CN106961602A - A kind of cross-platform incompressible color image information hidden algorithm based on RS and Hamming code - Google Patents

Abstract

The present invention relates to a kind of cross-platform incompressible color image information hidden algorithm based on RS and Hamming code, combining Reed Solomon code（Reed Solomon code, RS codings）Enter row information coded treatment to hiding information with hamming code, extract the DCT coefficient of JPEG carrier images and quantify its coefficient, pass through K mean clusters（K‑means）In the size of two intermediate frequency coefficients in the every 8*8 blocks of analytic statistics noise threshold adjustment, information insertion jpeg image most at last after coded treatment.The JPEG picture containing hiding information that the present invention is obtained is compressed after across the sharing and forward of heterogeneous networks platform, still can correctly, intactly extract hiding information.Therefore, the algorithm has good repellence and stronger stability to many second compressions of the anti-platforms of JPEG.

Description

Cross-platform anti-compression color image information hiding algorithm based on RS and Hamming codes

Technical Field

The invention relates to the field of image processing, in particular to a cross-platform anti-compression color image information hiding algorithm based on RS and Hamming codes.

Background

With the rapid development of networks and multimedia, information hiding technology becomes a research hotspot in the field of information security. The digital image is a widely applied mode in social networks (WeChat, QQ, microblog, email and the like), and naturally becomes a good propagation carrier in information hiding.

At present, there are two main types of information hiding algorithms: a spatial domain concealment algorithm and a transform domain concealment algorithm. The spatial domain hiding algorithm is easy to realize, the hiding capacity is large, and the robustness is not strong; the transform domain hiding algorithm has strong robustness, but the embedded information quantity is small and the algorithm is complex. Such as Tamimi^[1]The data embedding rate of the method proposed by the people is too low, and the plum-willow and the like^[2]The proposed algorithm mainly hides the watermark pattern in the carrier image and does not solve the problem of image compression in the network transmission process well.

[1]Tamimi A A,Abdalla A M,Al-Allaf O.Hiding an Image inside anotherImage using Variable-Rate Steganography[J].International Journal of AdvancedComputer Science&Application,2013,4(10):18-21。

[2] Plum, Yangmen, YCbCr color space and DCT based color image watermarking algorithm [ J ]. computer and information technology, 2016,24(1): 10-13.

Disclosure of Invention

In view of this, the present invention provides a cross-platform anti-compression color image information hiding algorithm based on RS and hamming codes, which has stable anti-compression performance, that is, after the image with hidden information is shared and forwarded by each platform, the hidden information can still be correctly extracted.

The invention is realized by adopting the following scheme: a cross-platform anti-compression color image information hiding algorithm based on RS and Hamming codes specifically comprises the following steps:

step S1: encrypting the hidden information into binary hidden data stream by using a specific coding mode, and obtaining check bits through double coding of RS codes and Hamming codes to form hidden data;

step S2: and (3) hiding information: extracting DCT coefficients of the JPEG carrier image, quantizing the coefficients, analyzing and counting a noise threshold value through K-means, and adjusting the size of two intermediate frequency coefficients in each 8 x 8 block;

step S3: and embedding the information after the coding processing into a JPEG image to obtain a JPEG cryptograph.

Further, in step S1, the specific encoding method is a digital-letter hybrid encoding method, the information to be hidden is divided into two character groups, the first character in each group is multiplied by 45 through a character index table, the second character index data is added and converted into a binary code of 11 bits, and if only one character is in number, the 6-bit binary code is used for representing the character.

Further, the encoding process of the RS code adopts a basic method [ J ] of Liuyan, Zhang, RS encoding and decoding, a scientific and technological information technology, 2011, (32) and 3-5, and the specific steps are as follows:

step S101: according to the primitive polynomial g (x) of GF field⁸+x⁴+x³+x²+1, solving all elements in the domain;

step S102: the check code generating polynomial is:xⁿ-1 ═ g (x) h (x), the check polynomial h (x) is determined from the operating rules in the galois field; where k is the total check code number, k₀Is usually 0 or 1, α is the root of the primitive polynomial g (x);

step S103: sequentially solving check elements: c_n-k-1,C_n-k-2,...,C₁,C₀(ii) a Wherein, the check element is the error correction data;

the decoding process of the RS code adopts a basic method [ J ] of Liuyan, Zhang Liang and RS encoding and decoding, a scientific and technological information technology, 2011, (32) and 3-5, and the specific steps are as follows:

step S111: receiving data code r (x) to obtain adjoint polynomial S_j；

Step S112: examination S_jIf all the received code words are 0, the received code words are valid code words, and go to step S118;

step S113: initialization:ω₀＝1+S(x),t_-1＝0,t₀＝1；

wherein d is_minRepresents the lowest power of the information polynomial, and S (x) represents the value of the adjoint polynomial x;

step S114: iteration:

ω_k＝α_k-1ω_k-2+α_k-2x^mω_k-1，

t_k＝α_k-1t_k-2+α_k-2x^mt_k-1；

therein, α_k-1And α_k-2Are each omega_k-1And ω_k-2M is ω_k-1And ω_k-2Until deg (ω) is reached, the iterative process of step S114 is performed_k)≤t；

Step 115: from S_jObtaining an error position polynomial A (x); solving the root of A (x) to obtain the number of error positions and determining the error positions; if the number of roots is less than the degree of A (x), which indicates that there is a heavy root or a root on the extension field, the decoding fails, and go to step S119; wherein,

A(x)＝e_n-1x^n-1+e_n-2x^n-2+...+e₀；

wherein e represents an error location;

step 116: solving an error value by a Forney algorithm, if the denominator is 0, failing to decode, and turning to the step S119;

step 117: subtracting the error value from the corresponding position of the received code word, and correcting errors;

step 118: outputting information bits of the correct code word;

step 119, outputting the information bits in the received code word to the decoding failure flag.

Further, the encoding rule of the hamming code includes the following steps:

step S121: calculating a check bit: n represents the data length of the added check code, K represents the effective information digit, r represents the added check code digit, and the relation is satisfied: k + r is less than or equal to 2^r-1；

Step S122: all the check code positions are 2ⁿThe power position, the available check bits are respectively: 1. positions 2, 4, 8 and 16, wherein the number of the leftmost bits is counted;

step S123: dividing each bit in the K + r bit Hamming code into r parity groups, and according to the grouping result, each group calculates the check bit according to odd or even check to form the Hamming check code.

Further, the step S2 is specifically: dividing data into preset class numbers K on the basis of a minimum error function by adopting a K-means clustering algorithm, dividing an image into a plurality of layers due to different texture complexity and color brightness of a carrier image, and introducing reasonable adjustment factors to hide information so as to balance the transparency and the robustness of the image; and calculating the noise sensitivity of the image block by adopting a human eye vision masking model to hide information.

Further, the step S3 specifically includes the following steps:

step S31: the secret information M generates binary data M1 in an encoding mode;

step S32: the M1 data are sequentially encoded by RS and Hamming to obtain data M2 containing error correction bits and check bits, namely the final content to be hidden;

step S33: extracting green channels G from the carrier image S, dividing the green channels G into 8-8 non-overlapped blocks, respectively performing DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S34: calculating a threshold jnd for each block of visual noise;

step S35: two coefficients are selected from the intermediate frequency coefficients, and are set as a and b, and the embedding process is described as follows:

when 0 is to be embedded, judging the relationship between a and b, when a-b < jnd, a-a + jnd, b-jnd; otherwise, the values of a and b are not changed;

when 1 is to be embedded, judging the relationship between a and b, when b-a < jnd, a-jnd and b-b + jnd; otherwise, the values of a and b are not changed;

step S36: DCT blocks are inversely transformed and inversely quantized, and stored as RGB color space.

Further, the method also includes step S4: the method for extracting the hidden information specifically comprises the following steps:

step S41: extracting a color RGB image G channel containing hidden information, dividing the color RGB image G channel into 8-8 non-overlapped blocks, respectively carrying out DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S42: selecting from each block a corresponding intermediate frequency coefficient pair F_ij(r₁,r₂) And F_ij(l₁,l₂) The extraction formula is as follows:

wherein V represents the extracted information data;

step S43: v, obtaining a binary character string through Hamming decoding and RS decoding;

step S44: and performing a reverse coding mode on the binary character string to obtain final hidden information.

Compared with the prior art, the invention has the following beneficial effects:

1. the hidden information is encrypted into binary hidden data stream by using a self-owned coding mode, and check bits are obtained by using RS and Hamming coding modes to form hidden data;

2. the invention preprocesses the carrier image, extracts the quantized DCT coefficient through the compression property of JPEG, and cuts the optimal adjusting factor through the pixel value cluster analysis of G channel, thereby achieving good image invisibility and robustness. And (4) hiding information by combining the adjustment factor and the quantized DCT coefficient.

3. The invention has good burst error correction capability based on RS codes; and the noise factor is calculated by adopting K-means clustering statistics, so that the method has a good embedding effect on images with different brightness and texture complexity. The invention has stable compression resistance, namely, after the picture with the hidden information is shared and forwarded by each platform, the hidden information can still be correctly extracted.

Drawings

FIG. 1 is a flow chart of the method principle of the present invention.

FIG. 2 is a table of character comparisons according to an embodiment of the present invention.

Fig. 3 shows the comparison result 1 of different images and different quantization factor images.

Fig. 4 shows the comparison result 2 of different images and different quantization factor images.

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

As shown in fig. 1, the present embodiment provides a cross-platform anti-compression color image information hiding algorithm based on RS and hamming codes, which specifically includes the following steps:

step S1: encrypting the hidden information into binary hidden data stream by using a specific coding mode, and obtaining check bits through double coding of RS codes and Hamming codes to form hidden data;

step S2: and (3) hiding information: extracting DCT coefficients of the JPEG carrier image, quantizing the coefficients, analyzing and counting a noise threshold value through K-means, and adjusting the size of two intermediate frequency coefficients in each 8 x 8 block;

step S3: and embedding the information after the coding processing into a JPEG image to obtain a JPEG cryptograph.

In this embodiment, in step S1, the specific encoding method is a digital-letter hybrid encoding method, the information to be hidden is divided into two character groups, the first character in each group is multiplied by 45 through a character index table, the second character index data is added and converted into an 11-bit binary code, and if only one character is in number, the 6-bit binary code is used for representing the character. Fig. 2 is a numeric alphabet comparison table of the present embodiment.

For example, the input: BeiKa #

Decimal system: be: 10 × 45+13 ═ 463, iK: 17 × 45+19 is 784, a #: 9 × 45+3 ═ 408;

binary system: 00111001111, respectively; 01100010000, respectively; 00110011000, respectively;

the decoding mode, namely the reverse process of the coding mode, obtains a binary system of 11 bits, converts the binary system into a corresponding 10-system, divides the binary system by 45 and rounds the binary system to obtain a number on ten bits, and obtains a number on one bit by modulo 45, and then obtains a corresponding character through a character comparison table.

In this embodiment, regarding RS encoding and decoding, a JPEG picture is strongly compressed during a cross-platform transmission process, which affects correct extraction of hidden information. The RS code can correct random errors and burst errors and has strong error correction capability.

The generation of RS error correcting code, namely the coding process of RS, the coefficients from (n-1) th to (n-k) th times of the code word polynomial are information bits, and the rest are check bits. An information polynomial: m (x) ═ m_k-1x^k-1+m_k-2x^k-2+m₁x+m₀(ii) a The information bit represents: m is_k-1,...,m₁,m₀(ii) a The check polynomial is expressed as: r (x) r_n-k-1x^n-k-1+...+r₁x+r₀(ii) a The data code polynomial is: c (x) ═ C_n-1x^n-1+C_n-2x^n-2+...+C_n-kx^n-k+C_n-k-1x^n-k-1+...+C₁x+C₀；

In this embodiment, the encoding process of the RS code adopts the basic method [ J ] of the "liuyan, zhang, RS codec, the scientific and technical information technology, 2011, (32): 3-5", and the specific steps are as follows:

step S101: according to the primitive polynomial g (x) of GF field⁸+x⁴+x³+x²+1, solving all elements in the domain;

step S102: check code generator polynomialComprises the following steps:xⁿ-1 ═ g (x) h (x), the check polynomial h (x) is determined from the operating rules in the galois field; where k is the total check code number, k₀Is usually 0 or 1, α is the root of the primitive polynomial g (x);

step S103: sequentially solving check elements: c_n-k-1,C_n-k-2,...,C₁,C₀(ii) a Wherein, the check element is the error correction data;

the decoding process of the RS code adopts a basic method [ J ] of Liuyan, Zhang Liang and RS encoding and decoding, a scientific and technological information technology, 2011, (32) and 3-5, and the specific steps are as follows:

step S111: receiving data code r (x) to obtain adjoint polynomial S_j；

Step S112: examination S_jIf all the received code words are 0, the received code words are valid code words, and go to step S118;

step S113: initialization:ω₀＝1+S(x),t_-1＝0,t₀＝1；

wherein d is_minRepresents the lowest power of the information polynomial, and S (x) represents the value of the adjoint polynomial x;

step S114: iteration:

ω_k＝α_k-1ω_k-2+α_k-2x^mω_k-1，

t_k＝α_k-1t_k-2+α_k-2x^mt_k-1；

therein, α_k-1And α_k-2Are each omega_k-1And ω_k-2M is ω_k-1And ω_k-2Until deg (ω) is reached, the iterative process of step S114 is performed_k)≤t；

Step 115: from S_jObtaining an error position polynomial A (x); solving the root of A (x) to obtain the number of error positions and determining the error positions; if the number of roots is less than the degree of A (x), which indicates that there is a heavy root or a root on the extension field, the decoding fails, and go to step S119; wherein,

A(x)＝e_n-1x^n-1+e_n-2x^n-2+...+e₀；

wherein e represents an error location;

step 116: solving an error value by a Forney algorithm, if the denominator is 0, failing to decode, and turning to the step S119;

step 117: subtracting the error value from the corresponding position of the received code word, and correcting errors;

step 118: outputting information bits of the correct code word;

step 119, outputting the information bits in the received code word to the decoding failure flag.

In this embodiment, regarding Hamming Code, Hamming Code (Hamming Code) has multiple check bits and error correction Code for detecting and correcting one bit error Code, and this embodiment applies Hamming Code to correct RS Code due to errors in transmission process, and combines with RS Code to achieve better error correction capability.

The encoding rule of the Hamming code comprises the following steps:

step S121: calculating a check bit: n represents the data length of the added check code, K represents the effective information digit, r represents the added check code digit, and the relation is satisfied: k + r is less than or equal to 2^r-1; in the present embodiment, K is 16, r is 5;

step S122: all the check code positions are 2ⁿThe power position, the available check bits are respectively: 1. positions 2, 4, 8, 16, wherein,counting from the leftmost digit;

step S123: dividing each bit in the K + r bit Hamming code into r parity groups, and according to the grouping result, each group calculates the check bit according to odd or even check to form the Hamming check code. The present embodiment adopts odd check calculation, and the rule is as follows: the number of "1" s in each group is odd.

In this embodiment, the step S2 specifically includes: dividing data into preset class numbers K on the basis of a minimum error function by adopting a K-means clustering algorithm, dividing an image into a plurality of layers due to different texture complexity and color brightness of a carrier image, and introducing reasonable adjustment factors to hide information so as to balance the transparency and the robustness of the image; and calculating the noise sensitivity of the image block by adopting a human eye vision masking model to hide information. The method comprises the following specific steps:

1. dividing the carrier image into blocks and calculating the mean value of each block;

2. determining a reasonable K value according to the complexity of the image;

3. initial centroid selection using Arthur&Vassilvitskii(2007)k-means++:The Advantagesof Careful Seeding^[5]The algorithm proposed in the method obtains an initial central value;

wherein [5] is Arthur D, Vassivskii S.k-means + +, the additives of the carboeffect cutting [ C ]// Eighteenth Acm-Simam Symposium on dispersed alloys, SODA2007, New Orleanes, Louisiana, Usa, January.2015:1027 + 1035.

4. And dividing K-means into K classes of layers, and calculating different layers and selecting different values. (numerical ranges are given below for experimental data).

The human eye vision masking model adopts 'Charebis, robust digital watermarking and encrypted digital watermarking related technology research [ D ]. Wuhan, Wuhan university of science and technology, 2005', and the specific calculation steps are as follows:

1. 8-8 blocking and DCT transformation are carried out on the carrier image:

the forward discrete cosine transform formula is as follows:

the inverse discrete cosine transform formula is as follows:

2. the contrast sensitivity of each sub-block was calculated:

C(u,v)＝5.05e^-0.178(u+v)(e^0.1(u+v)-1)；

3. visual sensitivity of individual sub-blocks to noise

Wherein u, v ∈ {0,1, 2.., n-1}, F_DCTAnd (u, v) are values of the blocks subjected to DCT transform. S_DCTThe visual sensitivity of human eyes to the image blocks is shown, the larger the value of the visual sensitivity, the more insensitive the human eyes to the noise in the image and the larger the intensity value of the information which can be hidden. If S is obtained by calculation_DCTWhen the information is hidden, the empirical value pair S is used as 0_DCTAnd carrying out assignment.

4. Calculating visual noise threshold of image, jnd- β log₂(S_DCT)/0.30103；

In this embodiment, regarding the loading process of information, a color image with a carrier image of 640 × 640 is used, the hidden information is a character string with any length, the information to be hidden is embedded into the quantized DCT coefficients, and the quantization factor is controlled by α. Suppose S represents the original RGB true-color image and M represents a character or character string to be hidden. The DCT domain is divided into low-frequency, medium-frequency and high-frequency regions, the low frequency is most sensitive to vision, the algorithm robustness can be increased by modifying the low frequency, and the invisibility of the algorithm is reduced; modifying the high frequency coefficient results in poor image robustness, so the present embodiment adopts modifying the intermediate frequency coefficient.

The step S3 specifically includes the following steps:

step S31: the secret information M generates binary data M1 in an encoding mode;

step S32: the M1 data are sequentially encoded by RS and Hamming to obtain data M2 containing error correction bits and check bits, namely the final content to be hidden;

step S33: extracting green channels G from the carrier image S, dividing the green channels G into 8-8 non-overlapped blocks, respectively performing DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S34: calculating a threshold jnd for each block of visual noise;

step S35: two coefficients are selected from the intermediate frequency coefficients, and are set as a and b, and the embedding process is described as follows:

when 0 is to be embedded, judging the relationship between a and b, when a-b < jnd, a-a + jnd, b-jnd; otherwise, the values of a and b are not changed;

when 1 is to be embedded, judging the relationship between a and b, when b-a < jnd, a-jnd and b-b + jnd; otherwise, the values of a and b are not changed;

step S36: DCT blocks are inversely transformed and inversely quantized, and stored as RGB color space.

In this embodiment, the method further includes step S4: extracting the hidden information, wherein the algorithm of the embodiment is a hidden technology of blind extraction, and the information extraction process and the information embedding process are mutually inverse processes; the method specifically comprises the following steps:

step S41: extracting a color RGB image G channel containing hidden information, dividing the color RGB image G channel into 8-8 non-overlapped blocks, respectively carrying out DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S42: selecting from each block a corresponding intermediate frequency coefficient pair F_ij(r₁,r₂) And F_ij(l₁,l₂) The extraction formula is as follows:

wherein V represents the extracted information data;

step S43: v, obtaining a binary character string through Hamming decoding and RS decoding;

step S44: and performing a reverse coding mode on the binary character string to obtain final hidden information.

Preferably, the experimental results and analysis of this embodiment are as follows.

In this embodiment, a 24-bit color image with an original image size of 640 × 640 is adopted, and the hidden information is a character string: ceshi0123456789abcdefghijklmnopqrstuvwxyz $% + -.

VS2010 and calling opencv2.4.9 library are taken as experimental tools. The image attack tool uses matlab2014a, with patch size of 8 x 8.

In the embodiment, a peak signal-to-noise ratio (PSNR) is used to measure the influence of subjective factors on the similarity between an image after information hiding and an original image, and usually, when the PSNR is greater than or equal to 30, the difference of the image after the information hiding cannot be visually perceived. PSNR is defined as follows:

calculating MSE value of each channel of RGB three channels, and calculating PSNR value after taking average value:

the quantization factor is tested as follows:

the size of the quantization factor alpha determines the transparency and robustness of the information hidden picture, and also affects the selection of the quantization matrix, and if the size of the quantization factor alpha is too large, the transparency of the carrier image is reduced, and if the size of the quantization factor alpha is too small, the robustness of the image is reduced. In a large number of experiments, the value of α is optimally: between 0.01 and 3, values below 1 being chosen in this experiment, the following results were achieved:

in the experimental process, when α is 0.01, correct hidden information cannot be extracted; when α is 0.5 or more, the image distortion is severe, so the value of the quantization factor α is selected here as: 0.05-0.15. Fig. 3 and 4 show the comparison results of two different images with quantization factors of 0.05 and 0.1.

The K-means cluster analysis adjusting factor selection experiment comprises the following steps:

when the image is hidden in the information, because the texture complexity or the brightness difference between the carrier images is too large, the selection is carried out according to the value empirical value of the adjusting factor, and the extraction accuracy of the hidden information is influenced. Therefore, the brightness of different levels of the picture is tested by adopting different adjustment factors. The results are shown in the following table:

from the two experimental results, the following test of this example selects α ═ 0.1 and β ∈ [0.4,1.0] to perform the cross-platform compression resistance test of the image.

Wherein, the compression resistance test result is as follows:

the cross-platform compression resistance test method comprises the following steps: testing mainstream interactive platforms such as WeChat point-to-point (mutual forwarding or downloading and forwarding of two parties), QQ point-to-point, QQ space, microblog sharing and the like, wherein the testing machine is selected from different types of mainstream mobile phones on the market, and the testing system is divided into android and IOS; testing the selected images: 640 x 640 of the 24-bit color images, wherein the quantization factor alpha is 0.1; the regulation factor is as follows: beta belongs to [0.4,1.0 ]. If all the test patterns can correctly extract information, the pressure resistance is stable. The tests in the following table are the robustness performance against JPEG/JPEG2000 attacks with quality factor (quality factor) of 20-100;

the tests in the table below are multiple cross-platform compression resistance tests.

The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (7)

1. A cross-platform anti-compression color image information hiding algorithm based on RS and Hamming codes is characterized in that: the method comprises the following steps:

step S1: encrypting the hidden information into binary hidden data stream by using a specific coding mode, and obtaining check bits through double coding of RS codes and Hamming codes to form hidden data;

step S2: and (3) hiding information: extracting DCT coefficients of the JPEG carrier image, quantizing the coefficients, analyzing and counting a noise threshold value through K-means, and adjusting the size of two intermediate frequency coefficients in each 8 x 8 block;

step S3: and embedding the information after the coding processing into a JPEG image to obtain a JPEG cryptograph.

2. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: in step S1, the specific encoding method is a digital-letter hybrid encoding method, the information to be hidden is divided into two character groups, the first character in each group is multiplied by 45 through the numerical value of the character index table, the second character index data is added and converted into 11-bit binary code, if the number of the characters is only one, the 6-bit binary code is used for representing the characters.

3. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: the encoding process of the RS code comprises the following specific steps:

step S101: according to the primitive polynomial g (x) of GF field⁸+x⁴+x³+x²+1, solving all elements in the domain;

step S102: the check code generating polynomial is:xⁿ-1 ═ g (x) h (x), the check polynomial h (x) is determined from the operating rules in the galois field; where k is the total check code number, k₀Values of 0 or 1, α being the root of primitive polynomial g (x);

step S103: sequentially solving check elements: c_n-k-1,C_n-k-2,...,C₁,C₀(ii) a Wherein, the check element is the error correction data;

the decoding process of the RS code comprises the following specific steps:

step S111: receiving data code r (x) to obtain adjoint polynomial S_j；

Step S112: examination S_jIf all the received code words are 0, the received code words are valid code words, and go to step S118;

step S113: initialization:ω₀＝1+S(x),t_-1＝0,t₀＝1；

wherein d is_minRepresents the lowest power of the information polynomial, and S (x) represents the value of the adjoint polynomial x;

step S114: iteration:

ω_k＝α_k-1ω_k-2+α_k-2x^mω_k-1，

t_k＝α_k-1t_k-2+α_k-2x^mt_k-1；

therein, α_k-1And α_k-2Are each omega_k-1And ω_k-2M is ω_k-1And ω_k-2Until deg (ω) is reached, the iterative process of step S114 is performed_k)≤t；

Step 115: from S_jObtaining an error position polynomial A (x); solving the root of A (x) to obtain the number of error positions and determining the error positions; if the number of roots is less than the degree of A (x), which indicates that there is a heavy root or a root on the extension field, the decoding fails, and go to step S119; wherein,

A(x)＝e_n-1x^n-1+e_n-2x^n-2+...+e₀；

wherein e represents an error location;

step 116: solving an error value by a Forney algorithm, if the denominator is 0, failing to decode, and turning to the step S119;

step 117: subtracting the error value from the corresponding position of the received code word, and correcting errors;

step 118: outputting information bits of the correct code word;

step 119, outputting the information bits in the received code word to the decoding failure flag.

4. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: the encoding rule of the Hamming code comprises the following steps:

step S121: calculating a check bit: n represents the data length of the added check code, K represents the effective information digit, r represents the added check code digit, and the relation is satisfied: k + r is less than or equal to 2^r-1；

Step S122: all the check code positions are 2ⁿThe power position, the available check bits are respectively: 1. positions 2, 4, 8 and 16, wherein the number of the leftmost bits is counted;

step S123: dividing each bit in the K + r bit Hamming code into r parity groups, and according to the grouping result, each group calculates the check bit according to odd or even check to form the Hamming check code.

5. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: the step S2 specifically includes: dividing data into preset class numbers K on the basis of a minimum error function by adopting a K-means clustering algorithm, dividing an image into a plurality of layers due to different texture complexity and color brightness of a carrier image, and introducing reasonable adjustment factors to hide information so as to balance the transparency and the robustness of the image; and calculating the noise sensitivity of the image block by adopting a human eye vision masking model to hide information.

6. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: the step S3 specifically includes the following steps:

step S31: the secret information M generates binary data M1 in an encoding mode;

step S32: the M1 data are sequentially encoded by RS and Hamming to obtain data M2 containing error correction bits and check bits, namely the final content to be hidden;

step S33: extracting green channels G from the carrier image S, dividing the green channels G into 8-8 non-overlapped blocks, respectively performing DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S34: calculating a threshold jnd for each block of visual noise;

step S35: two coefficients are selected from the intermediate frequency coefficients, and are set as a and b, and the embedding process is described as follows:

when 0 is to be embedded, judging the relationship between a and b, when a-b < jnd, a-a + jnd, b-jnd; otherwise, the values of a and b are not changed;

when 1 is to be embedded, judging the relationship between a and b, when b-a < jnd, a-jnd and b-b + jnd; otherwise, the values of a and b are not changed;

step S36: DCT blocks are inversely transformed and inversely quantized, and stored as RGB color space.

7. The RS and hamming code based cross-platform anti-compression color image information hiding algorithm of claim 1, wherein: further comprising step S4: the method for extracting the hidden information specifically comprises the following steps:

step S41: extracting a color RGB image G channel containing hidden information, dividing the color RGB image G channel into 8-8 non-overlapped blocks, respectively carrying out DCT (discrete cosine transform) transformation on each block and quantizing DCT coefficients;

step S42: selecting from each block a corresponding intermediate frequency coefficient pair F_ij(r₁,r₂) And F_ij(l₁,l₂) The extraction formula is as follows:

$\left\{\begin{array}{c}{F}_{ij}(r_1,r_2)\&GreaterEqual;F_{ij}(l_1,l_2),V=1\\ F_{ij}(r_1,r_2)<F_{ij}(l_1,l_2),V=0\end{array}\right.;$

wherein V represents the extracted information data;

step S43: v, obtaining a binary character string through Hamming decoding and RS decoding;

step S44: and performing a reverse coding mode on the binary character string to obtain final hidden information.