CN113032807B - Authenticatable (2,3) secret image sharing method and device based on mixed fractal matrix - Google Patents

Authenticatable (2,3) secret image sharing method and device based on mixed fractal matrix Download PDF

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CN113032807B
CN113032807B CN202110320437.3A CN202110320437A CN113032807B CN 113032807 B CN113032807 B CN 113032807B CN 202110320437 A CN202110320437 A CN 202110320437A CN 113032807 B CN113032807 B CN 113032807B
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高锴
张真诚
洪集辉
俞俊
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Shaoxing Tuxin Iot Technology Co ltd
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Abstract

The invention discloses an authenticable (2,3) secret image sharing method based on a mixed fractal matrix. Firstly, generating a mixed fractal matrix, wherein the fractal matrix consists of identical and continuous fractal groups; secondly, slightly modifying three different original images according to the mixed fractal matrix and confidential information to be embedded to form three camouflage images which are similar to the original images, and sending the three camouflage images to three participants for storage; and finally, when confidential information is to be extracted, first image re-authentication can be performed on three camouflage images, if authentication failure is found, second image re-authentication can be performed on every two camouflage images, and only two participants who pass the authentication can extract the confidential information. The invention combines secret sharing and information hiding, realizes the high-efficiency information hiding of a pixel domain, has high safety and has better total reserve than the prior method.

Description

Authenticatable (2,3) secret image sharing method and device based on mixed fractal matrix
Technical Field
The invention belongs to the field of confidential image sharing, and particularly relates to an authenticatable (2,3) confidential image sharing method and device based on a mixed fractal matrix.
Background
Nowadays, with the rapid development of the internet, people can continuously enjoy the results of the latest technological revolution. More and more information is being transmitted over the internet. However, network viruses, trojan horses and illegal organizations that steal information all pose a serious threat to information security. Therefore, security of information transmission becomes particularly important, particularly in the political, military and commercial fields. Although conventional encryption can ensure information security to some extent, this type of technique does not hide the content of the information. On the one hand, the secret keys generated for hiding information are often unordered symbols, which will be of interest to the tracker, increasing the risk of exposure. This has become the biggest weakness of conventional encryption algorithms. On the other hand, as the use of digital media has increased dramatically, it has become more and more urgent to protect intellectual property rights in digital media, prevent illegal copying and spreading of intellectual property products, and ensure information security. In order to solve the above problems, information hiding techniques have been developed. However, the conventional information hiding schemes have an obvious common disadvantage: only one carrier is used to embed the information. Once the carrier becomes the target of the attacker, the probability of the information being attacked is greatly increased. To solve this drawback, secret image sharing methods have been proposed.
Secret Image Sharing (Secret Image Sharing) enables one or more original images to be embedded with Secret information and then divided into a plurality of different camouflage images, each camouflage Image is held by a participant, and any participant cannot solve any Secret information by himself/herself, because the camouflage Image retained by one participant cannot extract any Secret-related content. When the confidential information is to be extracted, the participants must share the camouflage pictures of themselves and combine the correct camouflage pictures to correctly extract the hidden confidential information. Such methods have higher security and lower computational complexity and are now widely used in secure communications.
Disclosure of Invention
The invention aims to provide a novel three-dimensional reference matrix named as a mixed fractal matrix. The conception of the invention is as follows: firstly, a mixed fractal matrix is established, wherein the matrix is composed of a plurality of continuous and same fractal groups, each fractal group comprises 4 external elements, and each external element comprises 8 internal elements. Wherein each external element and internal element may represent 2-bit and 3-bit confidential information, respectively; secondly, generating three disguised images which are close to the original images by the three different gray level images according to the established mixed fractal matrix and the confidential information to be embedded, and sending the three disguised images to three participants for storage; finally, before extracting confidential information, first double-picture verification is carried out on the three camouflage pictures, if verification failure is found, second double-authentication is carried out on the three camouflage pictures in pairs, and illegal camouflage pictures can be found out; two pieces of confidential information can be extracted correctly by arbitrarily selecting them from the masquerading images that pass the authentication.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an authenticatable (2,3) confidential image sharing method based on a mixed fractal matrix comprises the following steps:
s1: a transmitting end generates a mixed fractal matrix with the size of 256 multiplied by 256, and the fractal matrix consists of continuous and same fractal groups with the size of 6 multiplied by 6; each fractal group has 4 external elements, and each external element contains 8 internal elements;
s2: filling confidential information with different lengths in one fractal group by using a random number generator, and copying the confidential information to each fractal group in the matrix;
s3: forming pixels at the same position in three original gray level images into a group of pixel pairs, taking out confidential information with different lengths, determining the range of external elements corresponding to the pixel pairs in the current fractal group, which is the same as the decimal confidential information, and then corresponding the pixel pairs to the position of an internal element in the selected external elements, which is the same as the pixel value of the decimal confidential information with the other length;
s4: generating three camouflage images with the same size as the original gray image, wherein the pixel values in the three camouflage images are respectively from the coordinates of the position determined in the S3; the three camouflage images are respectively sent to three participants by the sending end;
s5: after receiving the three camouflaged pictures from the participants, the receiving end firstly carries out tamper detection on the three pictures by using two detection algorithms; and after the detection is passed, arbitrarily selecting two images for information extraction.
Based on the technical scheme, the steps can be realized in the following preferred mode. The preferred embodiments may be combined with each other without any conflict, and are not limited.
Preferably, in S1, the method for generating the mixed fractal matrix is as follows:
s11: setting a mixed fractal matrix, wherein the matrix is a 256 × 256 × 256 matrix, the coordinates of X, Y and Z axes are all 0-255, and the coordinate value of each axis represents 256 pixels;
s12: filling the same fractal groups with the size of 6 multiplied by 6 from the coordinates (0, 0, 0) in the mixed fractal matrix; the coordinate values comprise coordinates of any integer pixel value from 252 to 255, the coordinates are not filled into a fractal group, the rest coordinates are contained in one fractal group with the size of 6 multiplied by 6, each fractal group comprises 4 external elements, and each external element is respectively used for representing decimal secret information 0 to 3 and can be used for embedding 2-bit secret information; each external element comprises 8 internal elements, each element in the internal elements is used for representing decimal secret information 0-7 and can be used for embedding 3-bit secret information; all fractal groups are continuous and non-overlapping;
for each fractal group, its outer elements and inner elements should satisfy the property of perfect projection: after the fractal group is projected to a plane formed by any two coordinate axes, all elements cannot be overlapped with other elements.
Preferably, the specific method of S2 is as follows:
s21: taking out a fractal group, firstly enabling a random number generator to generate 0-3 random arrangement by using a secret key, and distributing the arranged 0-3 to four external elements of the fractal group; generating 4 groups of 0-7 random arrays by using the same secret key, and sequentially distributing the four groups of arrays to internal elements in four external elements;
s22: the fractal group to which the number is allocated in S21 is copied to each fractal group in the mixed fractal matrix.
Preferably, the specific method of S3 is as follows:
s31: three pixel values p of the same position of three original gray level images1i，p2i，p3iForm a set of pixel pairs (p)1i，p2i，p3i) And mapped as coordinates to element M (p) in the mixed fractal matrix1i，p2i，p3i)；
S32: the element M (p)1i，p2i，p3i) Locate the group (Q) of the cluster in which it is locatedx，Qy，Qz) In (1), determining M (p)1i，p2i，p3i) In which it is locatedPosition (x) in groupt，yt，zt) (ii) a According to confidential information of different lengths, (x) ist，yt，zt) Move to an external element (x) corresponding to confidential informationO，yO，zO) And an internal element (x)I，yI，zI) Performing the following steps; s33: three camouflaged images with the same size as the original gray image are generated, and a group of pixel pairs (p) of the three original gray images1i，p2i，p3i) From the final pixel coordinates determined in S32
Figure BDA0002992591960000031
Will be provided with
Figure BDA0002992591960000032
Respectively assigning values to pixels p in the three camouflage images1iPixels in the same position.
Preferably, in S32, (Q)x，Qy，Qz) Is the coordinate of the current fractal group, (x)O，yO，zO) Is the coordinate of the external element in the fractal group, (x)I，yI，zI) Is the coordinates of the inner element in the outer element,
Figure BDA0002992591960000041
for the final moving coordinate of the pixel pair, the value calculation formula of each coordinate is as follows:
Figure BDA0002992591960000042
xt＝p1imod 6；yt＝p2imod 6；zt＝p3imod 6.
Figure BDA0002992591960000043
xI＝xtmod 3；yI＝ytmod 3；zI＝ztmod 3.
Figure BDA0002992591960000044
Figure BDA0002992591960000045
Figure BDA0002992591960000046
where the operator mod represents the modulo operation, the operator
Figure BDA0002992591960000047
Indicating a rounding down.
Preferably, the specific method of S5 is as follows:
s51: when extracting the confidential information, three participants share the respective camouflage images, and firstly, the pixels at the same positions of the three camouflage images form pixel pairs
Figure BDA0002992591960000048
And searching in the mixed fractal matrix
Figure BDA0002992591960000049
Whether the location has an element;
s52: if all the pixel pairs correspond to elements in the mixed fractal matrix, the three camouflage images pass verification; otherwise, entering a second re-verification link;
s53: in the second re-verification step, the pixel pairs are combined
Figure BDA00029925919600000410
Two-by-two combination of three pixels:
Figure BDA00029925919600000411
and
Figure BDA00029925919600000412
respectively substituting the three combinations into a projection matrix of the mixed fractal matrix to the coordinate axis corresponding to the mixed fractal matrix to check whether the mixed fractal matrix corresponds to a null element; if one group of the two masqueradings has corresponding elements in the projection matrix, the two masqueradings are legal, and the other masquerading is tampered;
s54: randomly taking out two pieces of camouflage images which pass the detection, and extracting the confidential information embedded in each group of pixel pairs; assuming that the first and second masquerading patterns are legal, the confidential information is the post-projection fractal matrix of mixture score
Figure BDA00029925919600000413
And confidential information corresponding to the external element and the internal element of the fractal group where the position is located.
In a second aspect, the present invention provides an authenticatable (2,3) confidential image sharing apparatus based on a hybrid fractal matrix, which includes a memory and a processor;
the memories are distributed in the sending end and the receiving end and are respectively used for storing computer programs;
the processor, when executing the computer program, is configured to implement the hybrid fractal matrix based authenticatable (2,3) secret image sharing method according to any of the first aspects.
Preferably, the computer program stored in the sender is used to implement S1 to S4, and the computer program stored in the receiver is used to implement S5.
Compared with the prior art, the invention has the advantages and beneficial effects that:
the invention combines secret sharing and information hiding, and realizes efficient information hiding of a spatial domain. Compared with other existing methods, the method has the advantages that the method has the advantage of easiness in operation in the confidential image sharing method, three different original images are used as carriers, the information complexity of the whole method is greatly increased, the safety is obviously improved, when the confidential information is extracted, only any two of the three authenticated disguised images are needed to extract the confidential information in percentage, the method is a characteristic that the existing methods do not have, and the total reserve is also superior to the existing methods.
Drawings
FIG. 1 is a schematic diagram of a sharing method according to the present invention;
FIG. 2 is a flowchart of confidential information embedding;
FIG. 3 is a flowchart of confidential information extraction;
FIG. 4 is a graph of the effects of two fractal models;
FIG. 5 is a graph of the effect of fractal groups;
FIG. 6 is a diagram of mixed fractal matrix effects;
fig. 7 is a diagram of the effect of the generated camouflage image.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings, but the embodiments of the present invention are only one possibility, and are illustrative and not restrictive.
The flow chart of the invention is shown in fig. 1, firstly, a mixed fractal matrix is generated, and the fractal matrix is composed of identical and continuous fractal groups; secondly, slightly modifying three different original images according to the mixed fractal matrix and confidential information to be embedded to form three camouflage images which are similar to the original images, and sending the three camouflage images to three participants for storage; and finally, when confidential information is to be extracted, first image re-authentication can be performed on three camouflage images, if authentication failure is found, second image re-authentication can be performed on every two camouflage images, and only two participants who pass the authentication can extract the confidential information.
In a preferred embodiment of the present invention, an authenticatable (2,3) secret image sharing method of a mixed fractal matrix is provided, which specifically includes two parts, namely, an information embedding method at a transmitting end and an image authentication and secret information extraction method at a receiving end.
As shown in fig. 2, the secret information embedding step at the sending end is as follows:
s1: generating a mixed fractal matrix with the size of 256 multiplied by 256, wherein the reference matrix is composed of continuous and same fractal groups with the size of 6 multiplied by 6, each fractal group has 4 external elements, and each external element contains 8 internal elements. The arrangement of the 4 external elements is shown in fig. 4(1), and the arrangement of the internal elements included in each external element is shown in fig. 4 (2). As shown in fig. 5, the fractal group is formed by mixing two models. Each pixel at the same position in the three original gray-scale images is formed into a pixel pair and corresponds to a fractal group in the matrix. In this embodiment, each group of conventional pixel pairs can be embedded with 5-bit confidential information, and the pixel pairs composed of special pixels cannot correspond to a complete fractal group, so that no information is embedded, and there are four special pixels 252, 253, 254 and 255.
In step S1 of the present embodiment, the mixed fractal matrix is generated as follows:
s11: setting a mixed fractal matrix, wherein the matrix is a 256 × 256 × 256 matrix, the coordinates of the X, Y and Z axes are all 0-255, the coordinate value of each axis represents 256 pixels, for example, (1, 2, 5) represents that the pixels at the same position of the three gray-scale images are respectively 1, 2 and 5.
S12: filling the same fractal groups with the size of 6 multiplied by 6 from the coordinates (0, 0, 0) in the mixed fractal matrix;
the coordinates of the pixel values of any one of the four integers 252 to 255 are not filled in the fractal group, and the rest coordinates are contained in one and only one fractal group with the size of 6 × 6 × 6, as shown in fig. 5, each fractal group contains 4 external elements, and each external element is respectively used for representing four decimal confidential information 0 to 3 and can be used for embedding 2-bit confidential information; each external element comprises 8 internal elements, each element in the internal elements is used for representing 8 decimal secret information 0-7 and can be used for embedding 3bit secret information; all fractal groups are contiguous and do not overlap;
for each fractal group, the external elements and the internal elements thereof should satisfy the characteristics of perfect projection: after the fractal group is projected to a plane formed by any two coordinate axes, all elements cannot be overlapped with other elements.
S2: filling confidential information with different lengths in one fractal group by using a random number generator, and copying the confidential information to each fractal group in the matrix;
the specific implementation method of step S2 in this embodiment is as follows:
s21: a fractal group is taken out. Firstly, a random number generator generates 0-3 random arrangement by using a secret key, and the arranged 0-3 is distributed to four external elements of the fractal group; generating 4 groups of 0-7 random arrays by using the same secret key, and sequentially distributing the four groups of arrays to internal elements in four external elements;
s22: copying the fractal group distributed with the numbers to each fractal group in the mixed fractal matrix;
s3: forming pixels at the same position in three original gray level images into a group of pixel pairs, taking out confidential information with different lengths, determining the range of an external element corresponding to the current pixel pair in the current fractal group, which is the same as the decimal confidential information, and then corresponding the pixel pair to the position of an internal element in a selected external element, which is the same as the pixel value of the decimal confidential information with the other length;
the specific implementation method of step S3 in this embodiment is as follows:
s31: pixel values p of three original gray level images at the same position1i，p2i，p3iForm a set of pixel pairs (p)1i，p2i，p3i) And mapped as coordinates to element M (p) in the mixed fractal matrix1i，p2i，p3i)；
S32: the element M (p)1i，p2i，p3i) Locate the group (Q) of the cluster in which it is locatedx，Qy，Qz) In (1), determining M (p)1i，p2i，p3i) Position (x) in the subgroup group in which it is locatedt，yt，zt) (ii) a According to confidential information of different lengths, (x) ist，yt，zt) Move to an external element (x) corresponding to confidential informationO，yO，zO) And an internal element (x)I，yI，zI) Performing the following steps;
at the beginning of the process; in the process of moving according to confidential information with different lengths, (Q)x，Qy，Qz) Is the coordinate of the current fractal group, (x)O，yO，zO) Is the coordinate of the external element in the fractal group, (x)I，yI，zI) Are the coordinates of the internal elements in the external elements,
Figure BDA0002992591960000071
for the final moving coordinate of the pixel pair, the value calculation formulas of the coordinates are as follows:
Figure BDA0002992591960000081
xt＝p1imod 6；yt＝p2imod 6；zt＝p3imod 6.
Figure BDA0002992591960000082
xI＝xtmod 3；yI＝ytmod 3；zI＝ztmod 3.
Figure BDA0002992591960000083
Figure BDA0002992591960000084
Figure BDA0002992591960000085
where the operator mod represents the modulo operation, the operator
Figure BDA0002992591960000086
Indicating a rounding down.
S33: three camouflaged images with the same size as the original gray image are generated, and a group of pixel pairs (p) of the three original gray images1i，p2i，p3i) From the final pixel coordinates determined in S32
Figure BDA0002992591960000087
Will be provided with
Figure BDA0002992591960000088
Respectively assigning values to pixels p in the three camouflage images1iPixels in the same position;
s4: generating three camouflage images with the same size as the original gray image, wherein the pixel values in the three camouflage images are respectively from the coordinates of the position determined in the S3; the three camouflage images are respectively sent to three receivers by the sending end, and each receiver stores one camouflage image.
For the above steps of S3 and S4, taking the pixel value at the same position of the three original gray scale images as 1, 2, 5 as an example, first, three pixels are grouped into a set of pixel pairs (1, 2, 5). The fractal group corresponding to (1, 2, 5) is shown in fig. 5. The confidential information to be embedded is 10111, and the confidential information is divided into 2-bit 10 and 3-bit 111. First, a representative 2 is sought (corresponding binary (10)2) Then look for a representation 7 (corresponding to binary (111)) in the range (3: 5) in which the external element of (2) is located2) And finally, assigning the coordinate values (5, 5, 3) to the three camouflage figures respectively.
S5: the flow chart for extracting the confidential information is shown in fig. 3, after the receiving end receives three camouflage images from participants, tampering detection is carried out on the three images by using two detection algorithms; after the detection is passed, two images can be arbitrarily selected for information extraction.
The specific implementation method for detecting the algorithm and extracting the confidential information in this embodiment is as follows:
S51: when extracting the confidential information, three participants share the respective camouflage images, and firstly, the pixels at the same positions of the three camouflage images form pixel pairs
Figure BDA0002992591960000089
And searching coordinates in the mixed fractal matrix
Figure BDA0002992591960000091
Whether there is an element in the location of (a);
s52: if all the pixel pairs correspond to elements in the mixed fractal matrix, the three camouflage images pass verification; otherwise, entering a second re-verification link;
s53: and a second re-verification step: couple pixels
Figure BDA0002992591960000092
Two-by-two combination of three pixels:
Figure BDA0002992591960000093
and
Figure BDA0002992591960000094
respectively substituting the three coordinate combinations into a projection matrix of the mixed fractal matrix to the coordinate axis corresponding to the mixed fractal matrix to check whether the projection matrix corresponds to a null element; if one of the groups has corresponding elements in the projection matrix, the two camouflage figures are legal, and the other camouflage figure is tampered.
S54: after the detection, two pieces of information are arbitrarily taken out from the camouflaged image that has passed the detection, and the confidential information embedded in each set of pixel pairs is extracted. Assuming that the first and second masquerading patterns are legal, the confidential information is the post-projection fractal matrix of mixture score
Figure BDA0002992591960000095
And confidential information corresponding to the external element and the internal element of the fractal group where the position is located.
The method can embed the confidential information into three camouflage images generated by three different original gray level images, and provides extremely high embedding amount of the confidential information on the premise of ensuring the quality of the camouflage images. Meanwhile, the safety and the information transmission quantity of the method are greatly ensured by using three different original gray level images. In order to further illustrate the technical effects of the present invention, the following specifically shows the corresponding test results of the method of the present invention.
As shown in table 1, in the case that the original image is completely embedded with confidential information, the quality of the three camouflage images is excellent, the PSNR (peak signal to noise ratio) reaches up to 40.43, and the SSIM (structural similarity index) reaches up to 0.97.
TABLE 1 Picture quality of camouflage prints from confidential information in the original image
Figure BDA0002992591960000101
Table 2 compares the functionality of the scheme of the present invention with other SIS processes. Modern lightweight computing-based SIS methods focus on generating meaningful camouflage images with good visual quality and large embedding power. As shown in the table, reversibility and the characteristics of different original images are contradictory. To restore a clear original image, three times as much information is required as a single original image. This is not worth doing, as the original image is only used to cover the secret information transfer. In addition, an attacker can analyze information from the differences in the disguised images generated from a single original image. Therefore, under steganalysis, the scheme based on a single original image is more vulnerable. The present invention proposes a method that offers three most compelling features: using completely different original images, extremely high embedding power and (2,3) secret sharing.
The scheme of the present invention has an advantage in that if one of the masqueradings is invalid, the other two masqueradings can be used to completely recover the secret data, but in the conventional SIS method, if one masquerading is invalid, the secret data cannot be recovered at all. Thus, the scheme of the present invention provides fault tolerance capabilities not available with conventional SIS schemes.
TABLE 2 comparison of characteristics with analogous methods
Figure BDA0002992591960000111
[1]K.Gao,J.-H.Horng and C.-C.Chang,"A novel(2,3)reversible secret image sharing based on fractal matrix,"IEEE Access,vol.8,pp.174325-174341,2020.
[2]X.-S.Li,C.-C Chang,M.-X.He and C.-C.Lin,"A lightweight authenticable visual secret sharing method based on turtle shell structure matrix,"Multimedia Tools and Applications,vol.79,pp.453-476,2019.
[3]Y.J.Liu,C.-C.Chang and P.C.Huang,"Security protection using two different image shadows with authentication,"Mathematical Biosciences and Engineering,vol.16,no.4,pp.1914–1932,2019.
[4]Y.J.Liu,C.-C.Chang and P.C.Huang,"Security protection using two different image shadows with authentication,"Mathematical Biosciences and Engineering,vol.16,no.4,pp.1914–1932,2019.
As shown in table 3, after the original image is completely embedded with the confidential information, when one of the camouflage images is subjected to different tampering (random image replacement, noise replacement, and special image replacement), the highest accuracy of the detection algorithm using three images can reach 94.3%, and the highest accuracy of the detection algorithm using two images can reach 68.5%. If the image is replaced by a common image, the accuracy of the two algorithms can reach 83.3% and 8.4% respectively.
TABLE 3 tamper Detection Rate (DR) of camouflaged pictures in different cases
Figure BDA0002992591960000121
In addition, in another embodiment, there is provided an authenticatable (2,3) confidential image sharing device based on a hybrid fractal matrix, which includes a memory and a processor;
the memories are distributed in the sending end and the receiving end and are respectively used for storing computer programs;
the processor, when executing the computer program, is configured to implement the hybrid fractal matrix based authenticatable (2,3) confidential image sharing method of any of claims 1 to 9.
Note that, the programs stored in the sender and the receiver are different, the computer program stored in the sender is used to implement S1 to S4, and the computer program stored in the receiver is used to implement S5.
The Memory may include a Random Access Memory (RAM) or a Non-Volatile Memory (NVM), such as at least one disk Memory. The Processor may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. Of course, the device should also have the necessary components to implement the program execution, such as power supply, communication bus, etc.
The above-described embodiments are merely preferred embodiments of the present invention, and are not intended to limit the present invention. Various changes and modifications may be made by one of ordinary skill in the pertinent art without departing from the spirit and scope of the present invention. Therefore, the technical scheme obtained by adopting the mode of equivalent replacement or equivalent transformation is within the protection scope of the invention.

Claims (8)

1. An authenticatable (2,3) confidential image sharing method based on a hybrid fractal matrix, characterized by the steps of:
s1: a transmitting end generates a mixed fractal matrix with the size of 256 multiplied by 256, and the fractal matrix consists of continuous and same fractal groups with the size of 6 multiplied by 6; each fractal group has 4 external elements, and each external element also comprises 8 internal elements;
s2: filling confidential information with different lengths in one fractal group by using a random number generator, and copying the confidential information to each fractal group in the matrix;
s3: forming pixels at the same position in three original gray level images into a group of pixel pairs, taking out confidential information with different lengths, determining the range of external elements corresponding to the pixel pairs in the current fractal group, which is the same as the decimal confidential information, and then corresponding the pixel pairs to the position of an internal element in the selected external elements, which is the same as the pixel value of the decimal confidential information with the other length;
s4: generating three camouflage images with the same size as the original gray image, wherein pixel values in the three camouflage images are respectively from the coordinates of the position determined in the S3; the three camouflage images are respectively sent to three participants by the sending end;
s5: after receiving the three camouflaged pictures from the participants, the receiving end firstly carries out tamper detection on the three pictures by using two detection algorithms; and after the detection is passed, arbitrarily selecting two images for information extraction.
2. The method for sharing an authenticatable (2,3) confidential image based on a hybrid fractal matrix according to claim 1, wherein in the S1, the hybrid fractal matrix is generated as follows:
s11: setting a mixed fractal matrix, wherein the matrix is a 256 × 256 × 256 matrix, the coordinates of X, Y and Z axes are all 0-255, and the coordinate value of each axis represents 256 pixels;
s12: filling the same fractal groups with the size of 6 multiplied by 6 from the coordinates (0, 0, 0) in the mixed fractal matrix; the coordinate values comprise coordinates of any integer pixel value from 252 to 255, the coordinates are not filled into a fractal group, the rest coordinates are contained in one fractal group with the size of 6 multiplied by 6, each fractal group comprises 4 external elements, and each external element is respectively used for representing decimal secret information 0 to 3 and can be used for embedding 2-bit secret information; each external element comprises 8 internal elements, each element in the internal elements is used for representing decimal secret information 0-7 and can be used for embedding 3-bit secret information; all fractal groups are continuous and non-overlapping;
for each fractal group, its outer elements and inner elements should satisfy the property of perfect projection: after the fractal group is projected to a plane formed by any two coordinate axes, all elements cannot be overlapped with other elements.
3. The method of claim 2, wherein the specific method of S2 is as follows:
s21: taking out a fractal group, firstly enabling a random number generator to generate 0-3 random arrangement by using a secret key, and distributing the arranged 0-3 to four external elements of the fractal group; generating 4 groups of 0-7 random arrays by using the same secret key, and sequentially distributing the four groups of arrays to internal elements in four external elements;
s22: the fractal group to which the number is allocated in S21 is copied to each fractal group in the mixed fractal matrix.
4. The method of claim 3, wherein the specific method of S3 is as follows:
s31: three pixel values p of the same position of three original gray level images1i，p2i，p3iForm a set of pixel pairs (p)1i，p2i，p3i) And mapped as coordinates to element M (p) in the mixed fractal matrix1i，p2i，p3i)；
S32: the element M (p)1i，p2i，p3i) Locate the group (Q) of the cluster in which it is locatedx，Qy，Qz) In (1), determining M (p)1i，p2i，p3i) Position (x) in the grouping group in which it is locatedt，yt，zt) (ii) a According to secret information with different lengths, (x) is addedt，yt，zt) Move to an external element (x) corresponding to confidential informationO，yO，zO) And an internal element (x)I，yI，zI) Performing the following steps; s33: three camouflaged images with the same size as the original gray image are generated, and a group of pixel pairs (p) of the three original gray images1i，p2i，p3i) From the final pixel coordinates determined in S32
Figure FDA0003630884570000021
Will be provided with
Figure FDA0003630884570000022
Respectively assigning values to pixels p in the three camouflage images1iPixels in the same position.
5. The hybrid fractal matrix-based authenticatable (2,3) secret image sharing method according to claim 4, wherein in the S32, (Q)x，Qy，Qz) Is the coordinate of the current fractal group, (x)O，yO，zO) Is the coordinate of the external element in the fractal group, (x)I，yI，zI) Are the coordinates of the internal elements in the external elements,
Figure FDA0003630884570000023
for the final moving coordinate of the pixel pair, the value calculation formula of each coordinate is as follows:
Figure FDA0003630884570000024
xt＝p1i mod 6；yt＝p2i mod 6；zt＝p3i mod 6.
Figure FDA0003630884570000031
xI＝xt mod 3；yI＝yt mod 3；zI＝zt mod 3.
Figure FDA0003630884570000032
Figure FDA0003630884570000033
Figure FDA0003630884570000034
where the operator mod represents the modulo operation, the operator
Figure FDA0003630884570000035
Indicating a rounding down.
6. The method of claim 4, wherein the specific method of S5 is as follows:
s51: when extracting the confidential information, three participants share the respective camouflage images, and firstly, the pixels at the same positions of the three camouflage images form pixel pairs
Figure FDA0003630884570000036
And searching in the mixed fractal matrix
Figure FDA0003630884570000037
Whether the location has an element;
s52: if all the pixel pairs correspond to elements in the mixed fractal matrix, the three camouflage images pass verification; otherwise, entering a second re-verification link;
s53: in the second re-verification step, the pixel pairs are combined
Figure FDA0003630884570000038
Two-by-two combination of three pixels:
Figure FDA0003630884570000039
and
Figure FDA00036308845700000310
and the three combinations are respectively substituted into the projection matrix of the coordinate axis corresponding to the mixed fractal matrix for projection to check whether the projection matrix corresponds to a null element; if one group of the masqueradings has corresponding elements in the projection matrix, the two masqueradings are legal, and the other masquerading is tampered;
s54: randomly taking out two pieces of camouflage images which pass the detection, and extracting the confidential information embedded in each group of pixel pairs; assuming that the first and second masquerading patterns are legal, the confidential information is the post-projection fractal matrix of mixture score
Figure FDA00036308845700000311
And confidential information corresponding to the external element and the internal element of the fractal group where the position is located.
7. An authenticatable (2,3) confidential image sharing apparatus based on a hybrid fractal matrix, comprising a memory and a processor;
the memories are distributed in the sending end and the receiving end and are respectively used for storing computer programs;
the processor, configured to, when executing the computer program, implement the hybrid fractal matrix based authenticatable (2,3) secret image sharing method according to any of claims 1 to 6.
8. The hybrid fractal matrix-based authenticatable (2,3) confidential image sharing apparatus according to claim 7, wherein the computer program stored in the transmitting side is configured to implement S1 through S4, and the computer program stored in the receiving side is configured to implement S5.
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