CN111179144B - Efficient information hiding method for multi-embedding of multi-system secret information - Google Patents
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Abstract
The invention relates to a high-efficiency information hiding method for multi-embedding of multi-system secret information, which is characterized in that a reference matrix is partitioned by utilizing a distribution rule of reference matrix values in a DE algorithm, a new reference matrix is formed in the center of each partition, the distribution rule of the new reference matrix is the same as that of an original reference matrix, and the like, the reference matrix newly generated after each partition has the same distribution rule as that of the original reference matrix. Through multiple embedding, the information hiding capacity is multiplied and obviously increased, and all embedded secret information can be recovered without distortion. In addition, the method has similar performance after hiding information by taking images with different complexities as carriers, has good adaptability to the complexity of the carrier images and is more widely applied. Finally, the secret information is embedded for multiple times, so that the anti-detection capability of the hidden information can be improved, and the security transmission of the secret information is guaranteed.
Description
Technical Field
The invention relates to a data communication method, in particular to a multi-system secret information multi-embedding efficient information hiding method, and belongs to the field of communication (such as data communication technology and the like).
Background
The information hiding technology utilizes the visual redundancy of human eyes to embed the secret information to be transmitted into a digital multimedia carrier to form a code stream which contains secret multimedia information or cannot be identified so as to achieve the purposes of safe storage, secret transmission and the like of the information. The information hiding capacity and the dense image quality are very important indexes for measuring the performance of the hiding algorithm.
The spatial domain information hiding method is widely applied in practice due to the characteristics of large hiding capacity, simple realization and the like. Typical methods, such as EMD, FEMD, DE, etc., match a value obtained by combining pixel values calculated according to a certain matching function with secret information, and if the two are not equal, modify the pixel value to make the result of the matching function equal to the secret information, thereby implementing information hiding. The method is very simple in extracting the secret information, large in hidden capacity and high in quality of the secret image, and therefore the method is widely concerned. The DE algorithm calculates a diamond characteristic value by using a carrier pixel pair, then modifies the diamond characteristic value into a value equal to secret information by adjusting the pixel value, and changes a parameter k to realize embedding of secret information with different capacities and different systems.
Disclosure of Invention
The technical problem solved by the invention is as follows: the defects of the prior art are overcome, and a high-efficiency information hiding method for embedding multi-system secret information for multiple times is provided; the method uses the distribution rule of reference matrix value in DE (Diamond Encoding) algorithm to divide the reference matrix into blocks, the center of each block forms a new reference matrix, the distribution rule is the same as the distribution rule of the original reference matrix, and so on, the newly generated reference matrix after each block has the same distribution rule as the original reference matrix, and by using the characteristic, the multiple embedding of secret information can be realized, and the correct extraction of the last embedded information can not be influenced by each embedding. Through multiple embedding, the information hiding capacity is remarkably increased by times, and all embedded secret information can be recovered without distortion. In addition, the performance of the method is similar after the information hiding is carried out by taking the images with different complexities as carriers, namely the method has good adaptability to the complexity of the carrier images and is more widely applied. Moreover, when the parameter k takes different values, the method can hide secret information of various systems, and changes the limitation of a single system of conventional secret information. Finally, the secret information is embedded for multiple times, so that the anti-detection capability of the hidden information can be improved, and the security transmission of the secret information is guaranteed.
The technical scheme for solving the problems is as follows: a multi-embedded efficient information hiding method for multi-system secret information comprises the following steps:
(1) Load settingThe volume is 8bit quantization image, according to secret information embedding quantity, with DE algorithm hidden capacity as reference, according to k =1, N increases 1 every time the hidden capacity increases 1.1bpp, k =2, N increases 1 every time the hidden capacity increases 1.8bpp, k =3, N increases 1 every time the hidden capacity increases nearly 2.3bpp, information embedding parameter k and information embedding times N are determined, wherein k is more than or equal to 1 and less than or equal to 3,1 and less than or equal to N and less than or equal to 4, so that the secret information to be hidden can be completely hidden in the carrier image, and the binary secret information to be hidden is converted into B scale, B =2k 2 +2k+1；
(2) Constructing a reference matrix M 1 ,M 2 ,…,M N ；
(3) Preprocessing the pixel values which possibly overflow in the carrier image according to the information embedding parameter k and the information embedding times N, and ensuring that the secret information can be extracted without damage;
(4) Pairing adjacent pixels in the carrier image, and applying DE algorithm to reference matrix M N The first information hiding is carried out, namely: given a pair of carrier pixels (g) 1 ,g 2 ) Calculating a pixel pair (g) 1 ,g 2 ) In the reference matrix M N Of (c) and corresponding pixel pair (g' 1 ,g' 2 )＝(floor(g 1 /s N-1 ),floor(g 2 /s N-1 ) Wherein g' 1 ,g' 2 The value range is [0,floor (256/s) N-1 )-1]Then using the reference matrix M in step (2 c) N And M 1 The pixel pair (g ') is obtained by calculation' 1 ,g' 2 ) Corresponding reference matrix value f 1 ＝M N [g' 1 ,g' 2 ]Judgment f 1 With secret bits b to be hidden 1 Whether they are equal;
(4a) If f is 1 ＝b 1 Then pixel pair (g' 1 ,g' 2 ) As a result of the first information hiding and in the reference matrix M N-1 Continuously hiding the next bit of secret information;
(4b) If f is 1 ≠b 1 Then in the reference matrix M N In pixel pair (g' 1 ,g' 2 ) As a center, searching in a block with the size of s multiplied by s, wherein the searching range is as follows: [g' 1 -(s-1)/2:g' 1 +(s-1)/2,g' 2 -(s-1)/2:g' 2 +(s-1)/2](ii) a According to the reference matrix pixel distribution rule, two groups satisfying M can be found N [g x ,g y ]＝b 1 Are respectively denoted as (g) x1 ,g y1 ) And (g) x2 ,g y2 ) As a result of the first information hiding;
(5) Using DE algorithm in reference matrix M N-1 Hiding next bit secret information b in 2 ；
(6) Completing the secret information b of the carrier pixel pair for the Nth time by class push N Then calculates all the dense pixel pairs and the carrier pixel pairs (g) separately 1 ,g 2 ) Selecting the closest pixel pair as the final hiding result;
(7) And (4) repeatedly executing the steps (4) to (6) until the secret information is completely hidden.
The specific process of the step (2) is as follows:
(2a) Using formula M 1 (g 1 ,g 2 )＝mod((2k+1)×g 1 +g 2 And B) constructing a reference matrix M 1 Wherein the pixel value g 1 ,g 2 Has a value of [0,255%]Reference matrix M 1 The size is 256 × 256;
(2b) Will refer to the matrix M 1 Dividing the data into blocks of s multiplied by s, wherein s =2k +1, and the rest data appear twice in each block except the central point; all block center points form a new reference matrix M 2 Floor (256/s) x floor (256/s), which represents rounding down, where the value distribution law and M are 1 Same, i.e. reference matrix M 2 The data are divided into blocks of size of s multiplied by s, and the rest data appear twice in each block except the central point, so that the requirement of embedding the secret information again is met;
(2c) By analogy, N new reference matrixes M are obtained 1 ,…,M N Where N = floor (log) s 256)；
When N is more than or equal to 2, the reference matrix M N Middle element and M N-1 The correspondence of (a) is as follows:
M N (x,y)＝M N-1 (sx+k,sy+k)
obtaining a reference matrix M through iterative operation N Middle element and M 1 The correspondence of (a) is as follows:
M N (x,y)＝M 1 (s N-1 x+(s N-2 +s N-3 +…+s+1)k,s N-1 y+(s N-2 +s N-3 +…+s+1)k)
＝mod(s×(s N-1 x+(s N-2 +s N-3 +…+s+1)k)+s N-1 y+(s N-2 +s N-3 +…+s+1)k,B)
＝mod(s N x+s N-1 y+s N-1 k+2(s N-2 +s N-3 +…+s)k+k,B)。
the calculation method for preprocessing the pixel values which may overflow in the carrier image in the step (3) comprises the following steps: calculate the lower limit of pixel values T =256-mod (256, (2k + 1) N-1 ) When the pixel value in the carrier image overflows the lower limit value T, the pixel value is set to [ T,255 ]]All pixels within the range are set to T-1.
The specific process of the step (5) is as follows:
(5a) F calculated if information is first hidden 1 ＝b 1 Then, the pixel pair (g ') is directly used' 1 ,g' 2 ) Corresponding to the reference matrix M N-1 Is divided into blocks to perform the second information hiding, namely in the pixel range of g' 1 ×s:(g' 1 +1)×s-1,g' 2 ×s:(g' 2 +1)×s-1]Find in and satisfy M N-1 [p 1 ,p 2 ]＝b 2 Pixel pair (p) 1 ,p 2 ) (ii) a If there are two pixel pairs satisfying the condition, they are respectively written as (g' x1 ,g' y1 ) And (g' x2 ,g' y2 ) As a result of the second information hiding;
(5b) F calculated if information is first hidden 1 ≠b 1 Then the secret information b is hidden according to step 4b 1 Then, two intermediate dense pixel pairs (g) are obtained x1 ,g y1 ) And (g) x2 ,g y2 ) (ii) a Using the two pairs of pixels separatelyCorresponding to the reference matrix M N-1 Is subjected to a second information hiding, i.e. in the pixel range g x1 ×s:(g x1 +1)×s-1,g y1 ×s:(g y1 +1)×s-1]Find in and satisfy M N-1 [p 1 ,p 2 ]＝b 2 If there are two pixel pairs satisfying the condition, they are respectively expressed as (m) 1 ,n 1 ) And (m) 2 ,n 2 ) (ii) a And in the pixel region g x2 ×s:(g x2 +1)×s-1,g y2 ×s:(g y2 +1)×s-1]Find in and satisfy M N-1 [q 1 ,q 2 ]＝b 2 If there are two pixel pairs satisfying the condition, the two pixel pairs are respectively expressed as (u) 1 ,v 1 ) And (u) 2 ,v 2 ) (ii) a All pixel pairs that satisfy the condition are taken as a result of the second information hiding.
Compared with the prior art, the invention has the advantages that:
the invention realizes the multiple embedding of various system secret information according to the distribution rule of the value taking of the DE reference matrix, and improves the embedding capacity and the anti-detection capability of the information hiding method.
Compared with the prior art, the invention has the following substantive differences and progresses:
(1) According to the distribution rule of the values of the DE reference matrix, the reference matrix is partitioned, the distribution rule of the reference matrix formed by the center of each partition is the same as that of the original reference matrix, and the characteristic is utilized to realize multiple embedding of secret information, so that the embedding capacity of the hiding method is improved in a multiplied way;
(2) The secret information can be selected from various systems, so that the limitation of the conventional single-system secret information is broken, and the requirements of more application scenes are met;
(3) One carrier pixel pair can realize multiple times of secret information embedding, the concealment is better under the condition of not knowing a concealment method, and the detection resistance of the secret information is improved;
(4) The method has the advantages that the information hiding performance is not influenced by the complexity of the carrier image, the application scene is wider, and the adaptability is stronger.
Drawings
Fig. 1 refers to a matrix schematic (k =1, b =5, n = 2);
fig. 2 shows that the carrier images used in the simulation of the present invention are all 8-bit quantized natural images, and the size is 512 × 512.
Detailed Description
The invention provides a high-efficiency information hiding method for multi-time embedding of multi-system secret information, which can improve the hiding capacity of a DE method by times when the parameters k are the same. Meanwhile, the method has the characteristics of no influence of the complexity of the carrier image, high safety and the like, thereby having practical value in ground systems and spacecraft engineering.
The following further describes embodiments of the present invention with reference to the accompanying drawings.
Fig. 1 shows a schematic diagram of a reference matrix, where k =1,b =5,n =2.
The process steps for realizing the secondary embedding of the five-system secret information by the method of the invention are as follows:
(1) The carrier is an 8-bit quantized image, and the binary secret information to be hidden is converted into a 5-system according to the information embedding parameter k.
(2) Constructing a reference matrix M 1 And M 2 。
The reference matrix M is constructed 1 And M 2 The method comprises the following steps:
(2a) Using the formula M 1 (g 1 ,g 2 )＝mod((2k+1)×g 1 +g 2 And B) constructing a reference matrix M 1 Wherein g is 1 ,g 2 Has a value of [0,255%]，M 1 The size is 256 × 256, as shown in fig. 1.
(2b) Will refer to the matrix M 1 Dividing the data into blocks with the size of 3 multiplied by 3, wherein the rest data of each block except the central point appear twice in the block; all block center points (shown in bold circle in FIG. 1) form a new reference matrix M 2 The size is 85 × 85, wherein the numerical distribution rule and M 1 Same, i.e. reference matrix M 2 The data is divided into blocks of 3 multiplied by 3, and the rest data of each block except the central point appears twice in the block, so that the requirement of embedding the secret information again is met.
Reference momentMatrix M 2 Middle element and M 1 The correspondence of (c) is as follows:
M 2 (x,y)＝M 1 (sx+k,sy+k)＝mod(s 2 x+sy+sk+k,5)
(3) And (5) preprocessing a carrier image. All of the pixel values 255 are set to 254.
(4) Pairing adjacent pixels in the carrier image, and applying DE algorithm to reference matrix M 2 The first information hiding is carried out, namely: given a pair of carrier pixels (g) 1 ,g 2 ) Calculating it at the reference matrix M 2 Of (c) and corresponding pixel pair (g' 1 ,g' 2 )＝(floor(g 1 /3),floor(g 2 /3)) wherein g' 1 ,g' 2 The value range is [0,84]Then using the reference matrix M of claim step 2c 2 And M 1 Calculating the corresponding reference matrix value f of the pixel pair 1 ＝M 2 [g' 1 ,g' 2 ]Judgment f 1 With secret bits b to be hidden 1 Whether or not equal.
(4a) If f is 1 ＝b 1 Then pixel pair (g' 1 ,g' 2 ) As a result of the first information hiding and in the reference matrix M 1 Continuously hiding the next bit of secret information;
(4b) If f is 1 ≠b 1 Then in the reference matrix M 2 In pixel pair (g' 1 ,g' 2 ) As a center, search within a block of size 3 × 3, the search range being: [ g' 1 -1:g' 1 +1,g' 2 -1:g' 2 +1]. According to the reference matrix pixel distribution rule, two groups satisfying M can be found 2 [g x ,g y ]＝b 1 Are respectively denoted as (g) x1 ,g y1 ) And (g) x2 ,g y2 ) As a result of the first information hiding;
(5) Using DE algorithm in reference matrix M 1 Hiding next bit secret information b in 2 ；
(5a) F calculated if information is first hidden 1 ＝b 1 Then the pixel pair (g ') can be directly utilized' 1 ,g' 2 ) Corresponding to the reference matrix M 1 Is divided into blocks to perform the second information hiding, namely in the pixel range of g' 1 ×3:(g' 1 +1)×3-1,g' 2 ×3:(g' 2 +1)×3-1]Find in and satisfy M 1 [p 1 ,p 2 ]＝b 2 Pixel pair (p) 1 ,p 2 ). If there are two pixel pairs satisfying the condition, they are respectively written as (g' x1 ,g' y1 ) And (g' x2 ,g' y2 ) As a result of the second information hiding;
(5b) F calculated if information is first hidden 1 ≠b 1 Then the secret information b is hidden according to step 4b 1 Thereafter, two intermediate dense pixel pairs (g) are obtained x1 ,g y1 ) And (g) x2 ,g y2 ). Corresponding to the reference matrix M by using the two pixel pairs respectively 1 Is subjected to a second information hiding, i.e. in the pixel range g x1 ×3:(g x1 +1)×3-1,g y1 ×3:(g y1 +1)×3-1]Find in and satisfy M 1 [p 1 ,p 2 ]＝b 2 If there are two pixel pairs satisfying the condition, they are respectively expressed as (m) 1 ,n 1 ) And (m) 2 ,n 2 ) (ii) a And in the pixel region g x2 ×3:(g x2 +1)×3-1,g y2 ×3:(g y2 +1)×3-1]Find in and satisfy M 1 [q 1 ,q 2 ]＝b 2 If there are two pixel pairs satisfying the condition, the two pixel pairs are respectively expressed as (u) 1 ,v 1 ) And (u) 2 ,v 2 ) Taking all pixel pairs meeting the condition as a result of the second-time information hiding;
(6) Calculating all dense pixel pairs and carrier pixel pairs (g) respectively 1 ,g 2 ) The closest pair of pixels is selected as the final concealment result.
(7) And repeating the steps 4 to 6 until the secret information is completely hidden.
The information extraction process is very simple, and the steps are as follows:
(1) Determining a secret information system number B (B = 5) according to the parameter k;
(2) Pairing adjacent pixels of the dense image (StegoP) 1 ,stogoP 2 ) Each pixel pair extracts 2 bits of secret information;
the secret information extraction step is as follows:
(2a) Computing dense pixel pairs in a reference matrix M 2 The formula is as follows:
g x ＝floor(stegoP 1 /s),g y ＝floor(stogoP 2 /s), wherein s =3;
(2b) According to b' 1 ＝M 2 [g x ,g y ]Extracting first bit secret information b' 1 ；
(2c) According to b' 2 ＝mod(3×stegoP 1 +stogoP 2 And 5) extracting 2 nd bit secret information b' 2 ；
(3) And (5) repeatedly executing the step (2) until all the secret information is extracted.
(4) And converting the 5-system secret information into binary data, namely the secret information which is recovered in a lossless mode.
To verify the performance of the present invention, 6 8-bit natural images (as shown in fig. 2) with a size of 512 × 512 were used in the simulation experiment. The invention is respectively adopted for information hiding of different images, and the results are shown in table 1 when the information hiding capacity is compared with that of different embedding times. Where the maximum number of embeddings N for k =2 and k =3 is 3 and 2, respectively.
TABLE 1 hidden Capacity comparison results
| Parameter k | N＝1 | N＝2 | N＝3 | N＝4 |
| k＝1 | 1.16bpp | 2.31bpp | 3.47bpp | 4.63bpp |
| k＝2 | 1.85bpp | 3.70bpp | 5.54bpp | / |
| k＝3 | 2.32bpp | 4.64bpp | / | / |
The hidden capacity when the number of embedding times N =2 was selected and compared with the hidden capacity of the classical DE algorithm, and the results are shown in table 2.
Table 2 hidden capacity comparison results with DE algorithm
Compared with the DE algorithm, the hidden capacity can be increased by 1 time under the condition that the value of the parameter k is the same, namely the hidden capacity of the method is 2 times of that of the DE algorithm, which shows that the method fully utilizes the distribution rule of the reference matrix value when embedding for multiple times, and realizes the multiple increase of the hidden capacity.
In addition, the quality of different dense images was also tested, and the experimental results are shown in table 3.
TABLE 3 concealment Performance of test images
From table 3, it can be found that the hidden capacity of the carrier images with different complexities is almost the same as the PSNR of the dense images, which indicates that these image differences hardly affect the hiding performance of the method, i.e. the method is not sensitive to the carrier complexity and is suitable for information hiding of various image data.
According to the distribution rule of the value of the DE reference matrix, the invention divides the DE reference matrix into blocks and then uses the center of each block to form a new reference matrix to embed the secret information for multiple times, and the secret information can be recovered without distortion, thereby multiplying the hidden capacity of the secret information. The method has the advantages that the information hiding performance is not influenced by the complexity of the carrier image, and the application scene is wider.
Those skilled in the art will appreciate that the details of the invention not described in detail in this specification are well within the skill of those in the art.
Claims (4)
1. A multi-embedded efficient information hiding method for multi-system secret information is characterized by comprising the following steps:
(1) Setting a carrier as an 8-bit quantized image, taking DE algorithm hidden capacity as reference according to secret information embedding amount, when N is increased by 1 every time when k =1, the hidden capacity is increased by about 1.1bpp, k =2, and N is increased by 1 every time when N is increased by 1 and the hidden capacity is increased by about 1.8bpp, k =3, and when N is increased by 1 and the hidden capacity is increased by about 2.3bpp, determining an information embedding parameter k and an information embedding time N, wherein k is more than or equal to 1 and less than or equal to 3,1 and more than or equal to N and less than or equal to 4, so that secret information to be hidden can be completely hidden in the carrier image, converting binary secret information to be hidden into a B scale, and B =2k 2 +2k+1；
(2) Constructing a reference matrix M 1 ,M 2 ,…,M N ；
(3) Preprocessing the pixel values which possibly overflow in the carrier image according to the information embedding parameter k and the information embedding times N, and ensuring that the secret information can be extracted without damage;
(4) Pairing adjacent pixels in the carrier image, and applying DE algorithm to reference matrix M N The first information hiding is carried out, namely: given a pair of carrier pixels (g) 1 ,g 2 ) Calculating a pixel pair (g) 1 ,g 2 ) In the reference matrix M N Of (c) corresponding pixel pair (g' 1 ,g' 2 )＝(floor(g 1 /s N-1 ),floor(g 2 /s N-1 ) Wherein g' 1 ,g' 2 The value range is [0,floor (256/s) N-1 )-1]Then using the reference matrix M in step (2 c) N And M 1 The pixel pair (g ') is obtained by calculation' 1 ,g' 2 ) Corresponding reference matrix value f 1 ＝M N [g' 1 ,g' 2 ]Judgment f 1 With secret bits b to be hidden 1 Whether they are equal;
(4a) If f is 1 ＝b 1 Then pixel pair (g' 1 ,g' 2 ) As a result of the first information hiding and in the reference matrix M N-1 Continuously hiding the next bit of secret information;
(4b) If f is 1 ≠b 1 Then in the reference matrix M N In pixel pair (g' 1 ,g' 2 ) As a center, searching in a block with the size of s multiplied by s, wherein the searching range is as follows: [ g' 1 -(s-1)/2:g' 1 +(s-1)/2,g' 2 -(s-1)/2:g' 2 +(s-1)/2](ii) a According to the reference matrix pixel distribution rule, two groups satisfying M can be found N [g x ,g y ]＝b 1 Are respectively denoted as (g) x1 ,g y1 ) And (g) x2 ,g y2 ) As a result of the first information hiding;
(5) Using DE algorithm in reference matrix M N-1 Hiding next bit secret information b in 2 ；
(6) The secret information b of the carrier pixel pair for the Nth time is finished by class deduction N Is then calculated separatelyAll dense pixel pairs and carrier pixel pairs (g) 1 ,g 2 ) Selecting the closest pixel pair as the final hiding result;
(7) And (4) repeatedly executing the steps (4) to (6) until the secret information is completely hidden.
2. The efficient information hiding method for multi-embedding of multilevel secret information according to claim 1, wherein: the specific process of the step (2) is as follows:
(2a) Using formula M 1 (g 1 ,g 2 )＝mod((2k+1)×g 1 +g 2 And B) constructing a reference matrix M 1 Wherein the pixel value g 1 ,g 2 Has a value of [0,255%]Reference matrix M 1 The size is 256 × 256;
(2b) Will refer to the matrix M 1 Dividing the data into blocks of s multiplied by s, wherein s =2k +1, and the rest data appear twice in each block except the central point; all block center points form a new reference matrix M 2 Floor (256/s) x floor (256/s), which represents rounding down, where the value distribution law and M are 1 Same, i.e. reference matrix M 2 The data are divided into blocks of s multiplied by s size, and other data appear twice in each block except the central point, so that the requirement of embedding secret information again is met;
(2c) By analogy, N new reference matrixes M are obtained 1 ,…,M N Where N = floor (log) s 256)；
When N is more than or equal to 2, the reference matrix M N Middle element and M N-1 The correspondence of (a) is as follows:
M N (x,y)＝M N-1 (sx+k,sy+k)
obtaining a reference matrix M through iterative operation N Middle element and M 1 The correspondence of (a) is as follows:
M N (x,y)＝M 1 (s N-1 x+(s N-2 +s N-3 +…+s+1)k,s N-1 y+(s N-2 +s N-3 +…+s+1)k)
＝mod(s×(s N-1 x+(s N-2 +s N-3 +…+s+1)k)+s N-1 y+(s N-2 +s N-3 +…+s+1)k,B)
＝mod(s N x+s N-1 y+s N-1 k+2(s N-2 +s N-3 +…+s)k+k,B)。
3. the efficient information hiding method for multi-embedding of multilevel secret information according to claim 2, wherein: the calculation method for preprocessing the pixel values which may overflow in the carrier image in the step (3) comprises the following steps: calculate the lower limit of pixel values T =256-mod (256, (2k + 1) N-1 ) When the pixel value in the carrier image overflows the lower limit value T, the pixel value is set to [ T,255 ]]All pixels within the range are set to T-1.
4. The method for efficient hiding of information of multilevel secret information multi-embedding according to claim 2, wherein: the specific process of the step (5) is as follows:
(5a) F calculated if information is first hidden 1 ＝b 1 Then, the pixel pair (g ') is directly used' 1 ,g' 2 ) Corresponding to the reference matrix M N-1 Is divided into blocks for the second information hiding, i.e. in the pixel range of g' 1 ×s:(g' 1 +1)×s-1,g' 2 ×s:(g' 2 +1)×s-1]Find in and satisfy M N-1 [p 1 ,p 2 ]＝b 2 Pixel pair (p) 1 ,p 2 ) (ii) a If there are two pixel pairs satisfying the condition, they are respectively written as (g' x1 ,g' y1 ) And (g' x2 ,g' y2 ) As a result of the second information hiding;
(5b) F calculated if information is first hidden 1 ≠b 1 Then the secret information b is hidden according to step 4b 1 Then, two intermediate dense pixel pairs (g) are obtained x1 ,g y1 ) And (g) x2 ,g y2 ) (ii) a Corresponding to the reference matrix M by using the two pixel pairs respectively N-1 Is subjected to a second information hiding, i.e. in the pixel range g x1 ×s:(g x1 +1)×s-1,g y1 ×s:(g y1 +1)×s-1]Find in and satisfy M N-1 [p 1 ,p 2 ]＝b 2 If there are two pixel pairs satisfying the condition, they are respectively expressed as (m) 1 ,n 1 ) And (m) 2 ,n 2 ) (ii) a And in the pixel region g x2 ×s:(g x2 +1)×s-1,g y2 ×s:(g y2 +1)×s-1]Interior found satisfies M N-1 [q 1 ,q 2 ]＝b 2 If there are two pixel pairs satisfying the condition, the two pixel pairs are respectively expressed as (u) 1 ,v 1 ) And (u) 2 ,v 2 ) (ii) a All pixel pairs that satisfy the condition are taken as a result of the second information hiding.
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