An Adaptive Dual-Image Invertible Information Hiding Method Based on Sudoku Matrix

Abstract

This invention discloses an adaptive dual-image reversible information hiding method based on a Sudoku matrix. First, an original carrier image is copied twice, and a Sudoku reference matrix is ​​established. Next, the secret information of the binary random bit string is divided into groups of 6 bits each, and each group is converted into two octal secret numbers. A pair of pixel values ​​from the original carrier image is mapped onto the Sudoku reference matrix, establishing a quantization distortion model. Then, based on the quantization distortion model, the optimal distance threshold and optimal embedding strategy are determined, and two cryptic images are generated. Finally, two receiving ends establish the same Sudoku reference matrix as the sending end, recover the pixel pairs of the original carrier image, traverse all pixel pairs of the cryptic images, and convert the extracted secret numbers into binary bit strings. This invention significantly improves image visual quality, is very simple and practical to operate, and effectively enhances the security of information transmission.

Description

Technical Field

[0001] This invention belongs to the field of information security technology, specifically relating to an adaptive dual-image reversible information hiding method based on Sudoku matrices. Background Technology

[0002] The rapid development of the internet has enabled people to access information quickly and conveniently. However, the transmission of large amounts of data faces the risk of information leakage and tampering, leading to various cybersecurity issues. Encryption technology provides protection for confidential information through encryption and decryption, but encrypted garbled information attracts the attention of hackers, and once the ciphertext is decrypted, its content is completely transparent. Conversely, information hiding technology ensures the anonymity of transmission by embedding confidential information into public carriers (such as images). After the confidential data is extracted, the carrier image will exhibit varying degrees of distortion. In certain specific fields, such as military intelligence, medical diagnosis, copyright protection, and evidence protection, it is necessary to protect both confidential data and the integrity of the original carrier. Therefore, extracting correct information and accurately restoring the carrier image are equally important. The emergence of reversible data hiding technology precisely solves the above problems.

[0003] Traditional reversible information hiding techniques are mainly divided into two categories: difference expansion and histogram translation. These two methods form the foundation of reversible information hiding technology. With further research, two-image reversible information hiding has emerged due to its more reliable security and the exploration of larger embedding capacities. Its characteristic lies in that the sender generates two encrypted images and transmits them to two different receivers. Only when the two encrypted images are combined can the correct secret information and the carrier be extracted. A single encrypted image cannot completely extract the information, let alone reconstruct the carrier. Currently, two-image reversible information hiding methods mainly include the reference matrix method, the center folding method, and the direction combination method. Among these methods, under a certain embedding capacity, there is still considerable room for improvement in image visual quality. At the same time, security also needs further enhancement. Summary of the Invention

[0004] This invention addresses the problems of low hiding capacity, large image distortion, and low security in traditional dual-image reversible information hiding methods. It proposes an adaptive dual-image reversible information hiding method based on Sudoku matrices, which not only improves the visual quality of the image when the embedding capacity is large, but also has a strong high-fidelity effect when the capacity is small, while improving the security of information transmission.

[0005] The present invention adopts the following technical solution:

[0006] An adaptive dual-image invertible information hiding method based on Sudoku matrices includes the following steps in the preprocessing stage:

[0007] S1. Duplicate the original carrier image CI twice to obtain two initial dense images, denoted as MI. 10 and MI 20 .

[0008] S2. Construct a Sudoku reference matrix M with a size of 256×256, where the horizontal and vertical coordinates represent pixel values ​​from 0 to 255. The Sudoku reference matrix M contains many complete 9×9 Sudoku matrices, and each Sudoku matrix includes one 3×3 center piece and eight 3×3 edge pieces surrounding it. Each center piece has nine small cells, and each small cell is labeled with the numbers "1", "2", "3", "4", "5", "6", "7", "8", and "9" in the raster scan order. Each Sudoku matrix has the following characteristics: the numbers 0 to 8 appear only once in each column and each row of the Sudoku matrix; the numbers 0 to 8 appear only once in each 3×3 center piece and each 3×3 edge piece.

[0009] S3. Preprocess the secret information by dividing the secret information of the binary random bit string into groups of 6 bits each, and converting each group into 2 octal secret numbers.

[0010] An adaptive dual-image invertible information hiding method based on Sudoku matrices, wherein the embedding process of secret information includes the following steps:

[0011] S4. Set a distance threshold D, and select two consecutive adjacent pixel values ​​x from the original carrier image CI. i and x i+1 Combining into a pair of pixel values ​​(x i ,x i+1 ), to transfer this pair of pixel values ​​(x i ,x i+1 The block is mapped onto the Sudoku reference matrix M, and a quantization distortion model is established according to the block matrix mapping rules and the required embedding capacity P; the center block and the edge block are collectively referred to as the block matrix.

[0012] S5. Based on the quantization distortion model described above, adaptively determine the optimal distance threshold D. opt .

[0013] S6. Based on the determined optimal distance threshold D opt The optimal embedding strategy can be determined, which is to raster scan each pair of pixel values ​​(x) of the original carrier image CI according to the block matrix mapping rule. i ,x i+1 According to the optimal embedding strategy, secret numbers are embedded respectively to generate two pairs of pixel values, denoted as (y i ,y i+1 ) and (z i ,z i+1This process continues until all information is embedded, ultimately generating two densely packed images, MI1 and MI2, that are very similar to the original carrier image CI.

[0014] An adaptive dual-image reversible information hiding method based on Sudoku matrices, which extracts information and restores the original carrier image includes the following steps:

[0015] S7. The two receiving ends establish the same Sudoku reference matrix M as the sending end.

[0016] S8. The two receiving ends receive the encrypted images MI1 and MI2 respectively, and combine two consecutive pixel values ​​into a pair of pixel values; copy the encrypted image MI1, denoted as CI′; raster scan each pair of pixel values ​​(y) of MI1 and MI2. i ,y i+1 ) and (z i ,z i+1 Comparing these two pairs of pixel values, if they are completely identical, it means that the original pixel pair was not used to hide information, and the pixel pair value (x) of the original carrier image is... i ,x i+1 ) and the values ​​of the current two pairs of pixels (y i ,y i+1 ) and (z i ,z i+1 If the pixel pairs (x, y) are equal, then the pixel pairs (x, y) of the original carrier image are equal; otherwise, the pixel pairs (x, y) of the original carrier image are equal. i ,x i+1 Secret information is embedded, which pairs the pixel values ​​(y) with the pixel values ​​(y). i ,y i+1 ) and (z i ,z i+1 Mapping these numbers onto the Sudoku reference matrix M, the corresponding two numbers become the secret numbers. Based on the block matrix mapping rules, the current two pairs of pixels (y...) can be uniquely determined. i ,y i+1 ) and (z i ,z i+1 The positional relationship of pixels is used to recover the pixel pair values ​​(x) of the original carrier image. i ,x i+1 ).

[0017] S9. Repeat S8, iterating through all pixel pairs (y) of the dense images MI1 and MI2. i ,y i+1 ) and (z i ,z i+1 By using this method, all pixel pairs of CI′ can be determined, resulting in the original carrier image CI = CI′. The extracted secret numbers are then converted into binary bit strings, which are the original secret information.

[0018] Furthermore, in step S4, the specific method for the block matrix mapping rule is as follows:

[0019] The original carrier image CI's pair of pixel values ​​(x) i ,x i+1 When mapped onto the Sudoku reference matrix M, its specific position corresponds to a labeled small cell in the center of the Sudoku puzzle, denoted as M(x). i ,x i+1 The mapping rule of the block matrix is ​​represented as {label, block}, where label represents the label number, and block represents the first number hidden in this 3×3 block matrix; it is stipulated that the second number is always hidden in a certain central block; if M(x i ,x i+1 If the tag number corresponding to M(x) is "1", then the embedding rule is {"1", block1}; if M(x) i ,x i+1 If the tag number corresponding to "2" is "2", then the embedding mapping is {"2", block2}. Correspondingly, the other embedding rules are the same as above. The mapping rules for tags "3", "4", "5", "6", "7", "8", and "9" are {"3", block3}, {"4", block4}, {"5", block5}, {"6", block6}, {"7", block7}, {"8", block8}, and {"9", block9}, respectively.

[0020] Furthermore, in step S4, establishing the quantization distortion model specifically includes:

[0021] Based on the block matrix mapping rule, an initial value D for the distance threshold is set, and the original pixel pair values ​​(x, y, y) are mapped. i ,x i+1 Find the corresponding tag, and then find the two octal numbers that need to be embedded in the two 3×3 block matrices corresponding to that tag; calculate the position coordinates (x, y) of the first number to the tag coordinates. i ,x i+1 The distance from the first number to the second number's position coordinates (x, y) and the distance from the second number to the label's coordinates (x, y). i ,x i+1 The distance ) is the total distance d, which is calculated according to formula (1):

[0022]

[0023] in and These represent the position coordinates of the first and second numbers, respectively; if the distance d exceeds the set distance threshold D, then the pixel pair (x, d) of the original carrier image... i ,x i+1If no information is hidden, and the distance d is less than or equal to the distance threshold, modify the pixel pair value (y). i ,y i+1 ) and (z i ,z i+1 () represents the position coordinates of the two numbers to be hidden. and This process can be represented as:

[0024]

[0025]

[0026] Calculate the embedding distortion (ED) of MI1 and MI2 separately, and then calculate their average value. Until the required embedding capacity is achieved, the average embedding distortion is... Within the minimum error range; embedding distortion ED is calculated using formula (4):

[0027]

[0028] Where H×W represents the pixel size of the carrier image, X mn and Y mn These are the original carrier image and the pixel values ​​after being modified by embedding secret information.

[0029] Therefore, for a given embedding capacity P, the quantization distortion model minimizes With the objective as the condition, P≤EC is the constraint, as shown in equation (5) below:

[0030]

[0031] EC represents the embedding capacity that can be achieved at a set distance threshold.

[0032] The optimal distance threshold D can be determined based on the quantization distortion model. opt This allows us to determine the optimal embedding strategy.

[0033] Furthermore, in step S6, the optimal distance threshold D can be determined based on the quantization distortion model. opt This allows us to determine the optimal embedding strategy. The optimal embedding strategy specifically includes:

[0034] Obtain the optimal distance threshold D opt Then, the pair of pixel values ​​(x, x) of the original carrier image CI are... i ,x i+1 When mapped onto a Sudoku matrix M, its specific position corresponds to a small cell in the center, denoted as M(x). i ,x i+1According to the block matrix mapping rule, find the two octal numbers that need to be embedded in the corresponding block matrix; calculate the pixel pair value (x) of the position coordinates of these two numbers to the original carrier image according to formula (1). i ,x i+1 If the total distance d exceeds the set optimal distance threshold D, then... opt Then the pixel pair value (x) of the original carrier image i ,x i+1 ) without hiding information, the pixel pair values ​​(y) of two dense images i ,y i+1 ) and (z i ,z i+1 ) and original pixel pair (x i ,x i+1 If the distance d is the same as the optimal distance threshold D, it remains unchanged; if the distance d is less than or equal to the optimal distance threshold D, it remains unchanged. opt The position coordinates of the two numbers to be hidden and That is, the values ​​of two new pixel pairs, this process is represented by equations (6) and (7):

[0035]

[0036]

[0037] Pixel pair values ​​(x) of raster scanned original carrier image CI i ,x i+1 Repeat the above steps until all secret information is embedded, and then determine the value (y) of each pair of pixels in the two secret images MI1 and MI2. i ,y i+1 ) and (z i ,z i+1 This generates two complete dense images, MI1 and MI2.

[0038] Furthermore, in step S6, the embedding process includes two special embedding scenarios:

[0039] If the boundary pixel range is [0,2] or [252,255], no information is hidden.

[0040] If M(x) i ,x i+1 If the corresponding label is 5 and the two octal numbers to be hidden are equal, then the position of the number 8 is found in the center block, and its coordinates are assigned to the pixel pair (z) of MI2. i ,z i+1 ).

[0041] Furthermore, in step S9, the method for extracting the secret number also includes a special case.

[0042] If the second extracted number is 8, then change the number 8 to the first number.

[0043] Compared with existing methods, the present invention has the following advantages:

[0044] This invention minimizes image distortion and significantly improves image visual quality by adaptively selecting the optimal distance threshold. Furthermore, the receiving end does not need additional information such as the distance threshold; it only needs to determine whether pixel pairs in two encrypted images are equal to accurately determine if hidden information is present, thereby extracting the complete hidden information and losslessly reconstructing the carrier image. Its operation is extremely simple and practical. This invention uses adaptive embedding by selectively choosing pixel pairs, ensuring that an attacker, even with a encrypted image, cannot extract any information or reconstruct the carrier image, whereas traditional sequential embedding methods can extract half the information. Moreover, the receiving end does not need prior knowledge of the amount of hidden information to determine when data extraction is complete. This invention also effectively resists steganography algorithms such as RS analysis and PDH analysis. Therefore, this invention effectively improves the security of information transmission. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method of the present invention;

[0046] Figure 2 This is a schematic diagram of a Sudoku reference matrix provided in an embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of the center block position labels of a Sudoku matrix provided in an embodiment of the present invention;

[0048] Figure 4 This is a block matrix mapping rule diagram provided in an embodiment of the present invention;

[0049] Figure 5 This is a comparison chart of PSNR performance obtained using the method proposed in this invention;

[0050] Figure 6 The result diagram of the RS analysis using the method proposed in this invention;

[0051] Figure 7 The image shows the results of PDH analysis using the method proposed in this invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the described embodiments are merely some embodiments of this application, and not all embodiments. 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.

[0053] This invention provides an adaptive dual-image reversible information hiding method based on Sudoku matrices. Figure 1 This is a flowchart illustrating the adaptive dual-image reversible information hiding method based on a Sudoku matrix provided in an embodiment of the present invention. Figure 1 As shown, assuming the secret information is {110100000011100100110101…}, following the raster scan order, the pixel pair values ​​(x) of the original carrier image CI are… i ,x i+1 The sequence is {(2,252),(9,9),(10,10),(10,10),(11,11)…}. The preprocessing stage includes the following steps:

[0054] S1. Copy an original carrier image CI to obtain two initial dense images, denoted as MI. 10 and MI 20 .

[0055] S2, such as Figure 2 As shown, a Sudoku reference matrix M with a size of 256×256 is established, where the horizontal and vertical coordinates represent pixel values ​​from 0 to 255 respectively; the Sudoku reference matrix M contains many Sudoku matrices, each of size 9×9; as shown Figure 3 As shown, each central block has 9 small squares. Each small square is labeled with the numbers "1", "2", "3", "4", "5", "6", "7", "8", and "9" in sequence according to the raster scanning order.

[0056] S3. Divide the above secret information into groups of 6 bits each, and convert each group into 2 octal numbers; that is, {6,4,0,3,4,4,6,5,…}.

[0057] Embedding secret information includes the following steps:

[0058] S4. Set the initial distance threshold D = 1.50, and convert a pair of pixel values ​​(x, y, x) of the original carrier image CI. i ,x i+1 Mapped onto the Sudoku reference matrix M, such as Figure 4As shown, according to the block matrix mapping rule, two secret numbers are embedded each time. Based on the required embedding capacity P, a quantization distortion model is established, and the position coordinates of the current two octal numbers to the original pixel pair value (x) are calculated according to formula (1). i ,x i+1 Total distance d:

[0059]

[0060] in and These represent the position coordinates of the two numbers respectively; if the distance d exceeds the set distance threshold D, then the pixel pair (x, d) of the original carrier image... i ,x i+1 If no information is hidden, and the distance d is less than or equal to the distance threshold, modify the pixel pair value (y). i ,y i+1 ) and (z i ,z i+1 ( ) represents the position coordinates of the two numbers to be hidden. and

[0061] S5. Further, for a given embedding capacity P, the quantization distortion model is minimized. As the objective, P≤EC is the constraint condition, as shown in equation (2) below:

[0062]

[0063] EC represents the embedding capacity that can be achieved at a set distance threshold.

[0064] The optimal distance threshold D can be determined based on the quantization distortion model. opt This allows us to determine the optimal embedding strategy.

[0065] S6. Assuming the optimal distance threshold D is obtained opt =3.00, the specific steps of the optimal embedding strategy include: (2,252) are boundary pixels, therefore, no information is hidden.

[0066] The label corresponding to M(9,9) is "1". Based on the numbers 6 and 4 to be hidden, find the positions of the two numbers in the corresponding matrix and calculate... At this point, the second set of pixel pairs (y) of the two dense images MI1 and MI2 are... i ,y i+1 ) and (z i ,z i+1 Change (x, 7) and (9, 9) to (8, 7) and (9, 9); scan the next pixel pair (x, 7). i ,x i+1 ).

[0067] The label corresponding to M(10,10) is "5", and the embedding rule is {"5", block5}. Based on the numbers 0 and 3 to be hidden, the positions of the two numbers are found in the corresponding matrix. d = 2 < 3.00 is calculated. At this point, the third group of pixel values ​​(y) of the two densely packed images MI1 and MI2 are... i ,y i+1 ) and (z i ,z i+1 Change (x) to (11,10) and (10,11); scan the next pixel pair (x) i ,x i+1 ).

[0068] The fourth pixel pair in the original carrier image is also (10,10), and the label corresponding to M(10,10) is "5". Based on the numbers 4 to be hidden, the position of the number 4 is found in the corresponding matrix, and the calculation is performed. At this point, since the numbers to be hidden are equal and M(10,10) corresponds to label 5, the second number is changed to 8. Therefore, the fourth pixel pair values ​​(y) of the two densely packed images MI1 and MI2 are... i ,y i+1 ) and (z i ,z i+1 Change (x) to (9,9) and (9,10); scan the next pixel pair (x) i ,x i+1 ).

[0069] The label corresponding to M(11,11) is "9". Based on the numbers 6 and 5 to be hidden, find the positions of the two numbers in the corresponding matrix and calculate... Continue scanning the next pixel pair until the numbers 6 and 5 are embedded. Then scan the pixel pairs until all information is embedded, finally generating two dense images MI1 and MI2 that are very similar to the original carrier image CI.

[0070] The specific steps for extracting secret information and restoring the original carrier image are as follows:

[0071] S7. The two receiving ends each establish the same Sudoku reference matrix M as the sending end.

[0072] S8. The two receiving ends receive two densely packed images MI1 and MI2 respectively, and their pixel pair values ​​(y i ,y i+1 ) and (z i ,z i+1), respectively {(2,252),(8,7),(11,10),(9,9),(11,11)…}, {(2,252),(9,9)(10,11),(9,10),(11,11)…}; copy the dense image MI1, denoted as CI′.

[0073] The first pair of pixels (y) in two dense images MI1 and MI2 i ,y i+1 ) and (z i ,z i+1 All are (2,252), no numbers are extracted, the pixel pair values ​​(x) of the original carrier image CI. i ,x i+1 (2,252); according to the mapping rules of the block matrix, the secret numbers 6 and 4 can be extracted through (8,7) and (9,9), because the positional relationship of (8,7) and (9,9) belongs to {"1", block1}, and the pixel pair values ​​(x) of the original carrier image CI can be recovered. i ,x i+1 The value is (9,9); the secret numbers 0 and 3 are extracted from (11,10) and (10,11), because (11,10) and (10,11) are both in the center block, and the pixel pair values ​​(x) of the original carrier image CI can be recovered. i ,x i+1 The value is (10,10); the secret numbers 4 and 8 are extracted from (9,9) and (9,10), and the number 8 is transformed into the number 4. Since (9,9) and (9,10) are also in the center block, the pixel pair value (x) of the original carrier image CI is recovered. i ,x i+1 The value is (10,10); due to the fifth pair of pixel values ​​(y) of the two dense images MI1 and MI2. i ,y i+1 ) and (z i ,z i+1 If all values ​​are (11, 11), then no numbers are extracted, and the pixel pair values ​​(x, y) of the original carrier image CI are... i ,x i+1 ) is also (11,11).

[0074] S9. Repeat S8 until all pixel pairs of the two secret images MI1 and MI2 have been traversed, and all pixel pairs of CI′ have been recovered to obtain the original carrier image CI. The extracted secret numbers {6,4,0,3,4,4,6,5,…} are converted into binary bit strings {110100000011100100110101…}, which is the original secret information.

[0075] The experiment of the method of this invention used seven standard 512×512 grayscale images from the USC-SIPI database: Lena, Baboon, Airplane, Barbara, Lake, Boat, and Peppers, and five 512×512 images downloaded from the Internet: Cartoon, Wolf, Bird, Street, and Home. Figure 5 The method proposed in this invention was used to conduct experiments on four different images (wherein) Figure 5 The left figure shows the experimental results of the second dense image MI2, and the right figure shows the experimental results of the first dense image MI1. The peak signal-to-noise ratio (PSNR) of the two dense images is compared. PSNR is calculated according to formulas (3) and (4):

[0076]

[0077]

[0078] Where H×W represents the pixel size of the carrier image, X mn and Y mn These are the pixel values ​​of the original carrier image and the image containing the image, respectively.

[0079] Analyzing the second dense image MI2, when the embedding rate is less than or equal to 0.6 (bit per pixel) bpp, the PSNR of the method of this invention is no lower than that of references [2] and [3]. However, the maximum embedding rates of references [2] and [3] are only 1.0 bpp and 1.07 bpp, respectively, while the embedding rate of this invention can reach 1.5 bpp. Compared with reference [4], the PSNR of this method is improved by 7.79 dB, 6.06 dB and 4.70 dB respectively when the embedding rate is 0.5 bpp, 1.0 bpp and 1.5 bpp. Analyzing the first dense image MI1, when the embedding rate is less than or equal to 0.3 bpp, the PSNR of this method has always maintained the highest level. When the embedding rate is 1.5 bpp, it is still 0.73 dB higher than that of reference [4] on average.

[0080] Table 1 below shows the PSNR performance comparison data of the method of the present invention with three other methods [5], [6], and [7] under small capacity conditions. It can be seen that the present invention shows obvious advantages in PSNR under very small load conditions.

[0081] Table 1

[0082]

[0083] Figure 6To test the RS analysis map obtained from the Lena image using the method of this invention, a masking operator M = {1, 0, 0, 1} is used. For pixel groups G consisting of four adjacent pixels, the flip function F is applied. M and F- M Performing a flipping operation increases the clutter of image patches to the same extent; that is, with the same embedding capacity ratio, at F... M Under the influence of the regularization group, the proportion Rm of all pixel groups is approximately equal to that in F- M Under the influence of the regularization group, the proportion Rm of all pixel groups is [value], in F [value]. M Under the influence of the effect, the proportion of singular groups to all pixel groups, Sm, is approximately equal to that at F- M The proportion Sm of singular groups to all pixel groups under the action indicates that the image has not been steganized, and the present invention can effectively resist RS analysis. Figure 7 To test the PDH analysis diagrams obtained from Boat and Peppers images using the method of this invention, the frequency of the pixel difference between the original carrier image and the dense image was statistically analyzed, and their histograms are shown in the figure. PDH analysis shows that the histograms of the pixel difference between the three images almost overlap, indicating that the dense image and the original carrier image are very similar. Therefore, this invention can effectively resist PDH analysis.

[0084] References:

[0085] [1]Huynh NT,Bharanitharan K,Chang CC.Quadri-directional searching algorithm for secret image sharing using meaningful shadows.Journal of VisualCommunication and Image RepresentationApril 2015;28:105-12.

[0086] [2]Liu Y,Chang CC.A Turtle Shell-based Visual Secret Sharing Scheme with Reversibility and Authentication.Multimedia Tools and ApplicationsFebruary 2018:1-16.

[0087] [3]Lin JY,Chen Y,Chang CC,Hu YC.Dual-image-based reversible datahiding scheme with integrity verification using exploiting modificationdirection.Multimedia Tools andApplications 2019;78:25855-72.

[0088] [4]Chen XF;Hong,C.An Efficient Dual-image Reversible Data HidingScheme Based on Exploiting Modifification Direction.J.Inf.Secur.Appl.2021;58:102702.

[0089] [5]Lee CF,Huang YL.Reversible data hiding scheme based on dualstegano-images using orientation combinations.Telecommunication SystemsJuly2013;52(4):2237-47.

[0090] [6]Chen XF,Guo WL.Reversible Data Hiding Scheme Based on FullyExploiting the Orientation Combinations ofDual Stego-images.InternationalJournal ofNetwork Security March,2019.

[0091] [7]Lin JY,Horng JH,Chang CC,Li YH.Asymmetric Orientation Combinationfor Reversible andAuthenticable Data Hiding ofDual Stego-images.SymmetryApirl2022;14:819.

[0092] The above description is only a few embodiments of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A self-adaptive dual-image reversible information hiding method based on Sudoku matrix, characterized in that, Includes the following steps: S1, copy the original carrier image twice to obtain two initial stego images, denoted as and ; S2, establishing a Sudoku reference matrix The horizontal and vertical coordinates represent 0-255 pixel values, respectively. Sudoku Reference Matrix It contains multiple 9×9 Sudoku matrices, each Sudoku matrix consisting of a 3×3 center piece and eight 3×3 edge pieces surrounding it; The central block has 9 grids, and each grid is labeled with "1", "2", "3", "4", "5", "6", "7", "8", and "9" in sequence according to the raster scanning order; S3. Preprocess the secret information by dividing the secret information of the binary random bit string into groups of 6 bits each, and converting each group into 2 octal secret numbers. S4. Set distance threshold The original carrier image Two consecutive adjacent pixel values and Combining into a pair of pixel values And mapped to a Sudoku reference matrix. Based on the block matrix mapping rules, a quantization distortion model is established according to the required embedding capacity P. The central block and the edge blocks are collectively referred to as the block matrix; In step S4, the block matrix mapping rule is as follows: Original carrier image A pair of pixel values Mapping to Sudoku reference matrix Above, its specific location corresponds to a labeled cell in a central block, denoted as ; The mapping rule of the block matrix is ​​expressed as follows: Where label represents the tag number, block represents embedding the first number in this 3×3 block matrix; the second number is always hidden in the central block; if If the corresponding tag number is "1", then the embedding rule is: ;like The corresponding tag number is "2", so the embedding mapping is Correspondingly, the other embedding rules are the same as above, and the mapping rules for tags "3", "4", "5", "6", "7", "8", and "9" are as follows: , , , , , , ; S5. Based on the quantization distortion model described above, determine the optimal distance threshold. ; S6. Based on the optimal distance threshold The optimal embedding strategy is determined by raster scanning the original carrier image according to the block matrix mapping rule. Each pair of pixel values Based on the optimal embedding strategy, secret numbers are embedded to generate two pairs of pixel values, denoted as... and Until all information is embedded, two encrypted images are finally generated. and ; S7. The two receiving ends establish the same Sudoku reference matrix as the sending end. ; S8, both receivers receive the encrypted image respectively. and , containing dense images and Two consecutive pixel values ​​are grouped into a pair of pixel values; Copying a dense image , recorded as ; raster scanning and Each pair of pixel values and Comparing these two pairs of pixel values, if they are completely identical, it means that the original pixel pair was not used to hide information, and the pixel pair values ​​of the original carrier image are... The values ​​of the current two pairs of pixels and If they are equal; otherwise, the pixel pair values ​​of the original carrier image are equal. Secret information was embedded, and the pixel-to-value pair was... and Mapping to Sudoku reference matrix The two corresponding numbers above are the secret numbers, and according to the block matrix mapping rules, they uniquely determine the current two pairs of pixels. and The positional relationship is used to recover the pixel pair values ​​of the original carrier image. ; S9. Repeat S8 to traverse the dense image. and All pixel pairs and , determine The original carrier image is obtained by taking all pixel pairs. The extracted secret numbers are converted into binary bit strings, which are the original secret information.

2. The adaptive dual-image reversible information hiding method based on Sudoku matrix according to claim 1, characterized in that, In step S2, in the Sudoku matrix: the numbers 0 to 8 appear only once in each column and each row of the Sudoku matrix; the numbers 0 to 8 appear only once in each 3×3 center block and edge block.

3. The adaptive dual-image invertible information hiding method based on Sudoku matrix according to claim 2, characterized in that, In step S4, the specific process of establishing the quantization distortion model is as follows: According to the block matrix mapping rules, the pixel pair values ​​are mapped... Find the corresponding tag, and then find the two currently embedded octal numbers in the two 3×3 block matrices corresponding to that tag; calculate the position coordinates of the first number from the coordinates of the tag. The distance and the position coordinates of the second number to the label coordinates Distance, total distance Calculate according to formula (1): ； in and These represent the position coordinates of the first and second numbers, respectively; if the distance... Exceeding the set distance threshold Then the pixel pairs of the original carrier image No information is embedded, if the distance If the distance is less than or equal to the threshold, modify the pixel pair value. and The position coordinates of the two numbers to be embedded and This process is represented as: ； ； Calculate separately and Embedding distortion Then calculate the average value. Until the embedding capacity is reached, the average embedding distortion is... Achieving minimal error; embedding distortion Calculated using formula (4): ； Where H×W represents the pixel size of the carrier image, and These are the original carrier image and the modified pixel values ​​after embedding secret information; Therefore, for a given embedding capacity P, the quantization distortion model minimizes With the goal, The constraints are as shown in equation (5) below: ； in, This indicates the embedding capacity that can be achieved at a set distance threshold.

4. The adaptive dual-image reversible information hiding method based on Sudoku matrix according to claim 3, characterized in that, In step S6, determining the optimal embedding strategy specifically includes the following process: Obtain the optimal distance threshold Then, the original carrier image A pair of pixel values Mapping to Sudoku matrix Above, its specific position corresponds to a central block cell, denoted as According to the block matrix mapping rule, find the two currently embedded octal numbers in the corresponding block matrix; calculate the pixel pair values ​​from the position coordinates of these two numbers to the original carrier image according to formula (1). Total distance If the distance Exceeding the set optimal distance threshold Then the pixel pair values ​​of the original carrier image Without embedding information, pixel pairs of two dense images and and original pixel pair If the distance is the same, it remains unchanged; if the distance is... Less than or equal to the optimal distance threshold The position coordinates of the two numbers to be embedded and That is, the values ​​of two new pixel pairs, this process is represented by equations (6) and (7): ； ； raster scan of raw carrier image pixel pair value Repeat the above steps until all secret information is embedded, thus identifying the two secret images. and Each pair of pixel values and This generates two dense images. and .

5. The adaptive dual-image reversible information hiding method based on Sudoku matrix according to claim 4, characterized in that, In step S6, the embedding process includes the following two special embedding scenarios: If the boundary pixel range is [0, 2] or [252, 255], no information is embedded; like If the corresponding tag is 5 and the two octal numbers to be embedded are equal, then find the position of the number 8 in the center block and assign its coordinates to it. pixel pairs .

6. The adaptive dual-image reversible information hiding method based on Sudoku matrix according to claim 5, characterized in that, In step S9, extracting the secret secret number also includes a special case: If the second extracted number is 8, then change the number 8 to the first number.

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