CN105404817A - (k,n) threshold based user-friendly visual secret sharing method - Google Patents

Abstract

The invention discloses a user-friendly visual secret sharing method based on (k, n) threshold, and mainly solves the problems of low security and low contrast in the prior art. The implementation steps are: 1. Perform (k, n) random grid processing on the binary secret image S to obtain n pieces of basic shared images of random grids; Block processing to find the gray level equivalent to the gray level of each small block of the image. 3. Perform half-tone processing on the divided cover image, and obtain the half-tone shared cover image according to the generated dithering matrix; 4. Divide the generated basic shared and cover image into blocks and press the fixed value δ Stacking ratios are combined, and sub-blocking is combined to generate a meaningful final shared image. The invention can prevent attackers from attacking, generate meaningful final shared images, and expand the application range of visible secret sharing.

Description

A User-Friendly Visual Secret Sharing Method Based on (k, n) Threshold

technical field

The present invention relates to the technical field of information security, and is a visual secret sharing method for information hiding, a user-friendly visual secret sharing method called (k, n) threshold, which can be used for image protection, image sharing, and real-time transmission of images Wait.

Background technique

In 1979, Blakley and Shamir respectively proposed the concept of secret sharing. The secret sharing method is to divide the secret into different shares, and any share greater than or equal to a certain number can recover the secret, and vice versa. Due to the widespread use of images in daily life, in 1995, Naor and Shamir introduced the secret sharing method into the field of image processing, and proposed the first visual secret image sharing method. The visual secret sharing method divides the secret image into different shares, and any share greater than or equal to a certain number can recover the secret image, and vice versa. The secret image sharing method provides an effective method for the security of secret images during transmission or storage, especially in military, commercial, financial and other fields. Secret image sharing methods are now divided into two. The first is visual secret sharing, that is, by superimposing a certain number of shares together, the secret image can be seen visually. The second is computable secret image sharing, that is, the secret image can only be recovered by computer processing a certain number of shares. Since computable secret image sharing requires complex algorithms and operations, and the recovery process is complex, visual secret sharing has received a lot of research. In the early stage of visual secret sharing, the share of converting the secret image is pixel-inflated, and the size of the converted image is much larger than the original image. Due to the existence of pixel expansion, it is impossible to restore the secret image without distortion. In 1987, Kafri and Keren proposed a visual secret sharing method based on a random grid, but it did not attract enough attention at that time. After 2006, many methods began to use a visual secret sharing method based on a random grid. This method has neither Pixel dilation also does not require making complex codebooks. However, in the process of generating shared images in this method, since the generated shared images are meaningless random grid images, it is easy to attract the attention of attackers, and then destroy the shared image or leak the secret image, and the restored secret The image contrast is also not high. At the same time, many people have proposed the visual secret sharing method based on the threshold scheme and the general access structure visual secret sharing method, which expands this method in terms of security and scope of application, but because the generated random grid image is meaningless, Security is still flawed. After 2011, the user-friendly visual secret sharing method was formally proposed for the first time, embedding the random grid image generated from the secret image into the cover image to form a meaningful share, becoming a user-friendly method. Compared to a single random grid image, the user-friendly shared image is restored visually identical to the shared image, so it prevents malicious attackers from attracting attention and damage. However, this method is only applicable to the (n, n) threshold scheme, and the contrast of the image after superposition is extremely low, and the image color is extremely black. In the user-friendly visual secret sharing method, the contrast is an important index to measure the performance. Generally, there are two coefficients: the contrast of the shared image and the contrast of the restored secret image. Generally, the more shared images, the restored secret The lower the image contrast, the more black pixels there will be.

The literature "Threshold visual secret sharing by random grids. The Journal of Systems and Software, 2011, 84 (2011) 1197–1208." proposed a (k, n) threshold based random grid visual secret sharing method, so that the visual secret sharing method can be used in transmission security and defense Deception is improved, where k represents the threshold value, which is the minimum number of participants required for decryption, and n represents the number of shared images, that is, the number of participants, where k≤n. The main steps of the method are: first, refer to the traditional random grid-based visual secret sharing method, and operate on the pixels of the secret image; second, operate on the pixels of the secret image according to the adopted random grid method , to generate k required pixels; third, the remaining n-k pixels determine their pixel values according to the method of tossing a coin; fourth, randomly assign the obtained n-bit pixels to n images, and each image The selected spatial positions must be consistent; fifth, continue to complete the above operations until all the pixels of the secret image are taken out, and finally n random grid images are obtained, and at least k images are superimposed to obtain the secret image. However, there are some defects in this method: first, the contrast ratio of this method is very low. Due to the random acquisition of n-k pixels in this method, the contrast after superimposing the image is particularly low. Second, the security of this method is particularly low. Randomly generated random grids are meaningless and inconvenient to manage. This can easily attract the attention of malicious attackers during transmission and storage, thereby destroying the integrity of the image, resulting in The secret image cannot be recovered, and sometimes even the shared share is stolen, resulting in the leakage of the secret image.

Contents of the invention

The object of the present invention is to address the deficiencies of the above-mentioned prior art, propose a user-friendly visual secret sharing method based on the (k, n) threshold scheme, and apply the method to the grayscale image to enhance the security of the visual secret image. The scope of application improves the security of image transmission and storage.

The main technical principle that realizes the object of the present invention is:

First, histogram equalization is used to improve the contrast of the final meaningful shared image and the restored secret image. The specific method is to divide the image into blocks, perform equivalent similarity to the average gray level of each block of the divided image, and obtain the gray level equivalent to the gray level of each small block of the image, and improve the cover image after sharing. contrast. The dithering method is used to process the halftone of the grayscale image to generate a dithering matrix. This method is fast and can be extended to grayscale images. At the same time, combined with the (k, n) threshold method, and combined with the above two methods to process the cover image and the secret image, the final meaningful shared image is obtained, which achieves the purpose of user-friendliness of the shared image and improvement of the contrast of the restored secret image.

According to the above principles, the implementation steps of the method include the following:

(1) Perform (k, n) random grid encryption on the binary secret image S to be protected to obtain k basic shared random grid images, and then generate the remaining n-k basic shared random grid images according to the method of coin tossing, A total of n basic shared random grid images are obtained, where k is the threshold value and n is the number of participants;

(2) Input n gray-scale cover images, first divide each gray-scale image into small blocks of the same size, use histogram equalization to process the image small blocks, and then perform an equivalent to the average gray level of each image small block Similar to get the gray level equivalent to each image patch;

(3) carry out dithering halftone processing to the cover image patch after step (2) histogram equalization process, first produce dither matrix, according to dither matrix, obtain the cover shared image after halftone process;

(4) Set the stacking ratio δ, where 0≤δ≤1, divide the basic shared random grid image generated in step (1) and the shared cover image generated in step (3) into blocks first, and divide the processed image into blocks Perform stacking to produce a user-friendly final shareable image.

(5) From the n final shared images generated in step (4), take any k final shared images greater than or equal to them and superimpose them to obtain the restored secret image.

Utilize histogram equalization process cover image method described in step (2) of the present invention, carry out as follows:

2a) Transform and decompose the cover images C ₁ , C ₂ ,...,C _n into small pixel blocks with a size of h×w, and the minimum h×w cannot be less than 2;

2b) Let D _i,j be the jth data block of the cover image C _i , find the β that satisfies the formulas (1) and (2) at the same time, let the series of D _i,j be equal to β,

β≤d≤β+1(1)

$\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&le;</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, D _{i, j} represents the jth data block in the original cover image C _i , and the average gray level of D _{i, j} is d, in the formula Represents the number of pixels with gray level k in the original image C _i , β∈{0,1,...,h×w-1} is the value of all series, and its value is determined by the size of the block Decision, where 1≤i≤n, 1≤j≤(r×c)/(h×w);

2c) After the series of all blocks are calculated by the formula in step 2b), the label matrix L ₁ , L ₂ ,...,L _n are respectively obtained from the corresponding cover images C ₁ , C ₂ ,...,C _n , L The size of _i is (r×c)/(h×w), store all the block series in the cover image C _i , process the image block, perform equivalent similarity on the average gray level of each block, and find The gray scale equivalent to the h×w gray scale of each small block of the image, where i=1,2,…,n.

In step (3) of the present invention, utilize dithering matrix to carry out halftone processing method to obtain as follows:

3a) Reconstruct n dithering matrices M ₁ , M ₂ ,…,M _n by using the original grayscale cover image C ₁ , C ₂ ,…,C _n , the size is h×w, and the pixel in the dithering matrix M _t is M ^t _i,j , where t=1,2,...,n, 1≤i≤h, 1≤j≤w;

3b) If the pixel value L _i,j of the label matrix L _t obtained in step (2) is ≤M _i,j , take a black pixel at the coordinate (i,j) of P _i ,j, otherwise at P _i,j The (i, j) position of the white pixel is taken, where t=1,2,...,n, 1≤i≤h, 1≤j≤w;

3c) Combine all halftone patterns P _{i, j} to generate the final halftone image, 1≤i≤r, 1≤j≤c, and then calculate the shared image P _t of all block covers, where t=1,2, ...,n;

3d) Transform the block matrix into the original matrix P _i , and then transform into n matrices with a final size of r×c as the desired shared cover image, where i=1, 2, . . . , n.

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

1. Since the present invention uses the dithering halftone technique, the (k, n) scheme can be applied to the grayscale cover image to improve the image application range of the scheme;

2. Since the present invention uses histogram equalization to obtain a clearer image profile of the grayscale image, improve the contrast of the final shared image and the restored secret image, and improve the visual effect of the cover shared image, thus the use of this scheme scope;

3. Since the present invention uses the cover image to be embedded in the basic shared random grid image of the secret image, the shared image becomes meaningful, and the security of the (k, n) scheme is improved, and the meaningful shared image is also convenient User manages many shared images.

Description of drawings

Fig. 1 is the realization overall flowchart of the present invention;

Fig. 2 is the greyscale cover image of 512 * 512 that four pieces of size used in the present invention, among the figure (a)-(d) are respectively four cover images;

Fig. 3 is the binary secret image S used in the present invention;

Fig. 4 is (a)-(d) corresponding to four final shared images that the present invention produces respectively;

Fig. 5 is that four simulation superposition result images of the present invention correspond to (a)-(d) respectively;

Figure 6 is the four final shared images generated by the traditional (k, n) scheme, corresponding to (a)-(d);

Fig. 7 is the traditional (k, n) scheme of the four simulation superimposed result images corresponding to (a)-(d) respectively.

detailed description

The specific embodiments of the present invention will be described below in conjunction with the accompanying drawings.

With reference to Fig. 1, the realization steps of the present invention are as follows:

Step 1, input a secret image S and n cover images C to be protected.

The secret image S is an image that needs to be protected, and the cover image C is used to hide the secret image S. The size of the cover image and the secret graphic must be equal, here it is set to r×c, r represents the height of the secret image and the cover image, and c represents the secret image and The width of the cover image.

Step 2: Use the traditional random grid-based method to generate a shared image. The secret image S uses a binary image. For the traditional random grid-based visible secret sharing method, firstly, the pixel S _i,j of the secret image S For coding, the following first introduces the traditional random grid.

2a) Generate a random grid G ¹ according to the way of flipping a coin;

2b) When the pixel S _i,j of the secret image S is white, then the pixel G ² _i,j in the second random grid G ² has the same value as the pixel G ¹ _i,j in the random grid G ¹ , On the contrary, the values are opposite, where 1≤i≤r, 1≤j≤c, where r and c are the width and height of the secret image S, respectively.

Step 3, generate the basic shared random grid image B _t of the (k, n) threshold method:

3a) According to the above step 2, encode all the pixels of S _i , j in sequence, and encode each pixel S _{i, j} of the secret image S in sequence, to obtain the pixel bit values g1 _{i, j} and g2' _{i, j} ; Encode g2' _i,j in the same way to obtain bit values g2 _i,j and g3' _i,j , and then encode g3' _i ,j in the same way to obtain bit values g3 _i,j and g4' _{i ,j} , repeat this operation to get g1 _i,j ,g2 _i,j ,…,gk _i,j , where gk _i,j and gk' _i,j represent the same bit, where i,j are secrets The pixel abscissa and ordinate of the image S, 1≤i≤r, 1≤j≤c;

3b) Randomly select k random grids, put the k bit values obtained in step 3a) into the pixels at the same spatial position of the k random grids, and form k subsets B ^*1 _i,j , B ^*2 _i,j ,…,B ^*k _i,j , where 1≤i≤r, 1≤j≤c;

3c) The pixels of the remaining nk random grid images {B ¹ ,B ² ,...,B ⁿ }-{B ^*1 ,B ^*2 ,...,B ^*k } are flipped a coin Randomly extract pixel values, these randomly obtained pixel values are consistent with the spatial positions taken by B ^*1 _i,j , B ^*2 _i,j ,…,B ^*k _i,j , where 1≤i≤r, 1≤j ≤ c;

3d) Steps 3a)-3b) are repeated until all pixels in the secret image S are encoded, thereby generating all basic shared random grid images B _i , where i=1, 2,...,n.

Step 4, perform histogram equalization on each cover image C, and decompose the cover image into small blocks with a pixel size of h×w, where h represents the height of the block, and w represents the width of the block.

The cover images are all grayscale images. The image is divided into blocks, and the average gray level of each block is equivalently similar to obtain the gray level equivalent to the gray level of each small block of the image. In order to improve the cover image after sharing Contrast, histogram equalization can obtain a clearer image contour of the grayscale image, and the contrast of the restored secret image is also high. Mapping the blocks of the secret image to the blocks of its shared image, this method uses the specific method of histogram equalization Proceed as follows:

4a) Transform and decompose the cover images C ₁ , C ₂ ,..., C _n into small pixel blocks with a size of h×w. For images of different sizes, h×w is also different. Generally, the smaller h×w is, the minimum h×w can be 2, and the better the visual quality shared by the back cover;

4b) Let D _i,j be the jth data block of the cover image C _i , find β that satisfies formulas (1) and (2) at the same time, let the series of D _i,j equal to β,

β≤d≤β+1(1)

$\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&le;</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, D _{i, j} represents the jth data block in the original cover image C _i , and the average gray level of D _{i, j} is d, in the formula Represents the number of pixels with gray level k in the original image C _i , β∈{0,1,...,h×w-1} is the value of all series, and its value is determined by the size of the block Decision, where 1≤i≤n, 1≤j≤(r×c)/(h×w);

4c) After the series of all blocks are determined by the formula in step 4b), the label matrices L ₁ , L ₂ ,...,L _n are respectively obtained from the corresponding C ₁ , C ₂ ,...,C _n . Label matrix L _i , the size of which is (r×c)/(h×w), which stores the series of blocks in the cover image C _i , blocks the image, and performs the average gray level of each block, etc. The effect is similar, and the gray scale equivalent to the gray scale of each small block h×w of the image is obtained to facilitate the halftone processing of the next gray scale image, where i=1,2,...,n.

Step 5, subject all resulting blocks to halftoning in dither mode:

5a) Reconstruct n dithering matrices M ₁ , M ₂ ,…,M _n by using the original grayscale cover image C ₁ , C ₂ ,…,C _n , the size is h×w, and the pixel in the dithering matrix M _t is M ^t _i,j , where t=1,2,...,n, 1≤i≤h, 1≤j≤w;

5b) If the pixel value L _i,j of the label matrix L _t obtained in step 4 ≤M _i,j , take a black pixel at the coordinate (i,j) of P _i ,j, otherwise at the position of P _i,j (i, j) position takes white pixel 1, where t=1,2,...,n, 1≤i≤h, 1≤j≤w;

5c) Combine all halftone patterns P _i,j to generate the final halftone image, and then calculate the shared image P _t of all block covers, where t=1,2,...,n, 1≤i≤h,1 ≤j≤w;

5d) Transform the block matrix into the original matrix P _i , and then transform into n matrices with a final size of r×c as the desired shared cover image, where i=1, 2, . . . , n.

Step 6, generate the final secret share:

The size of the basic shared random grid image and cover shared image described in the above steps is the same as the original secret image S, and the size of all images is expressed as r×c, corresponding to the obtained P _i and B _i , randomly selected from P _i δ×r×c pixels, where δ is the stacking ratio, and replaced by pixels at the same coordinate position in B _i to obtain the final shared image F _i , where i=1,2,…,n, and finally generate a user-friendly random-based The security of the grid's visual secret sharing method is determined by the corresponding (k, n) threshold scheme, and the obtained shared images are all meaningful.

Step 7, recover the secret image:

From the n final shared images generated in step 6, take any k final shared images greater than or equal to them and superimpose them to obtain the restored secret image.

Effect of the present invention can be further illustrated by simulation:

1. Simulation conditions

This example is under Intel (R) Core (i5) CPU3.20GHZ Windows7 system, on the Matlab2014a operation platform, completes the emulation experiment of the present invention.

2. Simulation experiment content

Select four grayscale images with a size of 512×512 as the cover image, as shown in Figure 2, and select a binary image with a size of 512×512 as the secret image S, as shown in Figure 3.

For the user-friendly visual secret sharing method based on (k,n) threshold, taking the (2,4) threshold scheme as an example, (a)-(d) in the final shared image in Figure 4 are the final generated 4 A user-friendly shared image is the same size as the original cover and the secret image S, and no secret information can be obtained from the four shared images alone, so the secret image S is safe, and the shared image is no longer meaningless A random grid of images, they are all meaningful images, making it easy for users to manage many shared images. Any two or more shared images can be superimposed to obtain the desired secret image, and then the four images are distributed to the four participants as the shared share owned by each person.

Figure 5 shows the image superposition results, where (a)-(d) are (a)+(b), (a)+(d), (b)+(c) and (a)+(b) in Figure 4 respectively )+(c)+(d), where '+' represents the superposition operation. It can be clearly seen from (a)-(d) in Figure 5 that the secret image can be obtained by superimposing any two images. In order to prove this method Superiority, also simulated the traditional (k, n) threshold visual encryption scheme for comparison, also take the (2, 4) scheme as an example, Figure 6 is the traditional 4 shared images, they are all meaningless random network grid, and the difference between the four images cannot be seen with the naked eye, so sometimes it is easy to attract the attention of the attacker, and it is difficult for the administrator to manage. Figure 7 shows the result of the traditional (k, n) threshold image superposition. (a)-(d) of 7 are (a)+(b), (a)+(d), (b)+(c) and (a)+(b)+(c)+ The superposition result of (d), the traditional (k, n) threshold image superposition result in Fig. 7 is basically consistent with the superposition result in Fig. 5 of this method.

Simulation experiments have proved that the shared images provided by this method are no longer meaningless random grids, but meaningful shared images, that is, user-friendly, easy to distinguish images, and the meaningful shared images generated by this method are superimposed Compared with the previous scheme, the contrast has not changed much, so this method is feasible and better than the previous scheme.

Glossary

S: secret image;

C _i : cover image, where i=1,2,...,n;

G ⁱ : random grid matrix, where i=1,2,…,k;

k: Threshold value, the minimum number of participants required for decryption;

n: The number of shared images is the number of participants;

B _i : base shared random grid image generated by secret image, where i=1,2,…,n;

D _{i, j} : Small blocks after cover image decomposition, where 1≤i≤n, 1≤j≤(r×c)/(h×w);

d: average gray level of D;

β: the equivalent gray level of each small gray block of the image;

L _i : label matrix, where i=1,2,…,n;

M _i : dithering matrix, where i=1,2,...,n;

r: number of rows for secret image and cover image;

c: number of columns for secret image and cover image;

h: the number of rows of the generated small block;

w: the number of columns of the generated small block;

g ₁ ,g ₂ ,…,g _k : K bits generated by random grid transformation;

δ: The coefficient to adjust the ratio of base shared random grid image to cover shared pixels, 0≤δ≤1;

P _i : shared cover image after halftone operation, where i=1,2,…,n;

F _i : the final shared image, where i=1, 2, . . . , n.

Claims (6)

1. A user-friendly visual secret sharing method based on (k, n) threshold, comprising the following steps: (1) Encrypt the secret image S to be protected based on a (k, n) threshold random grid to obtain k basic shared random grid images, and then generate the remaining n-k random grid images by flipping a coin. Obtain n basic shared random grid images, where k is the threshold value and n is the number of participants; (2) Input n gray-scale cover images, first divide each gray-scale image into small blocks of the same size, use histogram equalization to process the image small blocks, and then perform an equivalent to the average gray level of each image small block Similar to get the equivalent gray level of each small image block; (3) carry out dithering halftone processing to the cover image patch after step (2) histogram equalization process, first produce dithering matrix, after utilizing dithering matrix halftone processing, obtain cover shared image; (4) Set the stacking ratio δ, where 0≤δ≤1, the n basic shared random grid images generated in step (1) and the shared cover image generated in step (3) are first divided into blocks, and after the block processing The images are stacked to generate a user-friendly final shared image; (5) From the n final shared images generated in step (4), take any k final shared images greater than or equal to them and superimpose them to obtain the restored secret image. 2. The user-friendly visual secret sharing method based on (k, n) threshold according to claim 1, characterized in that: in step (1), the secret image S is encrypted with a random grid to generate ( k, n) threshold shared random grid steps are as follows: 2a) Generate a random grid G ¹ according to the way of flipping a coin; 2b) When the pixel S _i,j of the secret image S is white, then the pixel G ² _i,j in the second random grid G ² has the same value as the pixel G ¹ _i,j in the random grid G ¹ , On the contrary, it is opposite to the pixel G ¹ _i,j value, where 1≤i≤r, 1≤j≤c, r and c are the width and height of the secret image S respectively; 2c) According to the above steps 2a) and 2b), each pixel S _{i, j} in the secret image S is sequentially encoded to obtain pixel bit values g1 _{i, j} and g2' _{i, j} ; in the same way, g2' _{i , j} is encoded to obtain bit values g2 _i,j and g3' _i,j , and then encode g3' _i ,j in the same way to obtain bit values g3 _i,j and g4' _i,j , and repeat the encoding operation , get g1 _i,j ,g2 _i,j ,…,gk _i,j , where gk _i,j and gk' _i,j represent the same bit, where i,j are the pixel abscissas of the secret image S and ordinate, 1≤i≤r, 1≤j≤c; 2d) Randomly select k random grids, put the k bit values obtained in step 2c) into the pixels at the same spatial position of the selected k random grids, and form k subsets B ^*1 _{i, j} ,B ^*2 _i,j ,…,B ^*k _i,j , where 1≤i≤r, 1≤j≤c; 2e) The pixels of the remaining nk random grid images {B ¹ ,B ² ,...,B ⁿ }-{B ^*1 ,B ^*2 ,...,B ^*k } are flipped a coin Randomly extract pixel values, these randomly obtained pixel values are consistent with the spatial positions taken by B ^*1 _i,j , B ^*2 _i,j ,…,B ^*k _i,j , where 1≤i≤r, 1≤j ≤ c; 2f) Steps 2c)-2e) are repeated until all pixels in the secret image S are encoded, thereby generating all basic shared random grid images B _i , where i=1, 2,...,n. 3. The user-friendly visual secret sharing method based on (k, n) threshold according to claim 1, characterized in that: the method for utilizing histogram equalization to process the cover image described in step (2) is as follows conduct: 3a) Transform and decompose the cover images C ₁ , C ₂ ,...,C _n into small pixel blocks with a size of h×w, and the minimum h×w cannot be less than 2; 3b) Let D _i,j be the jth data block of the cover image C _i , find β that satisfies formulas (1) and (2) at the same time, let the series of D _i,j be equal to β, β≤d≤β+1(1) $\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&le;</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Among them, D _{i, j} represents the jth data block in the original cover image C _i , the average gray level of D _{i, j} is d, and n _i ^k in the formula represents the gray level k in the original image C _i The number of pixels, β∈{0,1,...,h×w-1} is the value of all series, and its value is determined by the size of the block, where 1≤i≤n, 1≤j≤( r×c)/(h×w); 3c) After the series of all blocks are calculated by the formula in step 3b), the label matrix L ₁ , L ₂ ,...,L _n are respectively obtained from the corresponding cover image C ₁ , C ₂ ,...,C _n , L The size of _i is (r×c)/(h×w), store all the block series in the cover image C _i , process the image block, perform equivalent similarity on the average gray level of each block, and find The gray scale equivalent to the h×w gray scale of each small block of the image, where i=1,2,…,n. 4. the user-friendly visual secret sharing method based on (k, n) threshold according to claim 1, is characterized in that: in step (3), utilize dithering matrix to carry out halftone processing method and obtain as follows: 4a) Reconstruct n dithering matrices M ₁ , M ₂ ,…,M _n by using the original grayscale cover images C ₁ , C ₂ ,…,C _n , the size is h×w, and the pixels in the dithering matrix M _t are M ^t _i,j , where t=1,2,...,n, 1≤i≤h, 1≤j≤w; 4b) If the pixel value L _i,j of the label matrix L _t obtained in step (2) is ≤M _i,j , take a black pixel at the coordinate (i,j) of P _i ,j, otherwise at P _i,j The (i, j) position of the white pixel is taken, where t=1,2,...,n, 1≤i≤h, 1≤j≤w; 4c) Combine all halftone patterns P _{i, j} to generate the final halftone image, 1≤i≤r, 1≤j≤c, and then calculate the shared image P _t of all block covers, where t=1,2, ...,n; 4d) Transform the block matrix into the original matrix P _i , and then transform into n matrices with a final size of r×c as the required shared cover image, where i=1, 2, . . . , n. 5. The user-friendly visual secret sharing method based on (k, n) threshold according to claim 1, characterized in that: the basic shared random grid image and cover in step (2) and step (4) The size of the shared image is the same as the original secret image S, and the size of all images is expressed as r×c, corresponding to the obtained P _i and B _i , and δ×r×c pixels are randomly selected from P _i , where δ is the stacking ratio , and replace them with pixels at the same coordinate position in Bi to obtain the final shared image F _i , where _i =1, 2,...,n. 6. The user-friendly visual secret sharing method based on (k, n) threshold according to claim 1, characterized in that: step (5) uses the generated final shared image to recover the secret image, as long as the generated Take n final shared images and take out any final shared images greater than or equal to k and superimpose them to obtain the restored secret image.