A variable direction gray scale density map progressive visual password method, system and electronic device

Abstract

The application discloses a variable direction gray density map progressive visual password method, system and electronic equipment, first, two gray density maps are converted into a first reduced gray density map and a second reduced gray density map; second, the first reduced gray density map is converted into a binary density map A, and the second reduced gray density map is converted into a binary density map B; third, a public share is randomly generated, the public share is combined with the binary density map A to generate a first intermediate share after a first variable direction operation is performed, and the public share is combined with the binary density map B to generate a second intermediate share after a second variable direction operation is performed; finally, the first intermediate share and the second intermediate share are fused to form a fused share; the fused share is split into distribution shares, and part or all of the distribution shares are selected to be superimposed in different directions corresponding to the first variable direction operation and the second variable direction operation along the public share, so that the binary density map A and the binary density map B are respectively revealed or progressively revealed.

Description

Technical Field

[0001] This invention belongs to the field of information security and relates to a variable-direction visual cryptography method, particularly a variable-direction grayscale image progressive visual cryptography method, system, and electronic device. Background Technology

[0002] Visual cryptography (VC) is an encryption method that reveals secret information by superimposing multiple segments of transparent and opaque pixels printed on a transparent film. This method does not require additional computing power or complex cryptographic knowledge for decryption; ordinary users can directly decrypt the secret information using their own human visual system (HSV).

[0003] Although various visual cryptography methods have been proposed, their underlying implementation models are mainly of two types: one is the probabilistic visual cryptography model (KAFRI O, 1987. Encryption of pictures and shapes by randomgrids [J]. Optics Letters, 1987, 12(6): 377-379.), and the other is the deterministic visual cryptography model (NAOR M, 1994. Visual cryptography [C] / / Workshop on the Theory and Application of Cryptographic Techniques. Berlin: Springer, 1994: 1–12.). Both models are based on the superposition of transparent and opaque pixels.

[0004] The difference lies in the approach: probabilistic visual cryptography identifies black and white pixels in a dense image by determining the different probabilities of recovering them after overlaying transparent pixels. This results in incomplete recovery of the dense image pixels, leading to poor visual quality. In contrast, deterministic visual cryptography breaks down the dense image pixels into multiple sub-pixels and uses the differences in contrast or Hamming weights of these sub-pixels during the overlay process to identify black and white pixels. This allows for complete recovery of the dense image pixels, but it causes image dilation. As the dilation increases, the contrast or difference between the black and white pixels in the dense image decreases, making pixel identification difficult.

[0005] To reduce pixel dilation in the recovery of the cryptographic image, among other things, Qiao Mingqiu, 2020 (Qiao Mingqiu, Zhao Zhenzhou. Variable visual cryptography[J]. Journal of Cryptologic, 2020,7(1): 48-55.), LIU F, 2012 (LIU F, WU C, QIAN L. Improving the visual quality of size invariant visual cryptography scheme[J]. Journal of Visual Communication and Image Representation, 2012,23(2): 331-342.), SUN R, 2021 (SUN R, FU ZX, LI XP, et al. A novel size-invariant visual cryptography scheme based on two-level threshold[J]. Journal of Cryptologic Research, 2021,8(4): (572-581.) presents a multi-pixel encryption VC, which uses pixel merging or block-based methods to merge multiple pixels and then split them into sub-pixels using a basic matrix. This is to reduce the inflation rate of the split share relative to the original encrypted image, eliminate inflation, or even further reduce the size of the split share, so as to achieve a balance between restoring the visual quality of the encrypted image and storage capacity. However, these methods will reduce the visual quality of the encrypted image and are only applicable to simple binary black and white images, and cannot be applied to grayscale images with rich texture details.

[0006] Considering that halftone images in the printing field can approximate textured continuous-tone images with simple binary tones, thus delivering better visual quality at the same scale. For example, YAN B, 2018 (YAN B, CHEN N, YANGH, et al. Local blackness preserving visual cryptography for grayscale secretimages[J]. Journal of Information Hiding and Multimedia Signal Processing,2018,9(2): 370-382.) and REN L, 2021 (REN L. A novel raster map exchange scheme based on visual cryptography[J]. Advances in Multimedia, 2021,2021: 1-7.) use halftone to convert grayscale secret images into binary secret images, and then use VC to achieve secret image sharing. YAN B, 2018(YAN B, The ABS (Analysis-by-Synthesis) architecture of threshold visual cryptography spreads the error between the reconstructed cryptographic image and the original cryptographic image to the high-frequency band, thereby improving the reconstruction quality of the cryptographic image. ZHOU J, 2020 (ZHOU J, LIN S. Block Halftoning for size-invariant visual cryptography based on two-dimensional lattices[C] / / 2020 IEEE 6th International Conference on Computer and Communications (ICCC). USA: IEEE Press, 2020:1450-1455.) further applies the techniques used in YAN B, 2018. Threshold VC extended to Threshold VC. SUN R, 2020 (SUN R, FU ZX, YU B. Size-invariant visual cryptography with improved perceptual quality for grayscale image[J]. IEEE Access, 2020,8: 163394-163404.) combines direct binary search halftone processing with multi-pixel cryptographic VC, using local search optimization and global iteration to obtain the optimal micromap reconstruction image. These methods can significantly improve the visual quality of micromap reconstruction. However, halftone processing only has two tones, and during the quantization process, even with error compensation, loss of micromap details is still unavoidable, thus the improvement in visual quality of the recovered micromap remains very limited.

[0007] To further improve image visual quality and reduce the loss of detail in dense images, LUKAC R, 2005 (LUKAC R, PLATANIOTIS K N. Bit-level based secret sharing for image encryption[J]. Pattern Recognition, 2005, 38(5): 767-772.) and TAGHADDOS D, 2014 (TAGHADDOS D, LATIF A. Visual cryptography for gray-scale images using bit-level[J]. Journal of Information Hiding and Multimedia Signal Processing, 2014, 5(1): 90-97.) directly map gray-scale pixels to binary numbers, thereby converting the gray-scale dense image into a bit plane, and then using conventional VC to split the bit plane into multiple partitions. Although this method does not cause a loss of dense image quality when splitting dense image pixels. However, for images, different planes have different weights. Therefore, when reconstructing the dense image, each plane must first recover its corresponding plane by superimposing transparent and opaque pixels using VC. Then, each recovered plane needs to be multiplied by its corresponding weight, and then additive operations are performed to recover the dense image. However, VC can only follow the superposition rule of transparent and opaque pixels and cannot satisfy multiplicative and additive operations, so additional calculations are inevitably involved.

[0008] To address this problem, LIU YL, 2022 (LIU YL, LIU T, YAN B, et al. Visualcryptography using computation-free bit-plane reconstruction[J]. Security and Communication Networks, 2022, 2022: 4617885-4617899.) proposed a grayscale visual cryptography scheme based on binary pattern combination. First, based on the principle that printer DPI (Dots Per Inc) is greater than PPI (Pixels Per Inc), the pixels of the encrypted image are subjected to multi-level halftone grayscale reduction. Second, the grayscale encrypted image pixels are decomposed into binary patterns with different random ink dot counts, using the different ink dot counts to reflect the weights of different binary patterns. Third, the grayscale encrypted image is decomposed into binary bit planes composed of these binary patterns, and bit plane splitting shares are further generated by VC. Finally, the encrypted image is recovered by superimposing the binary bit planes. While this method maintains good reconstruction quality of the VC dense image, it does not fully utilize the binary pixel matrix, and the binary pattern combination method also fails to fully utilize the grayscale levels that the binary pixel matrix can represent. Furthermore, the introduction of a binary pattern combination strategy for reducing grayscale density images generates multiple binary bit-plane images, each of which requires multiple distribution shares through VC, thus incurring additional computational costs and further increasing the channel transmission load.

[0009] In addition to improving the visual quality of the VC algorithm, a VC algorithm for recovering multiple dense images has also been implemented by superimposing distribution shares in different directions or with different translation amounts. For example, TSAO KH, 2008 (TSAO KH, WEI K C. Multiple-image encryption by rotating random grids[C] / / 2008 Eighth International Conference on Intelligent Systems Design and Applications. USA: IEEE, 2008:252-256.) uses random grids to recover two different dense images by superimposing distribution shares in the same direction and by flipping them 90 degrees. CHANG JY, 2010 (CHANG JY, LI MJ, WANG YC, et al. Two-image encryption by random grids[C] / / 2010 10th International Symposium on Communications and Information Technologies. USA: IEEE.2010:458-463.) builds on TSAO KH, 2008 by changing the horizontal translation amount to recover the second dense image. CHE TH, 2012 (CHE TH, TSAO KH, LEE Y S. Yet another multiple-image encryption by rotating random grids [J]. SignalProcessing, 2012, 92(9): 2229-2237.) extended the method of TSAO KH, 2008 to four directions, recovering four encrypted images by superimposing the distribution shares in four different directions. TSAO KH, 2008, CHANG JY, 2010, and CHE TH, 2012 all use random grids to recover encrypted images. Random grids themselves are probabilistic visual ciphers, which will reduce the visual quality of the recovered encrypted images.To improve the visual quality of multi-cryptographic visual cryptography (VC), deterministic visual cryptography was used to replace TSAO in several studies, including: LINS J, 2010 (LINS J, CHEN SK, LIN J C. Flip visual cryptography (FVC) with perfect security, conditionally-optimal contrast, and no expansion [J]. Journal of Visual Communication & Image Representation, 2010, 21(8):900-916.), WAG L, 2020 (WAG L, YAN B, YANG HM, et al. Flip extended visual cryptography for gray-scale and color cover images[J]. Symmetry, 2020, 13(1): 65-78.), and BHOSALE A, 2020 (BHOSALE A, PATIL V S. A (2,2) visual cryptography technique to share two secrets[C] / / 2020 International Conference on Inventive Computation Technologies (ICICT). USA:IEEE ,2020:563-569.). KH,2008, CHANG JY,2010, and CHE TH,2012 use random grids. LINS J,2010 constructs 16 basic matrices to avoid pixel conflicts when distribution shares overlap in different directions, satisfying the pixel position constraints after two dense images are positively superimposed and horizontally flipped. WAG L,2020, building on LINS J,2010, further implements a flipping scheme with a cover. However, this scheme, in addition to considering pixel conflicts when distribution shares overlap in different directions, also needs to solve the mutual interference between the cover image and the dense image, thus requiring complex constraints during construction, increasing the algorithm's complexity. BHOSALE A,2020 avoids pixel conflicts in distribution shares by adjusting pixel blocks, enabling the recovery of different dense images when distribution shares overlap in the same direction and horizontally flipped.The aforementioned methods essentially involve pixel-by-pixel adjustment and determination to reconstruct pixels in different dense images when different directions or translation amounts are superimposed between distribution shares. Their construction schemes are highly complex and tightly bound to specific superposition directions and translation amounts, lacking adaptability to changes in direction. While LINS J, 2010, WAG L, 2020, and BHOSALE A, 2020 improved the visual quality of the reconstructed dense images compared to TSAO KH, 2008, CHANG JY, 2010, and CHE TH, 2012, the constructed fundamental matrix further increases the complexity of the scheme. These methods target binary dense image reconstruction, making it difficult to deliver complex and detailed grayscale reconstruction effects. Furthermore, they all use (2,2) threshold visual codes, lacking flexibility and limiting their practical applications. Summary of the Invention

[0010] The purpose of this invention is to overcome the aforementioned deficiencies of the prior art and provide a method, system, and electronic device for progressive visual cryptography using variable-direction grayscale dense images. To achieve the above objective, this invention employs the following technical solutions:

[0011] A progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction includes the following steps:

[0012] Convert the two grayscale images into a first grayscale-reduced image and a second grayscale-reduced image, respectively.

[0013] Convert the first grayscale-decrease image to a binary image A, and convert the second grayscale-decrease image to a binary image B;

[0014] Randomly generate a common share, perform the first direction change operation on the common share and combine it with the binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common share and combine it with the binary dense graph B to generate the second intermediate share;

[0015] The first intermediate share and the second intermediate share are merged to form a merged share;

[0016] The fusion share is split into distribution shares. Some or all of the distribution shares are selected and superimposed on the public share along different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

[0017] Preferably, the specific methods for converting two grayscale dense images into a first grayscale dense image and a second grayscale dense image include: grayscale function mapping, grayscale interval mapping, and multi-tone error diffusion mapping;

[0018] The first grayscale-degraded dense image is converted into a binary dense image A, and the second grayscale-degraded dense image is converted into a binary dense image B, respectively, using the direct mapping method.

[0019] Preferably, the sizes of the grayscale density image, the first grayscale density image, and the second grayscale density image are: ;

[0020] The sizes of binary dense image A and binary dense image B are: , and The following relationship must be satisfied:

[0021] ;

[0022] The sizes of the public share, the first intermediate share, the second intermediate share, and the merged share are as follows: ,and The constraints are as follows:

[0023] ;

[0024] in, This is the size parameter of the binary pixel array.

[0025] Preferably, the first type of direction-changing operation is different from the second type of direction-changing operation, and both the first and second type of direction-changing operations include: maintaining the original direction, horizontal flipping, vertical flipping, and counterclockwise rotation. Rotate counterclockwise and counterclockwise rotation Or in a rotational direction equivalent to the above direction; the first intermediate share and the second intermediate share generated via the direction-changing operation are complementary.

[0026] Preferably, the methods for randomly generating common shares include: upper boundary method, lower boundary method, left boundary method, right boundary method, main diagonal method, and secondary diagonal method;

[0027] The methods for merging the first intermediate share and the second intermediate share to form a merged share include: top-bottom merging, bottom-top merging, left-right merging, right-left merging, main-auxiliary diagonal merging, and auxiliary-main diagonal merging.

[0028] Preferably, the specific method for splitting the fusion share into distribution shares is to split the fusion share into... Each distribution share, and each black pixel on the fusion share is split into... A black pixel, randomly placed Each distribution share and fusion share corresponds to the black pixel. At each of the following coordinate positions: .

[0029] Preferably, a portion or all of the distributed shares and the public shares are selected and superimposed along different directions corresponding to the first and second direction operations, respectively. The secret map A and secret map B are then revealed or gradually revealed through the human visual system, specifically:

[0030] 1) When the number of distribution shares participating in the restoration of the secret map is not less than When distributing shares:

[0031] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to directly reveal the binary dense map. ;

[0032] The distribution shares, when superimposed in the same direction, are then superimposed with the public share, which undergoes a directional change operation 2. This allows the binary dense map to be directly revealed by the human visual system. ;

[0033] 2) When the number of distribution shares participating in the restoration of the secret map is less than When distributing shares:

[0034] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to progressively reveal the binary dense map. And the closer it gets to The better the visual quality;

[0035] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to progressively reveal the binary dense map. And the closer it gets to The better the visual quality.

[0036] This invention also discloses a progressive visual cryptography system for variable-direction grayscale dense images based on share reconstruction, comprising:

[0037] First conversion unit: used to convert two grayscale dense images into a first reduced grayscale dense image and a second reduced grayscale dense image, respectively;

[0038] The second conversion unit is used to convert the first grayscale-decrease image into a binary image A, and the second grayscale-decrease image into a binary image B.

[0039] Generation unit: used to randomly generate common shares, perform the first direction change operation on the common shares and combine them with binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common shares and combine them with binary dense graph B to generate the second intermediate share;

[0040] Fusion Unit: Used to merge the first intermediate share and the second intermediate share to form a fused share;

[0041] Splitting and Restoration Unit: Used to split the fusion share into distribution shares, select some or all of the distribution shares and superimpose them with the public share along different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

[0042] The present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described above.

[0043] The present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described above.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] This invention discloses a progressive visual cryptography method for grayscale dense images based on share reconstruction. It converts two grayscale dense images into binary dense images, using binary pixel arrays to represent more grayscale levels, which helps maintain good visual quality in the reconstructed dense images. First and second intermediate shares are generated using different direction-changing operations, and these are merged to form a fused share. The fused share is then split into distribution shares, and some or all of these distribution shares are superimposed on the common share along different directions corresponding to the first and second direction-changing operations. This enables flexible reconstruction of dense images with different directions, solving the problem that existing direction-changing schemes require comprehensive consideration of the mutual influence and superposition conflicts of pixels in dense images with different directions, resulting in complex construction and a lack of adaptability to different directions. Furthermore, during this process, the hidden dense images do not interfere with each other, and when superimposed in different directions, no information from the other dense image is leaked. Recovery is only possible when superimposed in the correct direction, providing excellent security.

[0046] Furthermore, the first grayscale de-enhanced dense image is converted into a binary dense image A and the second grayscale de-enhanced dense image is converted into a binary dense image B using the direct mapping method. The multi-level halftone binary matrix direct mapping method can effectively avoid the high load problem of multiple bit plane splitting shares during channel transmission, and can make full use of the binary pixel matrix to represent more gray levels, thereby maintaining good visual quality of dense image reconstruction.

[0047] Furthermore, by using a main-secondary diagonal fusion method to fuse dense images in different directions, there is no need to consider matrix construction and pixel conflict issues;

[0048] Furthermore, it enables flexible reconstruction of variable-direction dense maps in different orientations, such as horizontal flipping, vertical flipping, and counter-clockwise rotation. Rotate counterclockwise Rotate counterclockwise Solving existing direction-changing schemes requires comprehensive consideration of the mutual influence and superposition conflicts of dense pixels in different directions, which is complex and lacks the ability to adapt to direction changes.

[0049] Furthermore, by splitting the fusion share into distribution shares and combining this with the splitting strategy of sharing shares among opaque pixels, the scheme can be flexibly reconfigured and the distribution shares can be universally applicable. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort, and therefore should not be regarded as a limitation on the scope.

[0051] Figure 1 This is a flowchart of the variable-direction grayscale progressive visual cryptography method based on share reconstruction according to an embodiment of the present invention;

[0052] Figure 2 For the confidentiality of embodiments of the present invention Figure 1 ,for Lena, an 8-level grayscale image with high resolution;

[0053] Figure 3 For the confidentiality of embodiments of the present invention Figure 2 ,for Monkey, an 8-level grayscale image with a resolution of [resolution value missing].

[0054] Figure 4 For the confidentiality of embodiments of the present invention Figure 3 ,for Parrot, an 8-level grayscale image with a resolution of [resolution value missing].

[0055] Figure 5 For the confidentiality of embodiments of the present invention Figure 4 ,for Pepper, an 8-level grayscale image with a resolution of [resolution value missing].

[0056] Figure 6 For the confidentiality of embodiments of the present invention Figure 5 ,for A boat with 8 levels of grayscale resolution;

[0057] Figure 7The diagram illustrates the multi-level halftone grayscale reduction strategy of this invention. In the diagram, (a) is the pixel result of the original image; (b) is the result of grayscale function mapping of (a); (c) is the result of grayscale interval mapping of (a); and (d) is the result obtained after multi-tone error diffusion mapping of (a).

[0058] Figure 8 The following diagram illustrates the direct mapping method of the present invention, wherein (a) is an example of a grayscale image; and (b) is an example of a binary image transformed from (a).

[0059] Figure 9 This is a verification example diagram of the variable-direction double-dense graph based on share fusion of the present invention; wherein, (a) is obtained by the direct mapping method. Binary dense map of size (b) is obtained by the direct mapping method. Binary dense map of size (c) Generating a random common share image (d) is a random common share image. Perform the first direction change operation: obtain the equivalent public share while maintaining the original direction. (e) represents the random common share image. Perform the second direction change operation: horizontally flip and stack the equivalent common shares. (f) represents the intermediate share. (g) represents the intermediate share. (h) represents the fusion share. (i) is the fusion share and The result of direct superposition (first type of direction change operation); (j) is the fusion share and The result of horizontal flipping and overlay (the second type of direction change operation);

[0060] Figure 10 This is an example diagram of the opaque pixel fusion share being split into distribution shares according to the present invention; wherein, (a1)~(a5) are Figure 9 (h) The distribution is divided into 5 parts, with the sum of the number of black pixels at each black pixel position in the 5 parts being 1. ;(b1)~(b5) are Figure 9 (h) The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 2. ;(c1)~(c5) are Figure 9 (h) The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 3. ; (d1)~(d5) are Figure 9 (h) The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 4. ;

[0061] Figure 11 This is an example diagram illustrating the restoration of partial or complete distribution shares according to the present invention; wherein, (a1) is... Figure 10 (a1) and Figure 10 (a3) The result of combining the two distribution shares; (a2) is... Figure 10 (a2) Figure 10 (a4) and Figure 10 (a5) The result of summing the three distribution shares; (a3) ​​is... Figure 10 (a1) Figure 10 (a2) Figure 10 (a3) and Figure 10 (a5) The result of the sum of the four shares; (a4) is... Figure 10 (a1)~(a5) are the summation results of all 5 distribution shares; (b1) is... Figure 10 (b2) and Figure 10 (b5) The result of combining the two distribution shares; (b2) is... Figure 10 (b1) Figure 10 (b4) and Figure 10 (b5) The result of the sum of the three distribution shares; (b3) is... Figure 10 (b1) Figure 10 (b2) Figure 10 (b4) and Figure 10 (b5) The result of summing the four distribution shares; (b4) is... Figure 10 (b1)~(b5) are the results of summing all five shares; (c1) is... Figure 10 (c1) and Figure 10 (c4) The result of combining the two distribution shares; (c2) is... Figure 10 (c1) Figure 10 (c3) and Figure 10 (c5) The result of summing the three distribution shares; (c3) is... Figure 10 The result of the summation of the four distribution shares (c1) to (c4); (c4) is... Figure 10 (c1)~(c5) is the sum of all 5 distribution shares; (d1) is... Figure 10 (d1) and Figure 10 (d4) The result of combining the two distribution shares; (d2) is... Figure 10 (d2) Figure 10 (d3) and Figure 10 (d5) The result of summing the three distribution shares; (d3) is... Figure 10 (d1) Figure 10 The result of the summation of the four distribution shares (d3)~(d5); (d4) is Figure 10The result of summing up all 5 distribution shares (d1) to (d5);

[0062] Figure 12 According to the present invention Figure 3 Example images of grayscale levels generated by different mapping methods are shown; (a) is a 17th-order grayscale image under multi-tone error diffusion mapping; (b) is a 37th-order grayscale image under multi-tone error diffusion mapping; (c) is an 82nd-order grayscale image under multi-tone error diffusion mapping; (d) is a 17th-order grayscale image under grayscale function mapping; and (e) is a 17th-order grayscale image under grayscale interval mapping.

[0063] Figure 13 According to the present invention Figure 3 and Figure 5 Example diagram of the generated double-dense graph with variable direction; where (a) is the common share; (b) is the merged share; (c) is the result of directly superimposing the common share and the merged share; and (d) is the result of superimposing the common share and the merged share after horizontal flipping.

[0064] Figure 14 According to the present invention Figure 5 and Figure 4 Example diagram of the generated double-dense graph with variable direction; where (a) is the common share; (b) is the merged share; (c) is the result of directly superimposing the common share and the merged share; and (d) is the result of superimposing the common share and the merged share after vertical flipping.

[0065] Figure 15 According to the present invention Figure 4 and Figure 2 Example of a generated double-dense graph with varying direction; where (a) represents the common share; (b) represents the merged share; (c) represents the direct superposition of the common share and the merged share; and (d) represents the inverse of the common share. The result of rotation and fusion fraction superposition;

[0066] Figure 16 According to the present invention Figure 2 and Figure 6 Generate inverse Example diagrams of double-dense graphs with varying directions; (a) common share; (b) merged share; (c) direct superposition of common share and merged share; (d) inverse common share. The result of rotation and fusion fraction superposition;

[0067] Figure 17 This invention is by Figure 13 Combination A diagram illustrating the verification of split distribution shares; where (a) represents the common share; and (b) represents the distribution share. Figure 13 (b) Merging share adopts Distribution share of the split method (c) is the result of directly superimposing (a) and (b); (d) is the result of horizontally flipping (a) and then superimposing (b) in the forward direction.

[0068] Figure 18 This invention is by Figure 13 Combination A diagram illustrating the verification of split distribution shares; where (a) represents the common share; and (b) represents the distribution share. Figure 13 (b) Merging share adopts Distribution share of the split method (c) is for Figure 13 (b) Merging share adopts Distribution share of the split method (d) is for Figure 13 (b) Merging share adopts Distribution share of the split method (e) is for Figure 13 (b) Merging share adopts Distribution share of the split method (f) is for Figure 13 (b) Merging share adopts Distribution share of the split method (g) is the result of directly superimposing (a) and (b); (h) is the result of directly superimposing (a) with (b) and (c); (i) is the result of directly superimposing (a) with (b), (c) and (d); (j) is the result of directly superimposing (a) with (b), (c), (d) and (e); (k) is the result of directly superimposing (a) with (b), (c), (d), (e) and (f); (l) is the result of superimposing (a) with (b) after horizontal flipping; (o) is the result of superimposing (a) with (b) and (c); (p) is the result of superimposing (a) with (b), (c) and (d) after horizontal flipping; (q) is the result of superimposing (a) with (b), (c), (d) and (e) after horizontal flipping; (r) is the result of superimposing (a) with (b), (c), (d), (e) and (f) after horizontal flipping.

[0069] Figure 19 This invention is by Figure 13 Combination A diagram illustrating the splitting strategy verification example. (a) represents the common share; (b) represents the shares held by the shareholder. Figure 13 (b) Merging share adopts Distribution share of the split method (c) is for Figure 13 (b) Merging share adopts Distribution share of the split method (d) is for Figure 13(b) Merging share adopts Distribution share of the split method (e) is for Figure 13 (b) Merging share adopts Distribution share of the split method (f) is for Figure 13 (b) Merging share adopts Distribution share of the split method (g) is the result of directly superimposing (a) and (c); (h) is the result of directly superimposing (a) with (c) and (e); (i) is the result of directly superimposing (a) with (c), (e) and (f); (j) is the result of directly superimposing (a) with (b), (c), (e) and (f); (k) is the result of directly superimposing (a) with (b), (c), (d), (e) and (f); (l) is the result of superimposing (a) with (c) after horizontal flipping; (o) is the result of superimposing (a) with (c) and (e); (p) is the result of superimposing (a) with (c), (e) and (f) after horizontal flipping; (q) is the result of superimposing (a) with (b), (c), (e) and (f) after horizontal flipping; (r) is the result of superimposing (a) with (b), (c), (d), (e) and (f) after horizontal flipping. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0071] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0072] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0073] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0074] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0075] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0076] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but are not limited to this embodiment.

[0077] Figure 1 A flowchart of a variable-direction grayscale progressive visual cryptography scheme based on share reconstruction is presented, including the following steps:

[0078] S1: Convert the two grayscale images into a first grayscale-reduced image and a second grayscale-reduced image, respectively;

[0079] S2: Convert the first grayscale-reduced dense image into a binary dense image A, and the second grayscale-reduced dense image into a binary dense image B;

[0080] S3: Randomly generate a common share, perform the first direction change operation on the common share and combine it with the binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common share and combine it with the binary dense graph B to generate the second intermediate share;

[0081] S4: Merge the first intermediate share and the second intermediate share to form a merged share;

[0082] S5: Split the fusion share into distribution shares, select some or all of the distribution shares and superimpose them with the public share along the different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

[0083] In the steps given above:

[0084] The sizes of the grayscale density image, the first grayscale density image, and the second grayscale density image involved in S1 are: ;

[0085] The sizes of binary dense maps A and B in S2 are: , and The following relationship must be satisfied:

[0086] ;

[0087] The sizes of the common share, first intermediate share, second intermediate share, and merged share in S3 are as follows: ,and The constraints are as follows:

[0088] ;

[0089] in: The size parameter of a binary pixel matrix is ​​used to solve the problem of generating different grayscale levels of pixels when using a single color of ink or toner in a printer. This involves using different grayscale levels of a single pixel to... The binary pixel array is represented by different numbers of ink dots of the same color. The more ink dots there are, the darker the ink dot color of the pixel, and vice versa, thus presenting different pixel grayscale levels under the visual effect of the human eye.

[0090] remember The grayscale density images of different sizes are respectively ,in For a positive integer, the specific processing procedure for S1 is as follows: convert it into a grayscale density image according to formula (1). The grayscale reduction operation here refers to compressing the grayscale range of a pixel without changing the number of pixels, thus reducing the grayscale range of the pixel.

[0091] (1)

[0092] Among them, the function This is a grayscale reduction function, where the first parameter is the input image and the second parameter is the grayscale level. There are multiple ways to implement this, such as: grayscale function mapping, grayscale range mapping, and multi-tone error diffusion mapping, etc.

[0093] The following is For example, the specific processing method will be explained in detail:

[0094] 1) Gray-scale function mapping

[0095] for Mapped according to equation (1a) as Repeat until All elements After processing, a grayscale image can be obtained. .

[0096] (1a)

[0097] Among them, symbols This indicates rounding to the nearest integer.

[0098] For example, suppose we take Assuming Then from:

[0099] therefore .

[0100] 2) Gray-scale range mapping

[0101] Will Divide equally Let the intervals be denoted as intervals. As shown in equation (1b1):

[0102] (1b1)

[0103] in: The interval length;

[0104] for ,like Then, according to formula (1b2) Mapped to Repeat until All elements After processing, a grayscale image can be obtained. .

[0105] (1b2)

[0106] For example, suppose we take Assuming Then, from equation (1b1), we know that: ,because Therefore, according to equation (1b2): ,therefore .

[0107] 3) Multitone error diffusion mapping

[0108] S1-1: Input The size of the grayscale image is ;

[0109] S1-2: For ,Will Quantized according to formula (1c1) ,in: To quantify the amplitude, the symbol This indicates rounding down. It is the first row scanned in row-first order. The first in the row 1 pixel, ;

[0110] (1c1)

[0111] S1-3: Calculate according to formula (1c2) and Quantization error ;

[0112] (1c2)

[0113] S1-4: Quantization error is calculated according to formula (1c3). Assigned to Among the surrounding valid pixels that were not scanned in row priority order, among which The set of coordinates of effective pixels, specifically defined in equation (1c4), i.e., located at... Within the effective range ( ,Right now ),and Adjacent and valid pixel coordinates that have not been scanned in row priority order; weight There are multiple allocation methods. The first potential decomposition method is shown in equation (1c5), where... The number of valid coordinates; weights The second potential allocation method is initialization. Then correct according to formula (1c6); the symbol [] is for rounding.

[0114] (1c3)

[0115] (1c4)

[0116] (1c5)

[0117] (1c6)

[0118] S1-5: Repeat steps S1-2 to S1-4 until... Once processing is complete, the grayscale image can be... Grayscale reduction .

[0119] Note: Equation (1c1) can also be in other forms, such as Equation (1c1a) and Equation (1c1b). In addition, S1-4 can also adopt other quantization error propagation methods, such as average distribution and other proportional distribution methods.

[0120] (1c1a)

[0121] (1c1b)

[0122] Among the symbols and These represent rounding up and rounding to the nearest integer, respectively. Figure 7 This is a verification diagram of the grayscale reduction method of the present invention.

[0123] For example: Suppose we take Assuming That is, corresponding to Figure 7 (a) Then, from equation (1c1), we know: According to equation (1c2): , The following are the valid pixels that were not scanned in row priority order: Therefore, according to equation (1c3): , , , ,in: And satisfy: Therefore, the weights are corrected according to equation (1c6), and the weights remain the same: The follow-up Continue to use the above method and calculate using the updated pixel values. Figure 7 (b) Figure 7 (c) and Figure 7 (d) are respectively Figure 7 (a) The result obtained after grayscale function mapping, grayscale interval mapping and multi-tone error diffusion mapping.

[0124] Let binary dense graph A and binary dense graph B in S2 be respectively Binary dense map of size Then S2 uses the direct mapping method to convert the first grayscale-degraded dense image into a binary dense image A, and the specific method for converting the second grayscale-degraded dense image into a binary dense image B is to... Convert according to formula (2) Binary dense map of size .

[0125] (2)

[0126] Where: function This is used to convert each pixel of an input grayscale image into a binary image of a specified size, where the first parameter is the input grayscale image and the second parameter is the size of the binary matrix for each pixel.

[0127] The following is For example, give Specific processing procedures

[0128] S2-1: Initialize size to binary image binary image All white;

[0129] S2-2: For Calculate according to formula (2a) Corresponding number of ink dots ;

[0130] (2a)

[0131] S2-3: Initialization Size of a binary matrix Choose from Set each unique position to a black dot;

[0132] S2-4: Will Placed above The coordinates of the top left corner are [coordinates] and the size is [value]. On the small pieces;

[0133] S2-5: Repeat steps S2-2 to S2-4 until all are completed. After processing, a value of [size] can be obtained. binary image .

[0134] For example: assuming , Then, from equation (2a), we know that: ,therefore .

[0135] Figure 8 This is an example diagram of the direct mapping method of the present invention, wherein... Figure 8 (a) is an example of a grayscale image. Figure 8(b) is Figure 8 (a) A sample of the transformed binary image, where... small pieces .

[0136] In this way, the proposed method can directly map downsampled pixels to a binary pixel matrix, and can fully utilize the binary pixel matrix to represent more gray levels; furthermore, with the development of printing technology, ink dots will become smaller and ink density (DPI) will become larger, thus increasing the scale of the binary pixel matrix. The size will increase, thus presenting more pixel grayscale levels. The proposed method is not limited to a binary pixel array of a specific size, so it will present more grayscale levels, resulting in better visual quality. The proposed method also avoids the multiple binary bit-plane images generated by the binary pattern combination strategy, and avoids the additional computational cost and transmission load caused by the bit-plane further forming a visual cryptographic distribution share.

[0137] Let the randomly generated common share be... , will public share The equivalent public share corresponding to performing the first type of direction change operation is , will public share The equivalent public share corresponding to performing the second type of direction change operation is , combined The first intermediate share generated by the binary dense graph A , combined Generate the second intermediate share from the binary dense graph B. The size of these images is Note: Equivalent public share refers to... The image appears when placed in different orientations. The available orientations are: keep original orientation, flip horizontally, flip vertically, and rotate counter-clockwise. Rotate counterclockwise and counterclockwise rotation Or in a rotational direction equivalent to the above direction, and in which Operations that place objects in different directions are called direction-changing operations.

[0138] The specific processing procedure for S3 is as follows:

[0139] First, generate a random common share image. :

[0140] S3-1a: Initialization Binary image of size and will Divided into Non-overlapping matrix blocks of varying sizes;

[0141] S3-1b: Note the first indivual Matrix blocks are ,right main diagonal element One element is randomly selected and assigned the value 0.

[0142] S3-1c: Repeatedly execute S3-1b until... All of the divisions After processing the non-overlapping matrix blocks, the final result will be... Output.

[0143] Note: The random common share image generated above uses the main diagonal method, i.e. Each division The main diagonal of the non-overlapping matrix blocks is randomly composed of one black and one white pixel, while the secondary diagonal consists entirely of white pixels. Since black pixels are opaque and white pixels are visually transparent or translucent, therefore... When superimposed along the main diagonal direction, two results can be achieved: one black and one white pixel, or both pixels completely black. This allows for the differentiation of different secret information based on different Hamming weights. However, in non-main diagonal directions, the random common share image... All pixels are completely transparent, thus preserving the original state of the superimposed shares, making it impossible to identify the corresponding secret information state. Similarly, for random common share images... Each division Non-overlapping matrix blocks can also be generated in other ways, such as: Upper boundary method: the two pixels at the upper boundary are randomly composed of one black and one white pixel, while the other two pixels remain white; Lower boundary method: the two pixels at the lower boundary are randomly composed of one black and one white pixel, while the other two pixels remain white; Left boundary method: the two pixels at the left boundary are randomly composed of one black and one white pixel, while the other two pixels remain white; Right boundary method: the two pixels at the right boundary are randomly composed of one black and one white pixel, while the other two pixels remain white; and Secondary diagonal method: the two pixels at the secondary diagonal are randomly composed of one black and one white pixel, while the other two pixels remain white. The upper boundary, lower boundary, left boundary, right boundary, main diagonal, and secondary diagonal correspond to the generation direction of the one black and one white pixel in the upper boundary method, lower boundary method, left boundary method, right boundary method, main diagonal method, and secondary diagonal method, respectively.

[0144] The first intermediate share is then generated. Here it is agreed that... The equivalent public share obtained by performing the first direction change operation Each division The generation direction of the non-overlapping matrix block of 1 black and 1 white pixels remains unchanged, and the generation direction is the main diagonal.

[0145] S3-2a: Initialization First intermediate share of size ,Will Divided into Non-overlapping matrix blocks of varying sizes;

[0146] S3-2b: Will Perform the first type of direction change operation to generate equivalent public shares The direction-changing operation here can be keeping the original direction unchanged, horizontal flipping, vertical flipping, or counterclockwise rotation. Rotate counterclockwise and counterclockwise rotation Or a rotational direction equivalent to the above direction;

[0147] S3-2c: For ,remember The division of the first Each matrix block is According to formula (3a) combined with equivalent public share Revise main diagonal element The state in which yes Elements on the main diagonal (by convention) The generation direction is the main diagonal).

[0148] (3a)

[0149] S3-2d: Repeat S3-2c until... All of the divisions After processing the non-overlapping matrix blocks, the final intermediate share is obtained. Output.

[0150] Note: For Equivalent public share obtained by performing a change-of-direction operation This will make Each division The generation direction of black and white pixels on non-overlapping matrix blocks remains unchanged or changes. For example, the main diagonal is transformed into the secondary diagonal by horizontal or vertical flipping, and the left boundary is transformed into the upper, lower, and right boundaries by rotating at a certain angle or by horizontal and vertical flipping operations.

[0151] Equation (3a) can also have other forms, such as: upper boundary as in equation (3a1), lower boundary as in equation (3a2), left boundary as in equation (3a3), right boundary as in equation (3a4), and auxiliary diagonal as in equation (3a5), etc.

[0152] Revise upper boundary element The state in which yes Elements on the upper boundary;

[0153] (3a1)

[0154] Revise lower boundary element The state in which yes Elements on the lower boundary;

[0155] (3a2)

[0156] Revise left boundary element The state in which yes Elements on the left boundary;

[0157] (3a3)

[0158] Revise right boundary element The state in which yes Elements on the right boundary;

[0159] (3a4)

[0160] Revise secondary diagonal elements The state in which yes Elements on the secondary diagonal;

[0161] (3a5)

[0162] From equation (3a) and its various other forms, from equation (3a1) to equation (3a5), it can be seen that and The generation direction remains consistent, and the second intermediate share is also generated. hour, and The generation direction remains consistent and satisfies and They are complementary. This is a convention for... The equivalent public share obtained by performing the second direction change operation Each division The generation direction of non-overlapping matrix blocks of 1 black and 1 white pixels and Each division The non-overlapping matrix blocks of 1 black and 1 white pixels are generated in complementary directions, which allows for further stipulation that the upper and lower boundaries are complementary, the left and right boundaries are complementary, and the main and secondary diagonals are complementary. (This is based on the example provided.) If the generation direction is the main diagonal, then... The generation direction is the secondary diagonal. The following is combined with... Give the first intermediate share Specific generation method:

[0163] S3-3a: Initialization First intermediate share of size ,Will Divided into Non-overlapping matrix blocks of varying sizes;

[0164] S3-3b: Will Perform the second type of direction change operation to generate equivalent public shares The direction-changing operation here can be horizontal flip, vertical flip, or counter-clockwise rotation. Rotate counterclockwise and counterclockwise rotation Or in a rotational direction equivalent to the above direction, and with Their generation directions are complementary;

[0165] S3-3c: For ,remember The division of the first Each matrix block is respectively Modify according to formula (3b) secondary diagonal elements The state in which yes Elements on the secondary diagonal (by convention) The generation direction is the secondary diagonal).

[0166] (3b)

[0167] S3-3d: Repeatedly execute S3-3c until... All of the divisions After processing the non-overlapping matrix blocks, the final intermediate share is obtained. Output.

[0168] Note: Equation (3b) may also have other forms, such as: upper boundary as Equation (3b1), lower boundary as Equation (3b2), left boundary as Equation (3b3), right boundary as Equation (3b4), and auxiliary diagonal as Equation (3b5), etc.

[0169] Revise upper boundary element The state in which yes Elements on the upper boundary;

[0170] (3b1)

[0171] Revise lower boundary element The state in which yes Elements on the lower boundary;

[0172] (3b2)

[0173] Revise left boundary element The state in which yes Elements on the left boundary;

[0174] (3b3)

[0175] Revise right boundary element The state in which yes Elements on the right boundary;

[0176] (3b4)

[0177] Revise main diagonal element The state in which yes Elements on the main diagonal;

[0178] (3b5)

[0179] From equation (3b) and its various other forms, from equation (3b1) to equation (3b5), it can be seen that and The generation direction remains consistent. Combining equation (3a) and other forms: equations (3a1) to (3a5) show that the first intermediate share With the second intermediate share They are complementary and will not cause any conflict.

[0180] The share of integration is The first intermediate share With the second intermediate share To perform fusion, the sizes of these images are all ;

[0181] The specific processing procedure for S4 is as follows:

[0182] S4-1: Initialize fusion share ;

[0183] S4-2: For ,remember The division of the first The number of non-overlapping matrix blocks of size is According to formula (4a) The main diagonal elements and The secondary diagonal elements are placed On the main and secondary diagonals (as agreed here) and (Main and auxiliary diagonal fusion)

[0184] (4a)

[0185] S4-3: Repeat step S4-2 until... All of the above divisions After processing the non-overlapping small blocks, the final result will be... Output.

[0186] Note: The above fusion method uses the main-secondary diagonal approach, based on the above... and In addition to the different generation methods, there are also the following fusion methods: top-bottom fusion as shown in equation (4a1), bottom-top fusion as shown in equation (4a2), left-right fusion as shown in equation (4a3), right-left fusion as shown in equation (4a4), and auxiliary-main fusion as shown in equation (4a5).

[0187] Integration of top and bottom:

[0188] (4a1)

[0189] bottom-up fusion:

[0190] (4a2)

[0191] Left and right integration:

[0192] (4a3)

[0193] Right and left fusion:

[0194] (4a4)

[0195] Supporting and supporting elements fusion:

[0196] (4a5)

[0197] For the share of integration ,when After performing the first direction change operation and Overlay can reveal binary dense maps. ;when After performing the second direction change operation and Overlay can reveal binary dense maps. . Figure 9 Verification examples for S3 and S4 are given. Figure 9 (a) and Figure 9 (b) are obtained by the direct mapping method. Binary dense map of size and binary dense graph ; Figure 9 (c) is the generation of a random common share image. ; Figure 9 (d) and Figure 9 (e) is a random common share image The equivalent common shares obtained by performing the first and second direction change operations respectively ; Figure 9 (f), 9(g) and 9(h) are intermediate shares respectively. and integration share ; Figure 9 (i) and Figure 9 (j) is related to The results of direct overlay (first type of direction change operation) and horizontal flip overlay (second type of direction change operation). From Figure 9 (c) It can be seen that the random public share Each division Each small block is a combination of 3 white pixels and 1 black pixel, therefore all The small Hamming weights show no difference and have corresponding secret diagrams. There is no real connection; from Figure 9 (d) and Figure 9 (e) It can be seen that the equivalent public share To maintain the original direction, therefore, and the random common share image Completely identical, equivalent public share Corresponding to The horizontal flip direction, therefore all The Hamming weights for small blocks are identical, as are those for the corresponding dense graphs. There is no real connection; from Figure 9 Looking at (f) and 9(g), the middle share Each The Hamming weights of small blocks are all combinations of 3 white pixels and 1 black pixel, with no difference in Hamming weights, and at the same time, they do not reveal the secret image. Any information; from Figure 9 (h) See, integration share All The Hamming weights of small blocks are all combinations of 2 white pixels and 2 black pixels, and their Hamming weights are identical, therefore they do not reveal the secret image. Any information; from Figure 9 (i) See, integration share and Direct superposition (i.e., fusion share) With equivalent share The direct overlay (the first type of directional operation) shows that after overlay, the top-left and bottom-right small blocks have 3 black pixels, while the remaining small blocks have 2 black pixels. This makes the top-left and bottom-right small blocks appear darker, while the remaining small blocks appear lighter. The resulting visual effect is similar to that of a dense image. It is consistent; from Figure 9 (j) Look at the integration share and Horizontal flip overlay (i.e., fusion share) With equivalent share (Direct overlay, second type of directional operation). We can see that after overlay, the small blocks in the upper right and lower left corners of the image have 3 black pixels, while the remaining small blocks have 2 black pixels. Therefore, the upper right and lower left corners are darker, while the remaining small blocks are whiter. This results in a visual effect similar to a dense image. They are consistent.

[0198] S5's processing method is: to merge the shares Split into There are distribution shares, denoted as distribution shares. Each black pixel on the fusion share is split into A black pixel, randomly placed Each distribution share and fusion share corresponds to the black pixel. At each of the following coordinate positions: , The number of shares to be distributed. The following describes the specific processing steps for determining the number of black pixels at each pixel location:

[0199] S5-1: Initialization Distribution share of size ;

[0200] S5-2: Notes yes superior The pixel of the position, denoted They are respectively superior The pixel of the position, for ,like Then from Select from the positions Let there be a random position, denoted as... ,Will Set to 0;

[0201] S5-3: Repeat S5-2 until... Once all pixels have been processed, the distribution share can be obtained. .

[0202] Figure 10 Is Figure 9 Based on (h), Size Different and Splitting instances under different value conditions Figure 10 (a1)~(a5) are The distribution is divided into 5 parts, with the sum of the number of black pixels at each black pixel position in the 5 parts being 1. ; Figure 10 (b1)~(b5) are The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 2. ; Figure 10 (c1)~(c5) are The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 3. ; Figure 10 (d1)~(d5) are The distribution is divided into 5 parts, with the total number of black pixels at each black pixel position in the 5 parts being 4. .

[0203] Note: when At this time , equivalent to No splitting was performed; at this point, it can be done through... After performing the first direction change operation and Direct overlay can reveal binary dense maps. ,when After performing the second direction change operation and Direct overlay can reveal binary dense maps. At this time, the corresponding verification instance and Figure 9 They are exactly the same.

[0204] when ,at this time All shares split and Same, that is At this time, it can be done After performing the first direction change operation and By directly superimposing any one or more of the elements, a binary dense map can be revealed. ,when After performing the second direction change operation, and By directly superimposing any one or more of the elements, a binary dense map can be revealed. At this time, the corresponding verification instance and Figure 9 They are exactly the same.

[0205] when and At the same time, the recovery status of the secret map can be discussed as follows:

[0206] 1) When the number of distribution shares participating in the restoration of the secret map is not less than When distributing shares:

[0207] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to directly reveal the binary dense map. ;

[0208] The distribution shares, when superimposed in the same direction, are then superimposed with the public share, which undergoes a directional change operation 2. This allows the binary dense map to be directly revealed by the human visual system. ;

[0209] 2) When the number of distribution shares participating in the restoration of the secret map is less than When distributing shares:

[0210] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to progressively reveal the binary dense map. And the closer it gets to The better the visual quality;

[0211] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to progressively reveal the binary dense map. And the closer it gets to The better the visual quality.

[0212] Note: At this time That is, when the number of distribution shares participating in the restoration of the secret map is not less than 1 distribution share:

[0213] The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 1, allowing the human visual system to directly reveal the binary dense map. ;

[0214] The distribution shares, when superimposed in the same direction, are then superimposed with the public share, which undergoes a directional change operation 2. This allows the binary dense map to be directly revealed by the human visual system. Therefore, this situation and and The cases where the values ​​are not both 1 are completely consistent.

[0215] Figure 11 Is Figure 10 right Figure 9 (h) Merging Share Based on the split, it gives and Not waiting, Verification example of recovering large and small dense images, where:

[0216] Figure 11 (a1) is Figure 10 (a1) and Figure 10 (a3) The result of combining the two distribution shares; Figure 11 (a2) is Figure 10 (a2) Figure 10 (a4) and Figure 10 (a5) The result of the sum of the three distribution shares; Figure 11 (a3) is Figure 10 (a1) Figure 10 (a2) Figure 10 (a3) and Figure 10 (a5) The result of the sum of the four shares; Figure 11 (a4) is Figure 10 (a1)~(a5) are the summation results of all 5 distribution shares; it can be seen that only when all 5 distribution shares are summed can the fusion share be achieved. Only then is it fully recovered, which is equivalent to Figure 9 (h); From this, we can know that: when hour, Therefore, only when all distribution shares are fully participated, All black pixels in the image are restored, allowing for the distribution of shares in the same direction, which is then superimposed with the public share through a direction-changing operation 1. This enables the human visual system to directly reveal the binary dense image. The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 2, allowing the human visual system to directly reveal the binary dense map. When the number of distribution shares participating in the restoration of the secret map is less than When distributing a share, then Since it cannot be fully restored, the superposition of the distributed shares in the same direction and the superposition of the public share in a different direction can be gradually revealed by the human visual system through the binary dense map. And the closer it gets to The better the visual quality, the more the distribution shares are superimposed in the same direction and then superimposed with the public share's direction-changing operation 1, the more the binary dense map can be gradually revealed by the human visual system. And the closer it gets to The better the visual quality.

[0217] Figure 11 (b1) is Figure 10 (b2) and Figure 10 (b5) The result of combining the two distribution shares; Figure 11 (b2) is Figure 10 (b1) Figure 10 (b4) and Figure 10 (b5) The result of the sum of the three distribution shares; Figure 11 (b3) is Figure 10 (b1) Figure 10 (b2) Figure 10 (b4) and Figure 10 (b5) The result of the sum of the four distribution shares; Figure 11 (b4) is Figure 10 (b1)~(b5) Results of all 5 shares being superimposed; it can be seen that only when 4 or more distribution shares are superimposed can the merged share be achieved. Only then is it fully recovered, which is equivalent to Figure 9 (h); From this, we can know that: when hour, Therefore, only when all four or more distribution shares participate, All black pixels in the image are restored, allowing for the distribution of shares in the same direction, which is then superimposed with the public share through a direction-changing operation 1. This enables the human visual system to directly reveal the binary dense image. The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 2, allowing the human visual system to directly reveal the binary dense map. When the number of distribution shares participating in the restoration of the secret map is less than When distributing a share, then Since it cannot be fully restored, the superposition of the distributed shares in the same direction and the superposition of the public share in a different direction can be gradually revealed by the human visual system through the binary dense map. And the closer it gets to The better the visual quality, the more the distribution shares are superimposed in the same direction and then superimposed with the public share's direction-changing operation 1, the more the binary dense map can be gradually revealed by the human visual system. And the closer it gets to The better the visual quality.

[0218] Figure 11 (c1) is Figure 10 (c1) and Figure 10 (c4) The result of combining the two distribution shares; Figure 11 (c2) is Figure 10 (c1) Figure 10 (c3) and Figure 10 (c5) The result of the sum of the three distribution shares; Figure 11 (c3) is Figure 10 The result of the summation of the four distribution shares (c1) to (c4); Figure 11 (c4) is Figure 10 The result of combining all 5 distribution shares (c1) to (c5); it can be seen that only when 3 or more distribution shares are combined can the fusion share be achieved. Only then is it fully recovered, which is equivalent to Figure 9 (h); From this, we can know that: when hour, Therefore, only when all three or more distribution shares participate, All black pixels in the image are restored, allowing for the distribution of shares in the same direction, which is then superimposed with the public share through a direction-changing operation 1. This enables the human visual system to directly reveal the binary dense image. The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 2, allowing the human visual system to directly reveal the binary dense map. When the number of distribution shares participating in the restoration of the secret map is less than When distributing a share, then Since it cannot be fully restored, the superposition of the distributed shares in the same direction and the superposition of the public share in a different direction can be gradually revealed by the human visual system through the binary dense map. And the closer it gets to The better the visual quality, the more the distribution shares are superimposed in the same direction and then superimposed with the public share's direction-changing operation 1, the more the binary dense map can be gradually revealed by the human visual system. And the closer it gets to The better the visual quality.

[0219] Figure 11 (d1) is Figure 10 (d1) and Figure 10 (d4) The result of superimposing the two distribution shares; Figure 11 (d2) is Figure 10 (d2) Figure 10 (d3) and Figure 10 (d5) The result of the sum of the three distribution shares; Figure 11 (d3) is Figure 10 (d1) Figure 10 The result of superimposing the four distribution shares (d3) to (d5); Figure 11 (d4) is Figure 10 The results of combining all 5 distribution shares (d1) to (d5); it can be seen that when two or more distribution shares are combined, the merged share... It can be fully restored, that is, it is equivalent to Figure 9 (h); From this, we can know that: when hour, Therefore, only when two or more distribution shares participate can the distribution proceed. All black pixels in the image are restored, allowing for the distribution of shares in the same direction, which is then superimposed with the public share through a direction-changing operation 1. This enables the human visual system to directly reveal the binary dense image. The distribution shares, when superimposed in the same direction, are then superimposed with the public share's direction-changing operation 2, allowing the human visual system to directly reveal the binary dense map. When the number of distribution shares participating in the restoration of the secret map is less than When distributing a share, then Since it cannot be fully restored, the superposition of the distributed shares in the same direction and the superposition of the public share in a different direction can be gradually revealed by the human visual system through the binary dense map. And the closer it gets to The better the visual quality, the more the distribution shares are superimposed in the same direction and then superimposed with the public share's direction-changing operation 1, the more the binary dense map can be gradually revealed by the human visual system. And the closer it gets to The better the visual quality.

[0220] Figures 2 to 6 The corresponding secrets of the embodiments of the present invention are as follows. Figure 1 Top Secret Figure 5 , respectively Lena, an 8-level grayscale image with a resolution of [resolution value missing]. Monkey, an 8-level grayscale image with a resolution of [resolution value missing]. Parrot, an 8-level grayscale image with a resolution of [resolution value missing] Pepper and 8-level grayscale image resolution A boat with 8 levels of grayscale resolution.

[0221] Figure 12 Give the binary images mapped under different gray levels. Figure 12 (a) under the condition of multitone error diffusion mapping That is, a 17-level grayscale image. Figure 12 (b) under the condition of multitone error diffusion mapping That is, a 37-level grayscale image. Figure 12 (c) under the condition of multitone error diffusion mapping That is, an 82-level grayscale image. Figure 12 (d) is under the condition of grayscale function mapping A 17-level grayscale image, Figure 12 (e) is under the condition of grayscale range mapping That is, a 17-level grayscale image.

[0222] Figure 13 The following is given Figure 3 and Figure 5 For a grayscale dense image, under the condition of multi-tone error diffusion mapping. A mapping method using a main and auxiliary diagonal approach is employed to achieve a horizontally flipped double-dense map scheme. Figure 13 (a) is the common share. Figure 13 (b) is the share of integration. Figure 13 (c) is the result of directly adding up the common share and the merged share. Figure 13 (d) is the result of the public share being flipped horizontally and then superimposed with the merged share.

[0223] Figure 14 The following is given Figure 5 and Figure 4 For a grayscale dense image, under the condition of multi-tone error diffusion mapping. A mapping method using a main-secondary diagonal approach is employed to achieve a vertically flipped double-dense map scheme. Figure 14 (a) is the common share. Figure 14 (b) is the share of integration. Figure 14 (c) is the result of directly adding up the common share and the merged share. Figure 14 (d) is the result of vertically flipping the public share and superimposing it with the merged share.

[0224] Figure 15 The following is given Figure 4 and Figure 2 For a grayscale dense image, under the condition of multi-tone error diffusion mapping. The mapping is performed using a main-secondary diagonal approach to achieve the inverse. Rotational double-dense diagram scheme, Figure 15 (a) is the common share. Figure 15 (b) is the share of integration. Figure 15 (c) is the result of directly adding up the common share and the merged share. Figure 15 (d) is the reverse of the public share The result is superimposed with the fusion fraction after rotation.

[0225] Figure 16 The following is given Figure 2 and Figure 6 For a grayscale dense image, under the condition of multi-tone error diffusion mapping. The mapping is performed using a main-secondary diagonal approach to achieve the inverse. Rotational double-dense diagram scheme, Figure 16 (a) is the common share. Figure 16 (b) is the share of integration. Figure 16 (c) is the result of directly adding up the common share and the merged share. Figure 16 (d) is the reverse of the public share The result is the result of superimposing the rotation and fusion fraction.

[0226] Figure 17 exist Figure 13 Based on this, Figure 13(b) Merging share adopts Splitting method Figure 17 (a) is the common share. Figure 17 (b) represents the split distribution shares. Figure 17 (c) is Figure 17 (a) and Figure 17 (b) Direct superposition results Figure 17 (d) is Figure 17 (a) After horizontal flipping and Figure 17 (b) Overlay results.

[0227] Figure 18 exist Figure 13 Based on this, Figure 13 (b) Merging share adopts Splitting method, randomly selected Each distribution share will be restored, among which Figure 18 (a) is the common share; Figure 18 (b) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 18 (c) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 18 (d) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 18 (e) For Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 18 (f) For Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 18 (g) is Figure 18 (a) and Figure 18 (b) Results of direct superposition; Figure 18 (h) is Figure 18 (a) and Figure 18 (b) and Figure 18 (c) Directly superimposed results; Figure 18 (i) is Figure 18 (a) and Figure 18 (b) Figure 18 (c) and Figure 18 (d) Direct superposition results; Figure 18 (j) is Figure 18 (a) and Figure 18 (b) Figure 18 (c) Figure 18 (d) and Figure 18 (e) Direct superposition results; Figure 18 (k) is Figure 18 (a) and Figure 18 (b) Figure 18 (c) Figure 18 (d) Figure 18 (e) and Figure 18 (f) Direct superposition results; Figure 18 (l) is Figure 18 (a) After horizontal flipping and Figure 18 (b) Overlay results; Figure 18 (o) is Figure 18 (a) After horizontal flipping and Figure 18 (b) and Figure 18 (c) Overlay results; Figure 18 (p) is Figure 18 (a) After horizontal flipping and Figure 18 (b) Figure 18 (c) and Figure 18 (d) Superposition result; Figure 18 (q) is Figure 18 (a) After horizontal flipping and Figure 18 (b) Figure 18 (c) Figure 18 (d) and Figure 18 (e) Overlay results; Figure 18 (r) is Figure 18 (a) After horizontal flipping and Figure 18 (b) Figure 18 (c) Figure 18 (d) Figure 18 (e) and Figure 18 (f) Superposition result.

[0228] Figure 19 exist Figure 13 Based on this, Figure 13 (b) Merging share adopts Splitting methods, among which Figure 19 (a) is the common share. Figure 19 (b) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 19 (c) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 19 (d) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 19 (e) is for Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 19 (f) For Figure 13 (b) Merging share adopts Distribution share of the split method ; Figure 19 (g) is Figure 19 (a) and Figure 19 (c) Directly superimposed results; Figure 19 (h) is Figure 19 (a) and Figure 19 (c) and Figure 19 (e) Direct superposition results; Figure 19 (i) is Figure 19 (a) and Figure 19 (c) Figure 19 (e) and Figure 19 (f) Direct superposition results; Figure 19 (j) is Figure 19 (a) and Figure 19 (b) Figure 19 (c) Figure 19 (e) and Figure 19 (f) Direct superposition results; Figure 19 (k) is Figure 19 (a) and Figure 19 (b) Figure 19 (c) Figure 19 (d) Figure 19 (e) and Figure 19 (f) Direct superposition results; Figure 19 (l) is Figure 19 (a) After horizontal flipping and Figure 19 (c) Overlay results; Figure 19 (o) is Figure 19 (a) After horizontal flipping and Figure 19 (c) and Figure 19 (e) Overlay results; Figure 19 (p) is Figure 19 (a) After horizontal flipping and Figure 19 (c) Figure 19 (e) and Figure 19 (f) Superposition result; Figure 19 (q) is Figure 19(a) After horizontal flipping and Figure 19 (b) Figure 19 (c) Figure 19 (e) and Figure 19 (f) Superposition result; Figure 19 (r) is Figure 19 (a) After horizontal flipping and Figure 19 (b) Figure 19 (c) Figure 19 (d) Figure 19 (e) and Figure 19 (f) Superposition result.

[0229] This invention also discloses a progressive visual cryptography system for variable-direction grayscale dense images based on share reconstruction, comprising:

[0230] First conversion unit: used to convert two grayscale dense images into a first reduced grayscale dense image and a second reduced grayscale dense image, respectively;

[0231] The second conversion unit is used to convert the first grayscale-decrease image into a binary image A, and the second grayscale-decrease image into a binary image B.

[0232] Generation unit: used to randomly generate common shares, perform the first direction change operation on the common shares and combine them with binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common shares and combine them with binary dense graph B to generate the second intermediate share;

[0233] Fusion Unit: Used to merge the first intermediate share and the second intermediate share to form a fused share;

[0234] Splitting and Restoration Unit: Used to split the fusion share into distribution shares, select some or all of the distribution shares and superimpose them with the public share along different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

[0235] The present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described above.

[0236] The present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described above.

[0237] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0238] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0239] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0240] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0241] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction, characterized in that, Includes the following steps: Convert the two grayscale images into a first reduced grayscale image and a second reduced grayscale image, respectively; Convert the first grayscale-reduced density image into a binary density image A, and convert the second grayscale-reduced density image into a binary density image B; Randomly generate a common share, perform the first direction change operation on the common share and combine it with the binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common share and combine it with the binary dense graph B to generate the second intermediate share; The first intermediate share and the second intermediate share are merged to form a merged share; The fusion share is split into distribution shares. Some or all of the distribution shares are selected and superimposed on the public share along different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

2. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 1, characterized in that: Specific methods for converting two grayscale dense images into a first reduced grayscale dense image and a second reduced grayscale dense image include: grayscale function mapping, grayscale interval mapping, and multi-tone error diffusion mapping; The first grayscale-degraded dense image is converted into a binary dense image A, and the second grayscale-degraded dense image is converted into a binary dense image B, respectively, using the direct mapping method.

3. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 1, characterized in that: The size of the grayscale density image, the first grayscale density image, and the second grayscale density image is m0×n0; Binary dense graphs A and B are of size m1×n1, and m1,n1 and m0,n0 satisfy the following relationship: The common share, the first intermediate share, the second intermediate share, and the merged share are all m0×n0 in size, and m0, n0, m2, n2 satisfy the following constraints: Where is the size parameter of the binary pixel matrix.

4. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 1, characterized in that, The first type of direction change operation is different from the second type of direction change operation, and both the first and second type of direction change operations include: keeping the original direction unchanged, horizontal flipping, vertical flipping, counterclockwise rotation of 90°, counterclockwise rotation of 180° and counterclockwise rotation of 270° or rotation directions equivalent to the above directions; the first intermediate share and the second intermediate share generated by the direction change operation are complementary.

5. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 1, characterized in that, There are several ways to randomly generate common shares: upper boundary method, lower boundary method, left boundary method, right boundary method, main diagonal method, and secondary diagonal method. The methods for merging the first intermediate share and the second intermediate share to form a merged share include: top-bottom merging, bottom-top merging, left-right merging, right-left merging, main-auxiliary diagonal merging, and auxiliary-main diagonal merging.

6. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 1, characterized in that, The specific way to split the fusion share into distribution shares is to split the fusion share into n distribution shares. Each black pixel on the fusion share is split into m black pixels and randomly placed at m coordinate positions corresponding to the black pixels of the fusion share and the distribution share, where: n≥m≥1.

7. The progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction according to claim 6, characterized in that, Select a portion or all of the distributed shares and the public shares, respectively, and superimpose them along different directions corresponding to the first and second direction operations. Then, reveal or gradually reveal the secret map A and secret map B through the human visual system, specifically as follows: 1) When the number of distribution shares participating in the restoration of the secret map is not less than n-m+1 distribution shares: After the distribution shares are superimposed in the same direction, they are superimposed with the public share's direction-changing operation 1, which can directly reveal the binary dense map A by the human visual system; After the distribution shares are superimposed in the same direction, they are superimposed with the public shares through the direction-changing operation 2, which can directly reveal the binary dense map B by the human visual system; 2) When the number of distribution shares participating in the restoration of the secret map is less than n-m+1 distribution shares: After the distribution shares are superimposed in the same direction, they are superimposed with the change-direction operation 1 of the public shares. The binary dense map A can be gradually revealed by the human visual system, and the closer it is to n-m+1, the better the visual quality. After the distribution shares are superimposed in the same direction, they are superimposed with the change-direction operation 1 of the public shares. The binary dense map B can be gradually revealed by the human visual system, and the closer it is to n-m+1, the better the visual quality.

8. A progressive visual cryptography system for variable-direction grayscale dense images based on share reconstruction, characterized in that, include: First conversion unit: used to convert two grayscale dense images into a first reduced grayscale dense image and a second reduced grayscale dense image, respectively; The second conversion unit is used to convert the first grayscale-decrease image into a binary image A, and the second grayscale-decrease image into a binary image B. Generation unit: used to randomly generate common shares, perform the first direction change operation on the common shares and combine them with binary dense graph A to generate the first intermediate share, and perform the second direction change operation on the common shares and combine them with binary dense graph B to generate the second intermediate share; Fusion Unit: Used to merge the first intermediate share and the second intermediate share to form a fused share; Split and Restore Unit: Used to split the fusion share into distribution shares, select some or all of the distribution shares and the public share and superimpose them along different directions corresponding to the first variable direction operation and the second direction operation, respectively, to reveal or gradually reveal the secret map A and secret map B.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the progressive visual cryptography method for variable-direction grayscale dense images based on share reconstruction as described in any one of claims 1-7.

Images