Robust image steganography against interpolation scaling attack

Abstract

The present application is directed to the limitations of the prior art, a kind of robust image steganography of anti-interpolation scaling attack, this method is equivalent to by anti scaling robust image steganography is reduced to a multi-objective optimization problem, while minimizing the difference between the scaling image X' and the secret image Y', the difference between the carrier image X and the secret image Y is minimized;In the method, a C∝C' mapping is constructed, i.e. the distortion cost function C of the carrier image X, the distortion cost C' of X'→Y' embedding is obtained by mapping, and the final secret image can effectively extract secret information from the attacked secret image by the receiver;Strong practicability, strong robustness for any scaling factor of bilinear scaling channel in the interval (0,1);And good security, i.e. good statistical undetectability.

Description

Technical Field

[0001] This invention relates to the field of multimedia content security; specifically, to an image steganography technique; more specifically, to a robust image steganography method resistant to interpolation scaling attacks. Background Technology

[0002] Image steganography refers to the process by which the sender embeds secret information into a carrier image without arousing suspicion from the detector, thus obtaining a steganographic image. This image is then transmitted over a public channel, allowing the receiver to extract the secret information using a specific key. Existing technologies using robust image steganography methods have achieved some success in resisting lossy channel attacks and statistical detection; however, they still have some shortcomings that need to be addressed, particularly in resisting scaling attacks.

[0003] Chinese Invention Application No. 24, 2020, entitled "An Image Steganography Method Resistant to Statistical Detection and Scaling Attacks," includes: calculating a scaling factor; preprocessing and scaling the carrier image by simulating the scaling factor; constructing actual information embedding rules based on inverse interpolation; employing a position-mapping-based information embedding algorithm; and extracting information. It proposes an algorithm for constructing information embedding rules based on inverse interpolation by establishing a one-to-one correspondence between the actual information embedding value and the actual information embedding point, aiming to ensure the accuracy of information extraction. This means it can correctly extract information from images subjected to scaling attacks, thereby improving the image steganography method's resistance to scaling attacks. By adopting a position-mapping-based information embedding algorithm, it aims to ensure the correct extraction of embedded information after the carrier image has been subjected to a scaling attack, thus improving the statistical detection resistance of the carrier image subjected to a scaling attack.

[0004] However, the above scheme has certain limitations in solving the inverse problem of image scaling. It is only effective for interpolation scaling algorithms in Matlab with scaling factors in the range [0, 0.5]. For general interpolation scaling, such as that in OpenCV, this scheme is not feasible. Therefore, the existing technology still has certain limitations. Summary of the Invention

[0005] To address the limitations of existing technologies, this invention proposes a robust image steganography method and system resistant to interpolation scaling attacks. The technical solution adopted by this invention is as follows:

[0006] A robust image steganography method resistant to interpolation scaling attacks includes the following steps:

[0007] S1, acquire the carrier image X to be processed and the secret information m, and perform bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain the scaled image X';

[0008] S2, calculate the distortion cost function C of the carrier image X, and map the distortion cost function C to the distortion cost function C' of the scaled image X';

[0009] S3, according to the distortion cost function C', the secret information m is embedded into the scaled image X' using STC encoding to obtain the secret image Y';

[0010] S4, perform inverse scaling on the carrier image Y' to obtain a carrier image Y with the same size as the carrier image X.

[0011] Compared to existing technologies, this invention essentially reduces the scaling-resistant robust image steganography to a multi-objective optimization problem, minimizing the difference between the scaled image X' and the steganographic image Y' while simultaneously minimizing the difference between the carrier image X and the steganographic image Y. The method constructs a C∝C′ mapping, where the distortion cost function C of the carrier image X is mapped to obtain the distortion cost C' of the X′→Y′ embedding. The resulting steganographic image allows the receiver to effectively extract secret information from the attacked steganographic image. It is highly practical, exhibiting strong robustness for bilinear scaling channels with any scaling factor taking values ​​in the (0,1) interval; and it boasts good security, i.e., good statistical undetectability.

[0012] As a preferred embodiment, for pixel x′ in the scaled image X' u,v The corresponding pixel in the carrier image X is The cost of distortion is Pixel impact is In the case of step S2, if If the influence value of each pixel is not 1, then pixel x′ u,v The distortion cost c′ u,v =10 10 .

[0013] Furthermore, in step S2, if If only one pixel has an influence value of 1, then pixel x′ u,v The distortion cost c′ u,v Solve it using the following method:

[0014] Solve for the pixel value modification Δ from X to Y of the image so that Established, and

[0015] If d exists s,t =1,x i,j The corresponding weight w i,j =w (V) (i)w (H) (j)≥τ and Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}, then c′ u,v =c s,t Otherwise, c′ u,v =10 10 .

[0016] Furthermore, in step S2, if If multiple pixels have an influence value of 1, then pixel x′ u,v The distortion cost c′ u,v Solve it using the following method:

[0017] For sets Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}; if the set Θ is not empty, and ∑ s,t w s,t If ≥τ, then c′ u,v =mean{c s,t}, (s,t)∈Θ; otherwise, c′ u,v =10 10 .

[0018] Furthermore, step S4 involves solving the following inverse image interpolation scaling problem:

[0019]

[0020]

[0021] In solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is not 1, the pixel y′ of the carrier image Y' u,v The corresponding pixel in the carrier image Y is assigned a value using the pixel at the corresponding position in the carrier image X.

[0022] Furthermore, in solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is 1, if y′ u,v -x′ u,v =0, then the pixel y′ of the image Y' is 0. u,v The corresponding pixel in the carrier image Y is assigned a value using the pixel at the corresponding position in the carrier image X.

[0023] Furthermore, in solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is 1, if y′ u,v -x′ u,v If ≠0, then solve as follows:

[0024] The pixel y′ of the carrier image Y' u，v The corresponding pixel in the image Y is Weight is Pixel impact is The set of pixel coordinates with a pixel influence degree of 1 is Γ={(s,t)|d s,t =1, (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}};

[0025] First, the pixels y′ of the image Y' are... u,v The pixel P corresponding to the image Y (u,v) Initialization is performed using the pixels at the corresponding positions in the carrier image X:

[0026]

[0027] Repeat the process including the following steps until...

[0028] Based on set Γ, find the set {w} consisting of the weights of pixels with a pixel influence degree of 1. s,t |{(s,t)∈Γ}};Find {w s,t The maximum value in the set |{(s,t)∈Γ}} corresponds to P. (u,v) The pixels, for P (u,v) Perform ±1 update;

[0029] judge Is it true? If it is true, then... Otherwise, find {w s,t The second-largest value in the set |{(s,t)∈Γ}} corresponds to P. (u,v) The pixels, for P (u,v) Update.

[0030] This invention also provides the following:

[0031] A robust image steganography system resistant to interpolation scaling attacks includes an image scaling module, a distortion cost calculation module, an embedding module, and a scaling inverse processing module; the image scaling module is connected to the distortion cost calculation module, the distortion cost calculation module is connected to the embedding module, and the embedding module is connected to the scaling inverse processing module; wherein:

[0032] The image scaling module is used to acquire the carrier image X to be processed and the secret information m, and to perform bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain the scaled image X'.

[0033] The distortion cost calculation module is used to calculate the distortion cost function C of the carrier image X, and map the distortion cost function C to the distortion cost function C' of the scaled image X'.

[0034] The embedding module is used to embed the secret information m into the scaled image X' using STC encoding according to the distortion cost function C', to obtain the secret image Y'.

[0035] The scaling inverse processing module is used to perform scaling inverse processing on the carrier image Y' to obtain a carrier image Y with the same size as the carrier image X.

[0036] A storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the aforementioned robust image steganography method resistant to interpolation scaling attacks.

[0037] A computer device includes a storage medium, a processor, and a computer program stored in the storage medium and executable by the processor, wherein the computer program, when executed by the processor, implements the steps of the aforementioned robust image steganography method resistant to interpolation scaling attacks. Attached Figure Description

[0038] Figure 1 A flowchart illustrating the robust image steganography method against interpolation scaling attacks provided by this invention.

[0039] Figure 2 A schematic diagram illustrating the principle framework of the robust image steganography method against interpolation scaling attacks provided by this invention.

[0040] Figure 3 This is a schematic diagram of bilinear interpolation of an image;

[0041] Figure 4 A schematic diagram illustrating the principle framework of the inverse problem of image interpolation and scaling;

[0042] Figure 5 This is a schematic diagram illustrating the image steganography and transmission process in an embodiment of the present invention;

[0043] Figure 6 The modified position and magnitude of the image are shown in the example image of this embodiment of the invention;

[0044] Figure 7 A schematic diagram of a robust image steganography system against interpolation scaling attacks provided by the present invention. Detailed Implementation

[0045] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0046] It should be understood that the described embodiments are merely some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of the embodiments of this application.

[0047] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the embodiments of this application. The singular forms “a,” “the,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0048] In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims. In the description of this application, it should be understood that the terms "first," "second," "third," etc., are used only to distinguish similar objects and are not necessarily used to describe a specific order or sequence, nor should they be construed as indicating or implying relative importance. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0049] Furthermore, in the description of this application, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. The invention will be further described below with reference to the accompanying drawings and embodiments.

[0050] To address the limitations of existing technologies, this embodiment provides a technical solution. The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] Please see Figure 1 A robust image steganography method resistant to interpolation scaling attacks includes the following steps:

[0053] S1, acquire the carrier image X to be processed and the secret information m, and perform bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain the scaled image X';

[0054] S2, calculate the distortion cost function C of the carrier image X, and map the distortion cost function C to the distortion cost function C' of the scaled image X';

[0055] S3, according to the distortion cost function C', the secret information m is embedded into the scaled image X' using STC encoding to obtain the secret image Y';

[0056] S4, perform inverse scaling on the carrier image Y' to obtain a carrier image Y with the same size as the carrier image X.

[0057] Compared to existing technologies, this invention essentially reduces robust image steganography to a multi-objective optimization problem, minimizing the difference between the scaled image X' and the steganographic image Y' while simultaneously minimizing the difference between the carrier image X and the steganographic image Y. The method constructs a C∝C′ mapping, where the distortion cost function C of the carrier image X is mapped to obtain the distortion cost C' embedded in X′→Y′. The resulting steganographic image allows the receiver to effectively extract secret information from the attacked steganographic image. It is highly practical, exhibiting strong robustness for bilinear scaling channels with any scaling factor taking values ​​in the (0,1) interval; and it boasts good security, i.e., good statistical undetectability.

[0058] Specifically, the solution provided in this embodiment can be regarded as a robust image steganography algorithm resistant to interpolation scaling.

[0059] When the secret image Y is uploaded to the scaling channel and transmitted to the receiver, it will be converted into a secret image Y that is completely identical to the secret image Y'. * The receiver will be able to extract the secret image Y from the data. * Extract secret information.

[0060] To facilitate better understanding, the relevant principles of this embodiment will be explained below.

[0061] 1. Bilinear interpolation scaling principle:

[0062] Typically, social channels scale down images to reduce image storage memory; that is, social channels are mostly lossy channels. In this embodiment, we only consider the case where the scaling factor α ∈ (0,1). For example... Figure 2 As shown, given the original image X = (x m,n ) M×N After passing through a scaled channel with a scaling factor of α, we get X′=(x′ u,v ) U×V ,in Given the embedding distortion cost C′ of X′, secret information m is embedded in X′ through STC encoding to obtain the secret-carrying image Y′; combined with the information of the original image X, an intermediate image Y of the same size as the original image X is obtained through inverse scaling processing; and the small image Y is obtained after the secret-carrying image Y is uploaded to the scaling channel. * Same as Y′.

[0063] For bilinear interpolation scaling, if a pixel x′ in image X′ u,v If the coordinates of the given image are (u, v), then its corresponding grid coordinates in the original image X are: x′ u,v The value is in the grid coordinates of the original image X. The weighted sum of the surrounding 4 pixels, and ( (This represents the set of natural numbers from 0 to 255). This can be represented as:

[0064] x′ u,v = <w (V) Pw (H) > (1)

[0065] Where <·> represents the rounding operator; P represents the floating-point coordinates of the original image X. A matrix consisting of the surrounding 4 pixels, where P is in like Figure 3 As shown; w (V) and w (H) Let P represent the weight matrices of P in the vertical and horizontal directions, respectively, with dimensions of 1×2 and 2×1.

[0066] 2. Definition of pixel influence:

[0067] In this embodiment, pixel influence is defined as follows: if each pixel x in the original image X... m,n The value of β pixels in the scaled image X′ is affected by β, which is defined as the pixel influence of the original image X at coordinates (m,n), and is abbreviated as d. m,n =β, the influence of the original image X at each pixel position is denoted as D = (d m,n ) M×N ,in ( (representing the set of natural numbers from 0 to 4)

[0068] In fact, given the scaling factor of the scaling channel, the pixel influence matrix D corresponding to the original image X can be uniquely determined according to the scaling principle of bilinear interpolation. Specifically, because the template for bilinear interpolation is 2×2, when the scaling factor α = 0.5, the matrix D = (d...m,n ) M×N All elements take the value 1; when the scaling factor 0 < α < 0.5, matrix D = (d m,n ) M×N All elements take values ​​of 0 or 1; when the scaling factor 1 > α > 0.5, matrix D = (d m,n ) M×N There are no elements with a value of 0. The number of elements with a value of 1 decreases as α increases, while the number of elements with a value of 2, 3, or 4 increases as α increases.

[0069] 3. The inverse problem of image interpolation and scaling and its solution.

[0070] The inverse problem of image interpolation scaling: Given the original image X = (x m,n ) M×N After passing through a scaled channel with a scaling factor of α, we get X′=(x′ u,v ) U×V Through channel inverse processing, a target image Y with the same size and minimal difference as the original image X is obtained. Furthermore, the image Y′ obtained after uploading Y to the scaling channel is identical to X′. Figure 4 As shown.

[0071] In fact, the inverse problem of image interpolation scaling is a constrained integer programming problem with the objective of minimizing the difference between X and Y. The constraints are: the image Y′ obtained after uploading Y to the scaling channel is identical to X′, and each element in Y... As shown below:

[0072]

[0073]

[0074] It is obvious that if X′ is not processed in any way, then the optimal solution Y to the above problem is X. However, directly solving the optimal solution to this type of integer programming problem is difficult because it can be reduced to an NP-hard problem. An effective method for solving this type of problem is the branch and bound method, which involves repeatedly dividing the entire solution space into increasingly smaller subsets and calculating a target lower bound for the solution set within each subset (for minimum value problems). Simply put, the branch and bound method for solving integer programming problems adds additional constraints to make the integer programming problem solvable in a finite time. Specifically, a solution space consists of feasible solutions with m×n pixel values, which can be divided into 5 classes with influence degrees of 0, 1, 2, 3, and 4. Then, using the inequality... (where x′) u,The inequality system composed of (v ∈ X′) contains a total of U × V inequalities, and each inequality contains 4 unknowns. Therefore, the entire inequality system contains at most 4(U × V) unknowns. According to the size of the scaling factor, it can be discussed in the following cases:

[0075] ① When 0 < α ≤ 0.5, from the inequality system (where x′ u,v ∈ X′) consists of U × V inequalities. Each inequality contains 4 unknowns, and there are a total of 4(U × V) unknowns. At this time, the pixel influence degree corresponding to each unknown is 1, that is, each unknown is only included in one inequality. At this time, it is easy to obtain the minimum lower bound of the difference between each unknown and the pixel value at the corresponding position in X. In addition to these 4(U × V) unknowns, there are M × N - 4(U × V) unknowns in Y, but the pixel influence degrees corresponding to these unknowns are all 0. That is to say, these pixels do not affect the values of the pixels in X′. Therefore, the minimum lower bound of the difference between these M × N - 4(U × V) unknowns and the pixel values at the corresponding positions in X is 0.

[0076] ② When 0.5 < α < 1, from the inequality system (where x′ u,v ∈ X′) consists of U × V inequalities. The number of unknowns Num satisfies: U × V < Num < M × N < 4(U × V), and the pixel influence degrees corresponding to these unknowns are 1, 2, 3, and 4. For an inequality equation It contains 4 unknown variables. If an element y in Y m,n is only in this inequality equation, that is, the pixel influence degree corresponding to y m,n is 1, then, through this inequality equation, it is easy to obtain the minimum lower bound of |x m,n -y m,n |. If an element y in Y m,n is in multiple inequality equations, that is, the pixel influence degree corresponding to y m,n is not 1, and the value of y m,n will also affect the values of other elements in Y, then it may be difficult to determine the minimum lower bound of the difference between y m,n and the pixel value x at the corresponding position in X m,n . However, obviously, if X′ has not been processed at all, then the minimum lower bound of the difference between y m,n and the pixel value at the corresponding position in X is 0.

[0077] Generally speaking, for the branch and bound solution process of the inverse problem of the above bilinear interpolation scaling, the additional constraint conditions added in this embodiment are: for y at the pixel positions in Y with an influence degree other than 1 m,n use the pixel value x at the corresponding position in Xm,n Replacement. For example, for a pixel x′ in X′. u,v Based on the bilinear interpolation scaling, it corresponds to 4 pixels in Y. And the pixel impact of these 4 pixels. If any of these four pixels has a pixel influence degree other than 1, then these pixels are used to assign values ​​to the corresponding pixels in X. That is, if d i,j ≠1, then y i,j =x i,j In particular, if If none of them are 1, then Therefore, after adding the above additional constraints, the optimization problem becomes:

[0078]

[0079]

[0080] In fact, in the optimization problem described above, only pixels with a pixel influence of 1 are unknown in Y, and these unknowns only exist in the system of inequalities. The optimal solution can be easily obtained from one of the inequalities.

[0081] 4. Image steganography problem in scaling-resistant channels:

[0082] An effective image steganography scheme resistant to scaling channels must be robust, and on this basis, as resistant to statistical detection as possible. Robustness requires that the intermediate image Y be uploaded to the image Y obtained through the scaling channel. * Similar to the carrier image Y′, resistance to statistical detection requires that the difference between the original image X and the intermediate image Y be sufficiently small.

[0083] Image steganography schemes that counter scaling channels rely on robustness. Therefore, the key is selecting pixels in X′ suitable for embedding secret information while simultaneously ensuring the solvability of the inverse problem of interpolation scaling after embedding. According to the definition of the aforementioned scaling inverse problem, the additional constraint for ensuring the solvability of the interpolation scaling inverse problem is: for pixels in Y with a non-zero influence value of 1... m,n Use the pixel value x at the corresponding position in X m,n Replacement. That is, if for a pixel x′ in X′... u,v The pixel influence of the four pixels in Y is 1, when x′ u,v Even when modified by ±1, the optimal solution for Y can still be obtained according to optimization problems (4)-(5). For example, if x′ u,v The pixel influence of the four pixels in Y is 1. Let's assume that d i,j =1 while the influence of other factors is not 1, when x′u,v When modified by ±1, then a Δ can be obtained such that This holds true. Therefore, while ensuring the robustness of the solution, the objective of the scale-resistant image steganography problem is to minimize the difference between the original image X and the intermediate image Y, given a relative embedding load l, which is the following optimization problem:

[0084]

[0085]

[0086]

[0087] Where <·> represents the rounding function, and Emb(X′,l) represents an embedding function with respect to the carrier image X′ and the relative embedding load l, such as the STC-coded embedding or the Simulator-simulated embedding function. π(y′) u,v ) represents pixel y′ u,v The probability of being modified.

[0088] The resistance to detection for image steganography schemes that are resistant to scaling channels depends on designing an effective embedding distortion cost function C′ for X′→Y′. As analyzed above, there are many pixels in image X′ that can be used to embed secret information, and changes in these pixels directly affect the changes in corresponding pixels in image Y. The modification of image Y relative to image X determines the algorithm's resistance to detection, as resistance to detection refers to the ability of a statistical detector to distinguish between image X and image Y. Therefore, it can be considered that when embedding secret information in X′, the embedding distortion cost of image X′ is determined by the distortion cost of image X.

[0089] This implementation is based on the premise that modifying pixels in the image texture region is safer. If the pixel changes from X to Y caused by embedding information in image X′ are concentrated in the texture region of image X, then the anti-scaling steganography scheme has relatively good anti-detection performance. To limit the pixel changes from X to Y to be concentrated in the texture region of image X, this embodiment uses an adaptive steganography scheme to calculate the distortion cost C of image X and map it to the distortion cost C′ of image X′. Taking bilinear interpolation as an example, assume that for a pixel x′ in X′... u,v The four pixels corresponding to X are The corresponding distortion cost is The corresponding pixel influence is in This embodiment calculates pixel x′ in X′ under the following conditions. u,v The distortion cost c′ u,v :

[0090] ① Does not include pixels with an influence value of 1

[0091] If the matrix All elements in X′ are not 1, meaning that pixel x′ in X′ is 1. u,v It cannot be modified, so pixel x′ u,v The corresponding distortion cost should be a relatively large number; in this embodiment, we take c′. u,v =10 10 .

[0092] ② Contains only one pixel with an influence value of 1.

[0093] Taking bilinear interpolation as an example, if the matrix Only one element in X′ is 1, meaning that pixel x′ in X′ is 1. u,v It is possible that it can be modified. Assume d i,j =1, when x′ u,v When modified by ±1, a Δ can be obtained such that Established and Furthermore, in order to further control the maximum magnitude of the image X→Y pixel value modification Δ, when x i,j The corresponding weight w i,j =w (V) (i)w (H) When (j)≥τ, x′ u,v Only then is modification allowed. Therefore, for pixel x′ u,v If there is d s,t =1, w i, j≥τ and Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}, then c′ u,v =c s,t Otherwise, c′ u,v =10 10 .

[0094] To further control the maximum magnitude of pixel value modification from X to Y in the image, this embodiment only modifies points with a weight sum greater than or equal to τ. This limits the maximum modification per pixel in the large image. In subsequent experiments of this embodiment, τ = 0.5 will be selected to ensure that the maximum modification value is 2.

[0095] ③ Contains multiple pixels with an influence value of 1

[0096] If the matrix There are multiple elements that are 1, meaning that pixel x′ in X′ is 1. u,v It is possible that it can be modified. Let the set be... Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}, if Θ is not empty and ∑ s,t w s,t If ≥τ, then c′ u,v =mean{c s,t}, (s,t)∈Θ; otherwise, c′ u,v =10 10 .

[0097] In subsequent experiments of this embodiment, τ is set to 0.5, meaning the maximum magnitude of the pixel value modification from X to Y in the image is 2. In this distortion cost function design scheme, this embodiment considers pixel x′ in X′ to be... u,v The distortion introduced by modifying ±1 is the same, i.e.: c(+1)′ u,v =c(-1)′ u,v =c′ u,v .

[0098] Therefore, as a preferred embodiment, for pixel x′ in the scaled image X' u,v The corresponding pixel in the carrier image X is The cost of distortion is Pixel impact is In the case of step S2, if If the influence value of each pixel is not 1, then pixel x′ u,v The distortion cost c′ u,v =10 10 .

[0099] Furthermore, in step S2, if If only one pixel has an influence value of 1, then pixel x′ u,v The distortion cost c′ u,v Solve it using the following method:

[0100] Solve for the pixel value modification Δ from X to Y of the image so that Established, and

[0101] If d exists s,t =1,x i,j The corresponding weight w i,j =w (V) (i)w (H) (j)≥τ and Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}, then c′ u,v =c s,t Otherwise, c′u,v =10 10 .

[0102] Furthermore, in step S2, if If multiple pixels have an influence value of 1, then pixel x′ u,v The distortion cost c′ u,v Solve it using the following method:

[0103] For sets Where (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}; if the set Θ is not empty, and ∑ s,t w s,t If ≥τ, then c′ u,v =mean{c s,t}, (s,t)∈Θ; otherwise, c′ u,v =10 10 .

[0104] 5. Solution to the image steganography problem in anti-scaling channels:

[0105] That is, solving the anti-scaling image steganography problem. In this embodiment, the distortion cost C′ of image X′ can be obtained. Given the effective embedding load l relative to image X′, the secret information msg can be embedded into image X′ to obtain image Y′. Then the optimization problem (6)-(8) of the anti-scaling image steganography problem becomes the inverse problem of image interpolation and scaling, as follows:

[0106]

[0107]

[0108] Regarding the solution to the inverse problem of image interpolation scaling, the pixel values ​​of all pixels in image Y with a non-influence degree of 1 are assigned the values ​​of the corresponding pixels in image X. For pixels in image Y with an influence degree of 1, this embodiment solves the problem in the following two cases:

[0109] ①y′ u,v -x′ u,v =0

[0110] pixel y′ u,v All pixels corresponding to the same position in Y are replaced with the corresponding pixels in X. Taking bilinear interpolation as an example, pixel y′... u,v Corresponding to 4 pixels in Y

[0111] ②y′ u,v -x′ u,v ≠0

[0112] Taking bilinear interpolation as an example, pixel y′ u,v The four corresponding pixels in Y are The corresponding weight is Pixel impact is The set of pixel coordinates with an influence degree of 1 is Γ={(s,t)|d s,t =1, (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}}, the specific solution steps are as follows:

[0113] Step 1: Pixel y′ u,v The four pixels corresponding to Y Initialize with the magnitude of the pixel value at the corresponding position in X, such as,

[0114]

[0115] Step 2: Find the set of weights with an influence of 1 pixel according to set Γ, denoted as: {w s,t |{(s,t)∈Γ}}。 Find {w s,t The maximum value in the set |{(s,t)∈Γ}} corresponds to P. (u,v) pixels, for example, y i,j If a pixel has an influence of 1 and the corresponding weight is the largest, then that pixel should be modified to y. i,j =x i,j +Δ i,j , where Δ i,j =y′ u,v -x′ u,v and update P (u,v) .

[0116] Step3:Judge Is it equal to y′? u,v If they are equal, then pixel y′ u,v The four pixels corresponding to Y Otherwise, find {w s,t The second-largest value in the set |{(s,t)∈Γ}} corresponds to P. (u,v Make the same modifications as in step 2 for the pixels of ).

[0117] Step4:Judge Is it equal to y′? u,v If they are equal, then pixel y′ u,v The four pixels corresponding to Y Otherwise, proceed to Step 3. Specifically, if w s,t All elements in |{(s,t)∈Γ}} correspond to P (u,v) Even after all pixels were modified, it still did not meet the requirements. Then repeat Steps 2-4 until the desired result is achieved. until.

[0118] Therefore, step S4 involves solving the following inverse problem of image interpolation scaling:

[0119]

[0120]

[0121] In solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is not 1, the pixel y′ of the carrier image Y' u,v The corresponding pixel in the carrier image Y is assigned a value using the pixel at the corresponding position in the carrier image X.

[0122] Furthermore, in solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is 1, if y′ u,v -x′ u,v =0, then the pixel y′ of the image Y' is 0. u,v The corresponding pixel in the carrier image Y is assigned a value using the pixel at the corresponding position in the carrier image X.

[0123] Furthermore, in solving the inverse problem of image interpolation and scaling, for the case where the pixel influence degree in the carrier image Y is 1, if y′ u,v -x′ u,v If ≠0, then solve as follows:

[0124] The pixel y′ of the carrier image Y' u,v The corresponding pixel in the image Y is Weight is Pixel impact is The set of pixel coordinates with a pixel influence degree of 1 is Γ={(s,t)|d s,t =1, (s,t)∈{(i,j),(i+1,j),(i,j+1),(i+1,j+1)}};

[0125] First, the pixels y′ of the image Y' are... u,v The pixel P corresponding to the image Y (u,v) Initialization is performed using the pixels at the corresponding positions in the carrier image X:

[0126]

[0127] Repeat the process including the following steps until...

[0128] Based on set Γ, find the set {w} consisting of the weights of pixels with a pixel influence degree of 1. s,t |{(s,t)∈Γ}};Find {w s,t The maximum value in the set |{(s,t)∈Γ}} corresponds to P. (u,v) The pixels, for P (u,v) Update;

[0129] judge Is it true? If it is true, then... Otherwise, find {w s,t The second-largest value in the set |{(s,t)∈Γ}} corresponds to P. (u,v) The pixels, for P (u,v) Update.

[0130] The following will illustrate this with specific examples and experimental results:

[0131] All experiments in this embodiment were conducted on the BOSSBase v1.0 dataset, which contains 10,000 images of size 512*512 pixels. Taking a 512×512 grayscale image as an example, the processing method of this embodiment was applied on a scaling channel with a scaling factor of 0.5. The example image steganography and transmission process are as follows. Figure 5 As shown, ① the carrier image X is first scaled using bilinear interpolation with a scaling factor α = 0.5, taking "1013.pgm" from the BOSSBase v1.0 database as an example; ② the distortion cost function C of the carrier image X is calculated and mapped to the distortion cost function C′ of the scaled image X'; ③ the secret information m is embedded into the scaled image X' using STC encoding to obtain the secret image Y'; ④ the secret image Y' is scaled inversely to obtain the secret image Y with the same size as the carrier image X; ⑤ the secret image Y is uploaded to the scaling channel to obtain the secret image Y' that is completely identical to the secret image Y'. * This is so that the recipient can extract confidential information.

[0132] Experimental results show that this implementation scheme is highly practical and robust to bilinear scaling channels with any scaling factor within the range. Please refer to Table 1, which shows the percentage of images that can correctly extract secret information after bilinear interpolation scaling attacks with different scaling factors, based on the SUNIWARD embedding distortion function design scheme, when the relative effective embedding payload is 0.1 bpp.

[0133] Table 1

[0134]

[0135] It can be observed that: when a secret image obtained based on existing technology, namely traditional image steganography, is subjected to a bilinear interpolation scaling attack, the secret information cannot be extracted from the attacked secret image; while the secret image obtained by the present invention can still effectively extract the secret information from the attacked secret image.

[0136] Experimental results show that this implementation scheme has good security, i.e., good statistical undetectability. On the one hand, this invention guides the steganographic embedding of the scaled carrier image based on the embedding cost of the carrier image X. This ensures that the differences between the carrier image Y obtained after the inverse scaling transformation of the scaled carrier image and the carrier image X remain concentrated in the texture region of the image, thus providing strong concealment. On the other hand, to maximize the security of the robust image steganography algorithm in this invention, please refer to... Figure 6 In this embodiment, the maximum amplitude of the difference between the carrier image X and the carrier image Y is limited to 2. The detection error rates of the anti-SRM detector based on the SUNIWARD and MiPOD distortion cost calculation methods of this invention under different scaling factors and different embedding loads are shown in Table 2.

[0137] Table 2

[0138]

[0139] It can be observed that when the scaling factor is constant, the security of the present invention decreases as the relatively effective embedding payload increases, because the length of the information embedded in the image continuously increases; when the effective embedding payload is fixed, the larger the scaling factor, the worse the security, because the larger the scaling factor, the longer the length of the information embedded in the image.

[0140] Example 2

[0141] A robust image steganography system resistant to interpolation scaling attacks, please refer to [link / reference]. Figure 7 It includes an image scaling module 1, a distortion cost calculation module 2, an embedding module 3, and a scaling inverse processing module 4; the image scaling module 1 is connected to the distortion cost calculation module 2, the distortion cost calculation module 2 is connected to the embedding module 3, and the embedding module 3 is connected to the scaling inverse processing module 4; wherein:

[0142] The image scaling module 1 is used to acquire the carrier image X to be processed and the secret information m, and to perform bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain the scaled image X'.

[0143] The distortion cost calculation module 2 is used to calculate the distortion cost function C of the carrier image X, and map the distortion cost function C to the distortion cost function C' of the scaled image X'.

[0144] The embedding module 3 is used to embed the secret information m into the scaled image X' using STC encoding according to the distortion cost function C', to obtain the secret image Y'.

[0145] The scaling inverse processing module 4 is used to perform scaling inverse processing on the carrier image Y' to obtain a carrier image Y with the same size as the carrier image X.

[0146] Example 3

[0147] A storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the robust image steganography method against interpolation scaling attacks in Embodiment 1.

[0148] Example 4

[0149] A computer device includes a storage medium, a processor, and a computer program stored in the storage medium and executable by the processor, wherein the computer program, when executed by the processor, implements the steps of the robust image steganography method against interpolation scaling attacks in Embodiment 1.

[0150] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A robust image steganography method against interpolation scaling attack, characterized in that, comprising the steps of: S1, acquiring a carrier image to be processed X and secret information m performing bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain a scaled image X' ; S2, computing a distortion cost function for the carrier image X S3, mapping the distortion cost function for the carrier image C S4, computing a distortion cost function for the scaled image C S5, mapping the distortion cost function for the scaled image X' S6, computing a distortion cost function for the scaled image C' ; wherein, for a pixel in the scaled image X' the corresponding pixel in the carrier image is X , the distortion cost is , the pixel influence degree is , , , ; wherein, denotes the image scaling ratio, and denote the horizontal coordinate and the vertical coordinate of the image pixel, respectively. If the value of each pixel influence degree is not 1, the pixel distortion cost ; If only one pixel in the block has a value of 1, then the pixel with the distortion cost is solved by: Solving images Pixel value modification amount So that Holds, and ; wherein, Is the target pixel value of the steganographic image at coordinates ( u , v ) if there is , a corresponding weight and wherein , then ; otherwise ; If the value of the pixel influence degree is 1, the pixel distortion cost is solved by the following way: For a set where ; if the set is not empty and then ; otherwise ; S3, obtaining the distortion cost function C' , embedding the secret information m into the scaled image X' , obtaining the stego image Y' ; S4, scaling inverse processing is performed on the steganographic image Y' to obtain a steganographic image with the same size as the carrier image X Y .​ 2. The robust image steganography method against interpolation scaling attack according to claim 1, characterized in that, In said step S4, it is involved the resolution of the inverse problem of image interpolation scaling: ； In solving the inverse problem of image interpolation scaling, for the image carrying... Y When the pixel influence is not 1, the carrier image Y' pixels The image on the record Y The corresponding pixels in the carrier image are used X Assign values ​​to the corresponding pixels in the formula; where, Represents a secret image Y In coordinates ( m, n The pixel value of M represents the image. Y Total number of rows ， N represents the image carrying the secret. Y Total number of columns, Representing the pixel matrix the number of rows, Representing the pixel matrix The number of columns.

3. The robust image steganography method against interpolation scaling attack according to claim 2, characterized in that, In solving the inverse problem of image interpolation scaling, for the carrier image Y If the mid-pixel influence is 1, then The image carrying the secret Y' pixels The image on the record Y The corresponding pixels in the carrier image are used X Assign values ​​to the corresponding pixels in the image.

4. The robust image steganography method against interpolation scaling attack according to claim 2, characterized in that, In solving the image interpolation scaling inverse problem, for the secret-carrying image Y If the pixel influence degree is 1, if then the following method is used to solve it: The image carrying secrets Y' pixels The image on the record Y The corresponding pixel in is The weight is Pixel impact is The set of pixel coordinates with a pixel influence degree of 1 is ; The steganographic image Y' pixels corresponding pixels Y in the steganographic image are initialized with the pixel values of the corresponding pixels in the carrier image X at the corresponding positions. ； The process comprising the following steps is repeated until : According to set Find the set of weights consisting of pixels with a pixel influence of 1. ;turn up{ The maximum value in the set corresponds to pixels, for Update; judge Is it true? If it is true, then... = Otherwise, find { The second largest value in the set corresponds to pixels, for Perform ±1 update.

5. A robust image steganography system against interpolation scaling attack, applied to the robust image steganography method against interpolation scaling attack according to any one of claims 1-4, characterized in that, The image scaling module (1) is connected to the distortion cost calculation module (2), the distortion cost calculation module (2) is connected to the embedding module (3), and the embedding module (3) is connected to the inverse scaling processing module (4); wherein: The image scaling module (1) is used for acquiring a carrier image to be processed X and secret information m , performing bilinear interpolation scaling on the carrier image with a preset scaling factor to obtain a scaled image X' ; The distortion cost calculation module (2) is used to calculate the carrier image. X Distortion cost function C The distortion cost function C Mapped to the scaled image X' Distortion cost function C' ; The embedding module (3) is used to determine the distortion cost function. C' The secret information is encoded using STC. m Embed the scaled image X' Obtain the secret image Y' ; The scaling inverse processing module (4) is configured to perform scaling inverse processing on the stego image Y' to obtain a stego image with the same size as the carrier image X . Y .

6. A storage medium having stored thereon a computer program, characterized in that: The computer program, when executed by a processor, implements the steps of the robust image steganography method against interpolation scaling attack according to any one of claims 1 to 4.

7. A computer device, characterized by: The computer program, when executed by a processor, implements the steps of the robust image steganography method against interpolation scaling attack according to any one of claims 1 to 4.

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