CN100536387C - Anti interference information hidding method based on turbo code and image carrier - Google Patents

Abstract

This invention provides a method for hiding anti-interference information based on Turbo code and image carrier, which contains making two dimension discrete cosine transform to image carrier in transmission terminal, making Turbo coding to information sequence to be hidden to obtain intermediate frequency area of coding sequence embedded discrete cosine transform block, sending channel for transmission, receive terminal taking Turbo coding sequence and Turbo decoding, recovering hidden image data from decoding sequence, the hidden information is arbitrary format text or arbitrary format image, converting to binary data before Turbo coding and converting to multi-number- system. Said invention realizes the anti-interference almost distortionless hiding using human vision insensitive property to intermediate area of image.

Description

Anti-interference information concealing method based on Turbo code and image-carrier

Technical field

The present invention relates to a kind of information concealing method, belong to information security, secure communication and multimedia application field.

Background technology

In information security, there are a kind of demand in secure communication and multimedia application field: certain specific information is hidden in the image, and this specific information is used as the sign of ownership or authentication, or as the secure communication data.What adopt the generation of existing encryption technology processing image is unreadable file, and require original image in information security, secure communication and multimedia application field must be readable and visible, and therefore to be not suitable for the image be the Information hiding of carrier to existing encryption technology.Adopt existing method, be that the Information hiding of carrier exists 3 problems with the image: 1, hiding Info does not have anti-interference or attacking ability, and 2, hiding Info makes the image-carrier distortion, 3, hiding Info changes the image-carrier data volume.

Existing digital information hidden method is anti-interference and anti-attack ability is poor, thereby when running into electronic jamming and electronic attack, hiding Info in the image-carrier lost substantially, can't use.If directly the image-carrier data that hide Info are carried out the Turbo coding, as adopt number of patent application: 200410046234.6, the method of denomination of invention " a kind of digital information anti-interference encryption method and system " based on the Turbo encoding and decoding, though can make image-carrier and hide Info possesses anti-interference or attacking ability simultaneously, but the traffic rate that makes communication system reduces 2-3 doubly, increase data volume 2-3 doubly, bring white elephant to communication system.

Disclosed Turbo decoding method document has: C.Berrou, A.Glavieux and P.Thitimajshima.Near Shannon limit error-correcting coding and decoding:Turbo-codes (1) .Proc.ICC ' 93.Geneva, Switzerland, May, 1993:1064～1074, yellow and refined, Xiao Yang, research of Turbo encoding and decoding algorithm and Performance Evaluation under the low signal-to-noise ratio, railway society, 2004,26 (2): 66-71.The Turbo decoding method has been applied to the communications field.

Summary of the invention

Technical problem to be solved by this invention: 1, hide Info and do not have anti-interference or attacking ability, 2, hiding Info makes the image-carrier distortion, 3, hiding Info changes the image-carrier data volume.

Do not have anti-interference or attacking ability for solution hides Info, the present invention proposes only hiding data to be carried out the Turbo encoding and decoding, the image-carrier that hides Info is carried out discrete cosine transform, intermediate frequency zone at the two-dimension discrete cosine transform of image-carrier hides the Turbo coded data, when image-carrier after the Channel Transmission process is interfered or attacks, the recipient still can utilize the Turbo decoding algorithm to recover the data that hide Info disturbed or that attack, avoids or reduces to hide Info and disturbed or attack and the distortion that produces.

For solution hides Info to make the image-carrier distortion and hide Info the image-carrier data volume is changed, the present invention utilizes people's visual experience insensitive to the data in vision intermediate frequency zone, with the intermediate frequency zone of the discrete cosine transformation block of the Turbo coded sequence embedded images carrier that hides Info.

Technical scheme of the present invention:

Anti-interference information concealing method based on Turbo code and image-carrier: transmitting terminal is done the piecemeal two-dimension discrete cosine transform with image-carrier, the information sequence that need are hidden carries out the Turbo coding simultaneously, the Turbo coded sequence that obtains embeds the intermediate frequency zone of discrete cosine transformation block, the transmission of delivering letters again; Receiving terminal is from the intermediate frequency extracted region Turbo coded sequence of the discrete cosine transformation block that receives view data and carry out the Turbo decoding, restore the data that hide Info by decoding sequence, the two-dimension discrete cosine transform piece after being hidden Info by extraction simultaneously recovers source image data; Wherein hiding Info is arbitrary format text data or arbitrary format view data, is converted to binary data before the Turbo coding, is converted to the multi-system data after the Turbo decoding.

The present invention compares the beneficial effect that is had with prior art:

Anti-interference information concealing method based on Turbo code and image-carrier proposed by the invention, the visual experience that has utilized the people has been realized anti-interference approximate undistorted hiding to security information to the vision intermediate frequency insensitive characteristic in zone and the excellent error-correcting performance of Turbo decoding.The present invention utilizes human eye to the insensitive visual characteristic of the intermediate frequency zone of view data, select the intermediate frequency zone of the piecemeal discrete cosine transform of image to embed binary hiding Info, replaced the image data value in discrete cosine transformation block intermediate frequency zone with the sequence that hides Info, embodiment verifies that method of the present invention had not only reduced to embed the distortion factor of image but also can not increase the memory space of image of hiding Info.The present invention utilizes the error-correcting performance and the antijamming capability of Turbo code excellence, has realized extracting the hi-fi that hides Info, and guarantees the integrality that hides Info.This method can expand in the approximate undistorted Information Hiding Techniques of multiple image sequence (being video), can avoid the less shortcoming of single image concealing amount of information; Can apply to hiding of security information, and the field that can apply to military affairs and have the height communication security to require.

Description of drawings

Fig. 1 Information hiding flow process.

Fig. 2 information extraction flow process.

The embedding grammar that Fig. 3 hides Info (is example with the multi-grey image).

The extracting method that Fig. 4 hides Info (is example with the multi-grey image).

Fig. 5 is original to hide Info.

Fig. 6 original image.

Fig. 7 embeds the image (before the image transmission) after hiding Info.

Image that Fig. 8 embedding hides Info and the pixel value error between original image.

Image after Fig. 9 is interfered (transmission back).

What Figure 10 extracted from disturbed image hides Info.

Embodiment

Based on the anti-interference information concealing method of Turbo code and image-carrier, the information sequence of hiding is carried out the Turbo encoding and decoding, making hides Info has certain anti-interference or attacking ability; Employing is to the piecemeal two-dimension discrete cosine transform of image-carrier, embeds the Turbo coded sequence that hides Info in the intermediate frequency zone of two-dimension discrete cosine transform piece and makes image-carrier not have obvious distortion and hide Info the image-carrier data volume is changed.The image-carrier data that embedding the hides Info transmission of delivering letters.The Turbo coded sequence of the information sequence that receiving terminal is hidden from the extraction of the view data that receives also carries out the Turbo decoding, recovers to hide Info data by decoding sequence.Carry out Data Format Transform during the Turbo encoding and decoding to hiding Info, thereby the information of hiding can be arbitrary format text data or arbitrary format view data.Embodiment is as follows.

1. transmitting terminal: based on the Information hiding of Turbo code

The flow process of Information hiding as shown in Figure 1, its step is as follows:

Step 1 is selected the source images among image-carrier such as Fig. 1, and image-carrier can be many gray scales black and white image and coloured image;

Step 2 is carried out the piecemeal two-dimension discrete cosine transform DCT of N * N to source images, adopts and realizes as " piecemeal two-dimensional dct " module among Fig. 1;

Step 3, the data that will hide Info are converted to binary data, adopt " being converted to two value informations " module among Fig. 1 to realize.

Step 4, carry out the Turbo coding to being converted to hiding Info behind the binary system, " Turbo coding " module among Fig. 1 is arranged in delegation head's sequence line by line with the binary sequence of conversion, and the information bit length of choosing can be divided exactly by the length of this length sequence, then carries out the Turbo coding;

Step 5, the information of hiding embeds, and " intermediate frequency zone embeds, and the gray value is replaced " module among Fig. 1 is replaced the value of two-dimension discrete cosine transform piece master clinodiagonal with the binary number behind the Turbo coding.

When image-carrier is many gray scales black and white image in the step 1, have only a pixel value matrix, and image-carrier is a coloured image three pixel value matrixes are arranged, so the suppressible amount of information of coloured image is three times of preceding two class images.

The implementation method of " piecemeal two-dimensional dct " module in the step 2 is, with source image data x (n ₁, n ₂) be divided into M ₁* M ₂Individual dimension is the data block of N * N, uses the spatial domain matrix Expression, M ₁And M ₂Be respectively source image data x (n ₁, n ₂) capable piece number and row piece number, m ₁And m ₂Be respectively

Row number and row number,

Be square formation, its line number and columns are N, source image data x (n ₁, n ₂) use the spatial domain matrix

Be shown

$x(n_1,n_2)=\left[x_{m_1{m}_2}(n_1,n_2)\right],$ 1≤m ₁≤M ₁，1≤m ₂≤M ₂

The spatial domain matrix

Dimension be N * N, generally select N=g or 16, n ₁And n ₂Be respectively the spatial domain matrix

Capable variable and row variable.

To the spatial domain matrix

Carry out two-dimension discrete cosine transform, obtain the frequency domain matrix

$X_{m_1{m}_2}(k_1,k_2)=C\underset{n_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{n_1=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_{m_1{m}_2}(n_1,n_2)\cos \frac{({2n}_1+1)k_1\mathrm{\π}}{2N}\·\cos \frac{(2n_2+1)k_2\mathrm{\π}}{2N}---\left(1\right)$

k ₁And k ₂Be respectively the frequency domain matrix

Capable variable and row variable, k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, in the formula (1),

$C=\left\{\begin{array}{c}\frac{1}{N},k_1=0,k_2=0\\ \frac{\sqrt{2}}{N},k_1=0,k_2\≠0\mathrm{or}{k}_1\≠0,k_2=0\\ \frac{2}{N},k_1\≠0,k_2\≠0\end{array}\right.---\left(2\right)$

In the step 3, the information of hiding can be the arbitrary format text data, the arbitrary format view data, but before carrying out the Turbo coding, all need be converted to binary data.When hiding Info to bianry image, the pixel value of two-value black and white image only is 0 or 255, but pixel value is can make the distortion that causes image-carrier at 255 o'clock.For addressing this problem, the present invention is multiplied by 1/255 coefficient to the pixel value of two-value black and white image, is converted to 0,1 binary sequence.Then, this binary sequence is carried out Turbo coding, be embedded into again among the image behind the dct transform.When hiding for multi-grey image when hiding Info, its gray value is the signless integer between 0～255, and each gray value that must will hide Info is converted into Turbo coding behind the binary number, is embedded among the image behind the dct transform again.

In the step 5, the two-dimension discrete cosine transform piece is N * N frequency domain matrix

k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, the intermediate frequency zone that its main clinodiagonal is a hiding data:

Wherein, * be

The data of non-main clinodiagonal, and

Promptly

Main clinodiagonal data.

Will

Main clinodiagonal data

Be replaced into the Turbo coded data that hides Info, use

Expression has promptly realized hiding of information.

2. receiving terminal: based on the information extraction flow process of Turbo code

The flow process of information extraction as shown in Figure 2, wherein " image that hides Info after being disturbed " be in transmission course or be subjected to attacked by noise after image affected by noise, comprised the information of hiding.The step of the flow process of information extraction is as follows.

Step 1 is extracted the Turbo coded data of hiding, and " extracting two-dimensional dct piece midband data " module among Fig. 2 is extracted the data of its leading diagonal to the two-dimension discrete cosine transform piece of each N * N (N=8 here);

Step 2 is decoded to extracting hiding Turbo coded data, is realized by " Turbo decoding " module among Fig. 2.The Turbo decoder module requires to choose 0, the 1 binary sequence length that information bit length should be able to be extracted and divides exactly;

Step 3 recovers to hide Info data by binary sequence, and " decimal system conversion " that provided by Fig. 2 realizes, and store hiding Info of extracting.

Data block after transmitting terminal will hide Info

The transmission of delivering letters, k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, if noiseless or electronic attack in the channel, the data block that receiving terminal is received in the step 1 is

Receiving terminal is right

Carry out the 2-D discrete cosine inverse transformation

$y_{m_1{m}_2}(n_1,n_2)=C\underset{k_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{k_1=0}{\overset{N-1}{\mathrm{\Σ}}}{Y}_{m_1{m}_2}(k_1,k_2)\cos \frac{({2k}_1+1)n_1\mathrm{\π}}{2N}\·\cos \frac{(2k_2+1)n_2\mathrm{\π}}{2N}---\left(4\right)$

The C here provides in formula (2), uses

Constitute matrix

$y(n_1,n_2)=\left[y_{m_1{m}_2}(n_1,n_2)\right],1\≤m_1\≤M_1,1\≤m_2\≤M_2$

Matrix y (n ₁, n ₂) be the data of image restored carrier.

Disturb or electronic attack if having in the channel, the data block that step (1) receiving terminal is received is

$Z_{m_1{m}_2}(k_1,k_2)=Y_{m_1{m}_2}(k_1,k_2)+V_{m_1{m}_2}(k_1,k_2)$

Wherein For disturbing or the electronic attack signal, this moment, receiving terminal was right

Carry out the 2-D discrete cosine inverse transformation,

$z_{m_1{m}_2}(n_1,n_2)=C\underset{k_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{k_1=0}{\overset{N-1}{\mathrm{\Σ}}}{Z}_{m_1{m}_2}(k_1,k_2)\cos \frac{({2k}_1+1)n_1\mathrm{\π}}{2N}\·\cos \frac{(2k_2+1)n_2\mathrm{\π}}{2N}---\left(5\right)$

Obtain the data of the image-carrier after disturbed or the electronic attack

$z(n_1,n_2)=\left[z_{m_1{m}_2}(n_1,n_2)\right],1\≤m_1\≤M_1,1\≤m_2\≤M_2.$

But receiving terminal from

The data extracted of main clinodiagonal carry out the Turbo decoding, that can recover that transmitting terminal sends hides Info.

Use-case:

Selecting image-carrier is that a width of cloth pixel is a width of cloth gray level image of 256 * 256, as shown in Figure 6, embeds hiding to its information of carrying out.In the example, the employing code check is 1/2 Turbo code.The parameter of Turbo code: information sequence length adds hangover length, and promptly weaving length is 259, and is pseudo random interleaving; Generator matrix is [13,17]; Iterations is 10.Signal to noise ratio snr=the 1.5dB of channel, and be Gaussian channel.

Multi-grey image Information hiding and extraction, the embedding grammar that the transmitting terminal that adopts Fig. 3 to provide hides Info:

Step 1, selection image-carrier are the original image among Fig. 6;

Step 2 is carried out 8 * 8 two-dimension discrete cosine transform to source images, and employing formula (1) is calculated;

Step 3 is converted to binary data with the data that hide Info of Fig. 5;

Step 4 is carried out the Turbo coding to being converted to hiding Info behind the binary system;

Step 5, the information of hiding embeds the main clinodiagonal of two-dimensional dct piece.

Image-carrier after the data that hide Info of embedding Fig. 5 is Fig. 7, without the interference channel transmission, calculates acquisition by formula (4).Compare no vision distortion with the original image of Fig. 6.

Fig. 8 provides and embeds the image hide Info and the pixel value error between original image, and pixels illustrated value error does not cause the image-carrier vision distortion.Therefore to embed in the intermediate frequency zone of the piecemeal discrete cosine transform of image-carrier that binary system hides Info be feasible in the present invention.

When the signal to noise ratio snr of channel=1.5dB, receiving terminal obtains image after being interfered as shown in Figure 9 with the algorithm of formula (5).

The extracting method that hides Info that adopts Fig. 4 to provide,

Step 1 is extracted the Turbo coded data of hiding, and promptly each 8 * 8 two-dimensional dct piece is extracted its main clinodiagonal data.

Step 2 to extracting hiding Turbo coded data, is decoded.The error rate of this example decoding is zero.

Step 3 by the binary sequence data of recovering to hide Info, and is the decimal system with it by Binary Conversion, the hiding Info as shown in figure 10 of extraction, with send shown in Figure 5 hide Info data relatively, no vision distortion hides Info.This is because the error rate of this example decoding is zero.

The present invention proposes only hiding data to be carried out the Turbo encoding and decoding, intermediate frequency zone at the two-dimension discrete cosine transform piece of image-carrier hides the Turbo coded data, can keep traffic rate and image data amount constant, under disturbed and the quilt situation of attacking, it is approximate undistorted to hide Info.

The present invention with the formal verification of example adopt the inventive method can make to hide Info to have stronger anti-interference and anti-attack ability, hiding Info does not make the obvious distortion of image-carrier, hiding Info changes the image-carrier data volume.

Claims (8)

1. based on the anti-interference information concealing method of Turbo code and image-carrier, it is characterized in that transmitting terminal does the piecemeal two-dimension discrete cosine transform with image-carrier, the information sequence that need are hidden carries out the Turbo coding simultaneously, the Turbo coded sequence that obtains embeds the main clinodiagonal of discrete cosine transformation block, the transmission of delivering letters again; Receiving terminal is from the intermediate frequency extracted region Turbo coded sequence of the discrete cosine transformation block of the view data that receives and carry out the Turbo decoding, restore the data that hide Info by decoding sequence, the two-dimension discrete cosine transform piece after being hidden Info by extraction simultaneously recovers source image data; Wherein hiding Info is arbitrary format text data or arbitrary format view data, is converted to binary data before the Turbo coding, is converted to the multi-system data after the Turbo decoding.

2. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 1, it is characterized in that transmitting terminal does the piecemeal two-dimension discrete cosine transform with image-carrier, the information sequence that need are hidden carries out the Turbo coding simultaneously, and the step of the main clinodiagonal of the Turbo coded sequence that obtains embedding discrete cosine transformation block is as follows:

Step 1, selecting many gray scales black and white image or coloured image is that source images is an image-carrier;

Step 2 is carried out the piecemeal two-dimension discrete cosine transform of N * N to source images;

Step 3, the Data Format Transform that will hide Info are binary data;

Step 4 is carried out the Turbo coding to the sequence that hides Info that is converted to behind the binary system;

Step 5, the embedding of the information sequence of hiding are the values with two-dimension discrete cosine transform piece master clinodiagonal, replace with the binary number behind the Turbo coding.

3. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 1, it is characterized in that receiving terminal extracts the Turbo coded sequence and carries out the Turbo decoding from the main clinodiagonal of the discrete cosine transformation block of the view data that receives, restore the data that hide Info by decoding sequence, the step that the two-dimension discrete cosine transform piece after being hidden Info by extraction simultaneously recovers source image data is as follows:

Step 1 is extracted the Turbo coded data of hiding, and is that each N * N two-dimension discrete cosine transform piece is extracted the data of its leading diagonal;

Step 2 is decoded to extracting hiding Turbo coded data;

Step 3 recovers to hide Info data by binary sequence.

4. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 2 is characterized in that being embodied as of the described piecemeal two-dimension discrete cosine transform of step 2, with source image data x (n ₁, n ₂) be divided into M ₁* M ₂Individual dimension is the data block of N * N, uses the spatial domain matrix

Expression, M ₁And M ₂Be respectively source image data x (n ₁, n ₂) capable piece number and row piece number, m ₁And m ₂Be respectively

Row number and row number,

Be square formation, its line number and columns are N, source image data x (n ₁, n ₂) use the spatial domain matrix

Be expressed as

$x(n_1,n_2)=\left[x_{m_1{m}_2}(n_1,n_2)\right],1\≤m_1\≤M_1,1\≤m_2\≤M_2$

The spatial domain matrix Dimension be N * N, generally select N=8 or 16, n ₁And n ₂Be respectively the spatial domain matrix Capable variable and row variable, to the spatial domain matrix

Carry out two-dimension discrete cosine transform, obtain the frequency domain matrix

$X_{m_1{m}_2}(k_1,k_2)=C\underset{n_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{n_1=0}{\overset{N-1}{\mathrm{\Σ}}}{x}_{m_1{m}_2}(n_1,n_2)\cos \frac{({2n}_1+1)k_1\mathrm{\π}}{2N}\·\cos \frac{({2n}_2+1)k_2\mathrm{\π}}{2N}---\left(1\right)$

k ₁And k ₂Be respectively the frequency domain matrix

Capable variable and row variable, k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, in the formula (1),

$C=\left\{\begin{array}{c}\frac{1}{N},k_1=0,k_2=0\\ \frac{\sqrt{2}}{N},k_1=0,k_2\≠0\mathrm{or}{k}_1\≠0,k_2=0\\ \frac{2}{N},k_1\≠0,k_2\≠0\end{array}\right..---\left(2\right)$

5. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 1 is characterized in that the two-dimension discrete cosine transform piece is N * N frequency domain matrix k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, its main clinodiagonal is the position of hiding data:

Wherein, * be

The data of non-main clinodiagonal, and

Promptly

Main clinodiagonal data, will

Main clinodiagonal data $X_{m_1{m}_2}(0,N-1),X_{m_1{m}_2}(1,N-2),\·\·\·,X_{m_1{m}_2}(N-\mathrm{1,0})$ Be replaced into the Turbo coded data that hides Info, use

Expression promptly realizes hiding of information.

6. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 1, it is characterized in that the information sequence that need are hidden is carried out the Turbo coding method is, the binary sequence of conversion is arranged in delegation head's sequence line by line, the information bit length of choosing should be divided exactly by the length of this length sequence, then carries out the Turbo coding.

7. the anti-interference information concealing method based on Turbo code and image-carrier according to claim 1 is characterized in that the data block after transmitting terminal will hide Info

The transmission of delivering letters, k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1, if noiseless or electronic attack in the channel, the data block that receiving terminal is received is

Main clinodiagonal extract the back zero setting that hides Info, right again

Carry out the 2-D discrete cosine inverse transformation

$y_{m_1{m}_2}(n_1,n_2)=C\underset{k_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{k_1=0}{\overset{N-1}{\mathrm{\Σ}}}{Y}_{m_1{m}_2}(k_1,k_2)\cos \frac{({2k}_1+1)n_1\mathrm{\π}}{2N}\·\cos \frac{({2k}_2+1)n_2\mathrm{\π}}{2N}---\left(4\right)$

The C here is

$C=\left\{\begin{array}{c}\frac{1}{N},k_1=0,k_2=0\\ \frac{\sqrt{2}}{N},k_1=0,k_2\≠0\mathrm{or}{k}_1\≠0,k_2=0\\ \frac{2}{N},k_1\≠0,k_2\≠0\end{array}\right.,$

With

Constitute matrix

$y(n_1,n_2)=\left[y_{m_1{m}_2}(n_1,n_2)\right],1\≤m_1\≤M_1,1\≤m_2\≤M_2$

Matrix y (n ₁, n ₂) be the data of image restored carrier.

8. according to the anti-interference information concealing method of the described image-carrier based on Turbo code of claim 1, it is characterized in that the data block after transmitting terminal will hide Info

The transmission of delivering letters, k ₁=0,1 ..., N-1, k ₂=0,1 ..., N-1 disturbs or electronic attack if having in the channel, and the data block that receiving terminal is received is

$Z_{m_1{m}_2}(k_1,k_2)=Y_{m_1{m}_2}(k_1,k_2){+V}_{m_1{m}_2}(k_1,k_2)$

Wherein For disturbing or the electronic attack signal, this moment, receiving terminal was right

Carry out the 2-D discrete cosine inverse transformation,

$z_{m_1{m}_2}(n_1,n_2)=C\underset{k_2=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{k_1=0}{\overset{N-1}{\mathrm{\Σ}}}{Z}_{m_1{m}_2}(k_1,k_2)\cos \frac{({2k}_1+1)n_1\mathrm{\π}}{2N}\·\cos \frac{({2k}_2+1)n_2\mathrm{\π}}{2N}---\left(5\right)$

The C here is

$C=\left\{\begin{array}{c}\frac{1}{N},k_1=0,k_2=0\\ \frac{\sqrt{2}}{N},k_1=0,k_2\≠0\mathrm{or}{k}_1\≠0,k_2=0\\ \frac{2}{N},k_1\≠0,k_2\≠0\end{array}\right.,$

Obtain the data of the image-carrier after disturbed or the electronic attack

$z(n_1,n_2)=\left[z_{m_1{m}_2}(n_1,n_2)\right],1\≤m_1\≤M_1,1\≤m_2\≤M_2,$

Receiving terminal from The data extracted of main clinodiagonal carry out the Turbo decoding, that can recover that transmitting terminal sends hides Info.

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