a transformation based on the optimal antibody. , Then flip it back into a cost matrix. , Based on the cost matrix Carrier image under optimal embedding simulation Embedding secret information yields a highly secure target encrypted image. , ; (1) The modified probability matrix The specific transformation form is as follows: first step ， Step 2 ； in, For pixels The original modification probability obtained under a specific basic steganography algorithm and Original modification probability The modification probabilities obtained after the first and second steps of transformation. , This indicates taking the maximum value; (2) Parameters , , , combination The specific value of the optimal antibody is obtained through a dynamic search based on the artificial immune system. , , , The process of dynamic immune optimization involves first initializing the antibody population based on the set antibody size. , For antibody scale, Let i be the i-th antibody in the antibody swarm; then calculate the fitness of each antibody. Fitness is calculated as follows: ； in, This represents the fitness of the i-th antibody. The number of carrier images, For the k-th carrier image, For carrier image Based on antibodies The resulting corresponding encrypted image, where the modification probability matrix is ​​based on antibodies. The transformation form is: ， ； and These are carrier images and encrypted images The SPAM (Subtractive Pixel Adjacency Matrix) feature matrix is ​​calculated as follows: in, This process involves extracting SPAM features from an image; selecting the antibody with the highest fitness based on both the number of antibodies selected and the number of antibody clones; then, for each selected antibody, randomly mutagenesis is used to search for better antibodies in its surrounding clonal antibody set, and the antibody with the best fitness from each derived clonal antibody set is added to a new antibody population to achieve the search and preservation of the optimal embedding method; finally, the remaining antibodies are randomly generated and added to the new antibody population to form a new generation of antibody population; this process is repeated iteratively until the maximum number of iterations is reached and the optimal antibody is obtained, at which point the search process terminates; the optimal antibody is then identified. As the final parameter value in the two-step transformation, the original modification probability distribution Perform the transformation.

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