CN104202412A - Image storage method and system based on multiple cloud terminals - Google Patents

Abstract

The invention discloses an image storage method and system based on multiple cloud terminals. The method includes: interference transformation is performed on a to-be-stored original image to obtain a preliminarily-encrypted image, Godel coding is used to separate the encrypted image into a certain number of sub-images, and the sub-images are stored at the cloud terminals. The method has the advantages that method storing the original image at the cloud terminal is replaced, and potential safety hazard of cloud terminal storage is solved while user image privacy protection and safety storage are achieved.

Description

A method and system for image storage based on multi-cloud

technical field

The present invention relates to the field of cloud image processing and cloud privacy protection, in particular to a multi-cloud-based image storage method and system.

Background technique

As the storage system develops from local direct connection to networked and distributed, and is shared by many computers on the network, the storage system becomes more vulnerable to attacks. Relatively static storage systems often become the preferred target of attackers. The purpose of stealing, falsifying or destroying data.

Cloud storage is a mode of network online storage, that is, data is stored in multiple virtual servers that are usually managed by a third party. Users can manage their files online anytime and anywhere. There is no fixed limit on the terminal, which is convenient and fast. However, for the storage of users' personal privacy files, whether the cloud can be secure is still controversial.

After research on the cloud, it is found that there are security risks in the cloud. The first is the hidden danger of personal privacy leakage. From the perspective of technology and cost, most of the pictures of cloud users are stored on the cloud in plain text. Cloud managers can easily view the pictures in the cloud, which is not expected by users. The second hidden danger of data security, the large amount of data stored in the cloud, makes it a target of hackers. Hackers may steal or modify data, causing irreparable losses.

There are two problems to be solved in secure storage. How to ensure that the file data is complete, reliable and not leaked? How to ensure that only legitimate users can access relevant files? The core methods used to solve the above two problems are data encryption and authentication and authorization management. However, most of the current image security storage schemes are based on file encryption, encrypting files, and then decrypting them with a decryption key. However, image encryption is relatively complicated, and encrypting a single file at the same time may result in the loss of the key or damage to the file, eventually resulting in the loss of the file. Most of the current cloud security storage solutions are based on the protection of the cloud itself, emphasizing the security of the cloud itself, so as to ensure the data security in the cloud. The encryption of the data itself is complex and easy to lose. Therefore, a secure multi-cloud image storage solution is necessary.

Contents of the invention

The technical problem to be solved by the present invention is: a multi-cloud-based picture storage method and system solves the security problems of pictures in the cloud, the problem of single point failure and the problem of privacy leakage.

In order to solve the above-mentioned technical problems, the present invention proposes a multi-cloud based image storage method and system.

The technical solution of the present invention is: a method for storing images based on multi-cloud, comprising the following steps:

Step 1: image storage step;

Step 1.1: Extract the pixel matrix A of the original image, add a unique flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^-1 , where, Matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C;

Step 1.2: Convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, and both N and T are positive numbers and T≤N;

Step 1.3: Perform Gödel coding on the i-th row of the disturbed pixel matrix B, the converted Gödel code number is Gi, and traverse each row of the pixel matrix; where: if the size of the image pixel matrix is r×c, i’s The value is (1,2,3,...,c), i, r and c are positive integers;

Step 1.4: Construct a polynomial according to Gi and flag. The polynomial constructed by Gi can obtain the pixel matrix (P ₁ , P ₂ , ..., P _N ) of N subimages. According to the generated pixel matrix (P ₁ , P ₂ , ..., P _N ) constitutes a subgraph; meanwhile, the polynomial constructed by flag obtains an additional verification mark, and adds additional verification mark information for the subgraph;

Step 1.5: Add secondary marks to each subgraph, and then distribute the marked subgraphs randomly and evenly to multiple clouds;

Step 2: Picture Recovery Steps:

Step 2.1: Select subgraphs from multiple clouds;

Step 2.2: Perform secondary label verification on the selected subgraph, if the subgraph label verification is passed, keep the current subgraph and enter step 2.3, otherwise, discard the subgraph and return to step 2.1;

Step 2.3: Determine whether the number of subgraphs reaches T; if yes, enter step 2.4, otherwise return to step 2.1;

Step 2.4: Extract pixel matrices (P ₁ , P ₂ , ..., P _T ) of T subimages, and convert the i-th row of T pixel matrices into Gödel code numbers S _i ^t , where i represents the i-th pixel matrix row, t represents the t-th sub-image, t is between 1 and T, and S _i ^t represents the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image;

Step 2.5: According to S _i ^t obtained in Step 2.4, use Lagrangian interpolation at the same time Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵;

Step 2.6: Obtain T (t, H(t)) coordinate points according to the additional verification mark H(t) of the t-th sub-image, find out the constant term of the polynomial, and use Lagrangian interpolation Get the flag‵ to be matched;

Step 2.7: Compare the flag‵ value to be matched with the flag value of the original image, if flag‵ and flag are not equal, return to step 2.1; if flag‵=flag, determine B‵=B, and enter step 2.8;

Step 2.8: Restore B‵ from interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^{- 1} = C ^-1 B C ^-1 = C ^-1 CAC C ^-1 , to obtain the original image.

Described step 1.4 comprises the following steps:

Step 1.4.1: Construct the conversion polynomial according to Gi, Among them: mod p is the polynomial modulus, p is a large prime number, j is a variable with a value from 1 to T-1, a _j means (a ₁ , a ₂ ,..., a _T-1 ), x ^j means The j-th power of x is calculated to obtain the value of group c (Fi(1),...,Fi(N)), and then convert these Gödel code numbers into the pixel value of the i-th row to obtain the pixel of the i-th row, And get N r×c row pixel matrix (P ₁ , P ₂ ,..., P _N ); wherein, the system randomly generates T-1 numbers (a ₁ , a ₂ , ..., a _T-1 ), provide coefficients for creating polynomials, and P is the modulus of a large prime number;

Step 1.4.2: Construct a flag polynomial according to flag j is a variable whose value ranges from 1 to T-1, a _j represents (a ₁ , a ₂ ,..., a _T-1 ), x ^j represents the jth power of x, and the calculated H(t) is distributed Give the tth subgraph as an additional verification mark, and the value of t is (1, 2, ..., N); the calculated result is the additional verification mark of each subgraph.

The values of N and T in the step 1.2 are respectively N=5 and T=3.

A picture storage system based on multi-cloud, characterized in that it includes a picture storage module and a picture recovery module;

The picture storage module includes:

The first extraction module: used to extract the pixel matrix A of the original image, add a unique identification flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^{- 1} , where matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C;

Parameter construction module: used to convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, N and T are both positive numbers and T≤N;

Coding module: used to perform Gödel encoding on the i-th row of the disturbed pixel matrix B, the converted Gödel encoding number is Gi, and traverse each row of the pixel matrix; where: if the size of the image pixel matrix is r×c, The value of i is (1,2,3,...,c), i, r and c are positive integers;

Polynomial construction module: used to construct a polynomial according to Gi and flag, the polynomial constructed by Gi obtains pixel matrices (P ₁ , P ₂ , ..., P _N ) of N subimages, and generates pixel matrices (P ₁ , P ₂ , ... ..., P _N ) constitute a subgraph; meanwhile, the polynomial constructed by flag gets an additional verification mark, and adds additional verification mark information for the subgraph;

Allocation module: used to add secondary marks to each sub-image, and then distribute the marked sub-images randomly and evenly to multiple clouds;

Image recovery modules include:

selection module: used to select subgraphs from multiple clouds,

Verification module: perform secondary mark verification on the selected sub-graph, if the sub-graph mark verification is passed, keep the current sub-graph and enter the judgment module, otherwise, discard the sub-graph and return to the selection module;

Judgment module: judge whether the number of subgraphs reaches T; if yes, enter the second extraction module, otherwise return to the selection module;

The second extraction module: used to extract the pixel matrix (P ₁ , P ₂ , ..., P _T ) of T subimages, and convert the i-th row of the T pixel matrix into a Gödel coded number S _i ^t , where i represents a pixel In the i-th row of the matrix, t represents the t-th sub-image, and t is between 1 and T, so S _i ^t represents the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image.

Restoration module: used to use Lagrangian interpolation at the same time according to the Sit obtained by the extraction module Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵;

Matching module: According to the additional verification mark H(t) of the t-th sub-image, T (t, H(t)) coordinate points are obtained, the constant term of the polynomial is obtained, and Lagrangian interpolation is used Get the flag‵ to be matched;

Comparison module: used to compare the flag‵ value to be matched with the flag value of the original image, if flag‵ and flag are not equal, return to the selection module; if flag‵=flag, determine B‵=B, and enter the calculation module;

Calculation module: used to restore B‵ to interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^-1 ＝C ^-1 B C ^-1 ＝C ^-1 CAC C ^-1 , to obtain the original image.

The beneficial effects of the present invention are:

First of all, a multi-cloud-based image storage method is a multi-cloud-based image security storage solution, which mainly solves the security problem of image storage in the cloud by using the idea of image sharing, and prevents the privacy of cloud images from being leaked and inappropriate for images. Deleting images with caution caused a single point of failure, and successfully protected the security of the images by splitting an original image into multiple clouds.

Secondly, this method is based on a multi-cloud image security storage solution, which uses elementary transformations and Gödel coding to solve the inefficiency problem in image processing, makes full use of the computing power of the cloud, and solves complex problems through simple transformations. So that the efficiency of the program is greatly improved.

Description of drawings

Fig. 1 is the schematic flow chart of image storage step;

Fig. 2 is a schematic flow chart of the picture recovery step;

Fig. 3 is a schematic flow chart of the present invention.

Detailed ways

The implementation process of this solution will be clearly and completely described below in conjunction with the accompanying drawings of this solution. Apparently, the described implementation is the core process of the solution. Based on the embodiments in this scheme, all implementation steps are within the scope of protection of this scheme on the premise that those skilled in the art do not make innovative efforts.

A method for storing images based on multiple clouds, comprising the steps of:

Step 1: image storage step;

Step 1.1. Extract the pixel matrix A of the original image, add a unique flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^-1 , where, Matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C.

The user logs in to the cloud through a mobile device or a connected device such as a PC, and selects the picture P ₁ to be saved, extracts the pixel matrix A of the picture, and the system generates a unique flag, which is added to the matrix A as additional information. The flag value can be A random integer is obtained (A, flag), and the system generates an elementary transformation matrix C and an inverse matrix C ^-1 , and the scale of the elementary matrix is equal to the size of the pixel matrix. The original pixel matrix A is subjected to elementary transformation to obtain B, that is, A is multiplied by C to the left for row transformation, and then C is right-multiplied for column transformation to obtain the post-disturbance matrix (B, flag). In this embodiment, the model demonstration is assuming that matrix A is a 3×3 matrix $\left[\begin{array}{ccc}7& 8& 9\\ 4& 5& 6\\ 1& 2& 3\end{array}\right],$ The system generates a random number 1 as the value of flag, that is, flag=1, and the elementary transformation matrix C is a 3×3 matrix $\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right],$ The inverse matrix C-1 is $\left[\begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 1& 0\end{array}\right]$ The starting data is ( $\left[\begin{array}{ccc}7& 8& 9\\ 4& 5& 6\\ 1& 2& 3\end{array}\right],$ 1), B=C×A×C after transformation. $B=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right]\×\left[\begin{array}{ccc}7& 8& 9\\ 4& 5& 6\\ 1& 2& 3\end{array}\right]\×\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right],$ calculated to $B=\left[\begin{array}{ccc}6& 4& 1\\ 3& 1& 2\\ 9& 7& 8\end{array}\right]$ It can be seen that the interference effect is obvious, and the data obtained after this step is (B, 1).

Step 1.2. Convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, and both N and T are positive numbers and T≤N. After step 1.1, the scheme provides two data N, T. Both N and T are positive numbers and T<=N, N represents the number of sub-images to be converted from the original image, and T represents the minimum number of sub-images that can restore the original image. Respectively N=5, T=3, system parameters are provided for subsequent steps;

Step 1.3. Perform Gödel encoding on the i-th row of the disturbed pixel matrix B, the converted Gödel encoding number is Gi, and traverse each row of the pixel matrix; where: if the size of the picture pixel matrix is r×c, the value of i The value is (1,2,3,...,c), i, r and c are positive integers. In this embodiment, for the disturbed pixel matrix $B=\left[\begin{array}{ccc}6& 4& 1\\ 3& 1& 2\\ 9& 7& 8\end{array}\right]$ Performing the Gödel transformation, B is generated from 1. Then the first row G ₁ =2 ⁶ ×3 ⁴ ×5 ¹ =64×81×5=25920.G ₂ =2 ³ ×3 ¹ ×5 ² =600, G ₃ =2 ⁹ ×3 ⁷ ×5 ⁸ = 512×27×390625＝5400000000,

Step 1.4. Construct a polynomial according to Gi and flag. The polynomial constructed by Gi obtains the pixel matrix (P ₁ , P ₂ , ..., P _N ) of N subimages. According to the generated pixel matrix (P ₁ , P ₂ , ..., P _N ) constitutes a subgraph; meanwhile, the polynomial constructed by flag obtains an additional verification mark, and adds additional verification mark information for the subgraph;

Step 1.4.1: Construct the conversion polynomial according to Gi, Among them: mod P is the polynomial modulus, P is a large prime number, j is a variable with a value from 1 to T-1, a _j means (a ₁ , a ₂ ,..., a _T-1 ), x ^j means The j-th power of x is calculated to obtain the value of group c (Fi(1),...,Fi(N)), and then convert these Gödel code numbers into the pixel value of the i-th row to obtain the pixel of the i-th row, And get N r×c row pixel matrix (P ₁ , P ₂ ,..., P _N ); wherein, the system randomly generates T-1 numbers (a ₁ , a ₂ , ..., a _T-1 ), provide coefficients for creating polynomials, and P is the modulus of a large prime number;

In this embodiment, the system generates T-1=3-1=2 random numbers (a ₁ , a ₂ ), divided into a ₁ =1, a ₂ =2. Then three polynomials can be constructed as F ₁ ( x)=G ₁ +x+2x ² , F ₂ (x)=G ₂ +x+2x ² , F ₃ (x)=G ₃ +x+2x ² , x is expressed as an equation variable, calculation (Fi(1 )Fi(2),...,Fi(5)) to get three sets of data (F ₁ (1)=25923, F ₁ (2)=25930, F ₁ (3)=25941, F ₁ (4)=25956 , F ₁ (5)=25975), (F ₁ (1)=603, F ₂ (2)=610, F ₂ (3)=618, F ₂ (4)=636, F ₂ (5)=655 ), (F ₃ (1)=5400000003, F ₃ (2)=5400000010, F ₃ (3)=5400000018, F ₃ (4)=5400000036, F ₃ (5)=5400000055), according to the Fundamental Theorem of Arithmetic, and Known as the unique decomposition theorem of positive integers, every natural number greater than 1 can be written as a product of prime numbers, and after these prime factors are arranged in size, there is only one way to write them, so each Gödel coded number obtained by calculation can be converted into a new set of numbers, and the converted set of numbers is used as a row of the pixel matrix of the sub-image, so the implementation converts these into a pixel matrix form to obtain five pixel matrices, which are P ₁ , P ₂ , P ₃ , P ₄ , _P5 . As P ₁ , it consists of $\left[\begin{array}{c}{f}_1\left(1\right)\\ f_2\left(1\right)\\ f_3\left(1\right)\end{array}\right]$ Right now $\left[\begin{array}{c}25923\\ 603\\ 5400000003\end{array}\right],$ It is decomposed by prime number and converted into a pixel matrix as $\left[\begin{array}{ccc}3& 8641& 0\\ 3& 3& 67\\ 2^2\&times;3& 17& 257\end{array}\right].$ Others and so on, decompose each number.

Step 1.4.2: Construct a flag polynomial according to flag j is a variable whose value ranges from 1 to T-1, a _j represents (a ₁ , a ₂ ,..., a _T-1 ), x ^j represents the jth power of x, and the calculated H(t) is distributed Give the tth subgraph as an additional verification mark, and the value of t is (1, 2, ..., N); the calculated result is the additional verification mark of each subgraph.

In this embodiment, flag=1, random number (a ₁ , a ₂ ) structure H(x)=1+x+2x ² . Calculation (H(1)=4, H(2)=11, H(3)=19, H(4)=37, H(5)=56), after the above process, you can get five similar to the original picture The structure of (P ₁ ,4)(P ₂ ,11)(P ₃ ,19)(P ₄ ,37)(P ₅ ,56).

Step 1.5. Add a mark to each subgraph, such as a digital signature, and then distribute the marked subgraphs randomly and evenly to multiple clouds. Add a mark to each sub-graph, and then distribute the marked sub-graphs randomly and evenly to multiple clouds to avoid storing too many sub-graphs in a single cloud. Subgraph 1, Subgraph 2, Subgraph 3, Subgraph 4, Subgraph 5 after marking. Stored in three clouds, cloud 1 saves sub-picture 1 and sub-picture 2, cloud 2 saves sub-picture 3 and sub-picture 4, cloud 3 saves sub-picture 5.

The following are the steps for image recovery:

Step 2.1. Select subgraphs from multiple clouds. Since T=3 in this embodiment, it only needs to find 3 subgraphs to restore.

Step 2.2. Carry out secondary label verification on the selected subgraph, if the subgraph label verification is passed, then keep the current subgraph and enter step 2.3, otherwise, return to step 2.1 after discarding the subgraph;

In the mark verification process, select sub-graph 3 in cloud 2, verify the mark of sub-graph 3, and keep sub-graph 3 after passing the verification. The number of reserved sub-graphs is currently 1. Since it is less than T, continue to verify the sub-graph. Select the destroyed subgraph 1' from cloud 2, verify the subgraph, and discard it if the verification fails.

Step 2.3. Determine whether the number of subgraphs reaches T; if yes, enter step 2.4, otherwise return to step 2.1;

In this embodiment, select sub-image 4 from cloud 2, verify the mark, and retain sub-image 4 through verification, select sub-image 5 from cloud 3, verify the mark, and retain sub-image 5 through verification. The number of currently reserved sub-images is 3 is equal to T.

Step 2.4. Extract the pixel matrix of T subimages, and convert the i-th row of the T pixel matrix into a Gödel coded number S _i ^t , where i represents the i-th row of the pixel matrix, and t represents the t-th subimage, and t is between 1 and T Between, so S _i ^t is expressed as the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image.

In this embodiment, the pixel matrix P _{3 of the sub-image 3} and the pixel matrix P 4 of the sub-image 4 are obtained through step 2.3, the pixel matrix P ₅ of the sub-image ₅ is obtained, and the additional information H(3), H of the three sub-images (4), H(5), namely (P ₃ ,19), (P ₄ ,37), (P ₅ ,56). Convert each row of the sub-picture pixel matrix P ₃ , P ₄ and P ₅ into a Gödel code number. Since the three matrices are all 3*3 square matrices, three groups of data are obtained, and the data one is ((3, 25941 ), (3, 618), (3, 5400000018)), data two is ((4, 25956), (4, 636), (4, 5400000036)), data three is ((5, 25975), (5 , 655), (5, 5400000055)).

Step 2.5. According to the S _i ^t obtained in step 2.4, use Lagrangian interpolation at the same time Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵;

In this embodiment, from the data obtained in step 2.4, according to Lagrangian interpolation, it can be known that three points on the quadratic polynomial are known, and the quadratic polynomial can be obtained, because the three points in step 3 are obtained according to the three sets of data. function F1(x), F2(x), F3(x), and then set x equal to 0 to find the constant term. When calculating three functions, the applied Lagrangian interpolation formula is Calculate F1 (0) = 25920, F2 (0) = 600, F3 (0) = 5400000000, and then convert the obtained Gödel code number into a matrix with the first row (6,4,1) and the second row (3,1 ,2), the third row (9,8,7) can get the pixel matrix $B=\left[\begin{array}{ccc}6& 4& 1\\ 3& 1& 2\\ 9& 7& 8\end{array}\right].$

Step 2.6. According to the additional verification mark H(t) of the t-th sub-graph, T (t, H(t)) coordinate points are obtained, and the constant term of the polynomial is obtained, and Lagrangian interpolation is used Get the flag‵ to be matched.

In this embodiment, the additional marks (P ₃ , 19), (P ₄ , 37), (P ₅ , 56) of the three sub-pictures are extracted, and using these three data, according to the Lagrangian difference, calculate the flag‵=1.

Step 2.7. Compare the flag‵ value to be matched with the flag value of the original image, if flag‵ is not equal to flag, return to step 2.1; if flag‵=flag, determine B‵=B, and enter step 2.8;

In this embodiment, if the to-be-matched flag‵=1 is equal to the saved flag, it proves that the restoration is correct, and if the to-be-matched flag‵ is not equal to the flag, it is restored again.

Step 2.8. Restore B‵ from interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^{- 1} = C ^-1 B C ^-1 = C ^-1 CAC C ^-1 , to obtain the original image. Compare the calculated flag with the flag reserved in step 1, if flag,=flag, it means that the restoration is correct, and the restored pixel matrix $B=\left[\begin{array}{ccc}6& 4& 1\\ 3& 1& 2\\ 9& 7& 8\end{array}\right]$ Perform inverse transformation to obtain the pixel matrix A of the original image, and the system provides the inverse matrix of the retained elementary transformation $C^{-1}\left[\begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 1& 0\end{array}\right]\text{,}$ Then A＝C ^-1 B‵ C ^-1 ＝C ^-1 B C ^-1 ＝C ^-1 CAC $C^{-1}=\left[\begin{array}{ccc}7& 8& 9\\ 4& 5& 6\\ 1& 2& 3\end{array}\right].$ So far, the pixel matrix of the original image is obtained, and the restoration of the original image is completed.

A picture storage system based on multi-cloud, characterized in that it includes a picture storage module and a picture recovery module;

The picture storage module includes:

The first extraction module: used to extract the pixel matrix A of the original image, add a unique identification flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^{- 1} , where matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C;

Parameter construction module: used to convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, N and T are both positive numbers and T≤N;

Coding module: used to perform Gödel encoding on the i-th row of the disturbed pixel matrix B, the converted Gödel encoding number is Gi, and traverse each row of the pixel matrix; where: if the size of the image pixel matrix is r×c, The value of i is (1,2,3,...,c), i, r and c are positive integers;

Polynomial construction module: used to construct a polynomial according to Gi and flag, the polynomial constructed by Gi obtains pixel matrices (P ₁ , P ₂ , ..., P _N ) of N subimages, and generates pixel matrices (P ₁ , P ₂ , ... ..., P _N ) constitute a subgraph; meanwhile, the polynomial constructed by flag gets an additional verification mark, and adds additional verification mark information for the subgraph;

Allocation module: used to add secondary marks to each sub-image, and then distribute the marked sub-images randomly and evenly to multiple clouds;

Image recovery modules include:

selection module: used to select subgraphs from multiple clouds,

Verification module: perform secondary mark verification on the selected sub-graph, if the sub-graph mark verification is passed, keep the current sub-graph and enter the judgment module, otherwise, discard the sub-graph and return to the selection module;

Judgment module: judge whether the number of subgraphs reaches T; if yes, enter the second extraction module, otherwise return to the selection module;

The second extraction module: used to extract the pixel matrix (P ₁ , P ₂ , ..., P _T ) of T subimages, and convert the i-th row of the T pixel matrix into a Gödel coded number S _i ^t , where i represents a pixel In the i-th row of the matrix, t represents the t-th sub-image, and t is between 1 and T, so S _i ^t represents the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image.

Restoration module: used to use Lagrangian interpolation at the same time according to the Sit obtained by the extraction module Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵;

Matching module: According to the additional verification mark H(t) of the t-th sub-image, T (t, H(t)) coordinate points are obtained, the constant term of the polynomial is obtained, and Lagrangian interpolation is used Get the flag‵ to be matched;

Comparison module: used to compare the flag‵ value to be matched with the flag value of the original image, if flag‵ and flag are not equal, return to the selection module; if flag‵=flag, determine B‵=B, and enter the calculation module;

Calculation module: used to restore B‵ to interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^-1 ＝C ^-1 B C ^-1 ＝C ^-1 CAC C ^-1 , to obtain the original image.

Claims (4)

1. A picture storage method based on multi-cloud, is characterized in that, comprises the steps: Step 1: image storage step; Step 1.1: Extract the pixel matrix A of the original image, add a unique flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^-1 , where, Matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C; Step 1.2: Convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, and both N and T are positive numbers and T≤N; Step 1.3: Perform Gödel coding on the i-th row of the disturbed pixel matrix B, the converted Gödel code number is Gi, and traverse each row of the pixel matrix; where: if the size of the image pixel matrix is r×c, i’s The value is (1,2,3,...,c), i, r and c are positive integers; Step 1.4: Construct a polynomial according to Gi and flag. The polynomial constructed by Gi can obtain the pixel matrix (P ₁ , P ₂ , ..., P _N ) of N subimages. According to the generated pixel matrix (P ₁ , P ₂ , ..., P _N ) constitutes a subgraph; meanwhile, the polynomial constructed by flag obtains an additional verification mark, and adds additional verification mark information for the subgraph; Step 1.5: Add secondary marks to each subgraph, and then distribute the marked subgraphs randomly and evenly to multiple clouds; Step 2: Picture Recovery Steps: Step 2.1: Select subgraphs from multiple clouds; Step 2.2: Perform secondary label verification on the selected subgraph, if the subgraph label verification is passed, keep the current subgraph and enter step 2.3, otherwise, discard the subgraph and return to step 2.1; Step 2.3: Determine whether the number of subgraphs reaches T; if yes, enter step 2.4, otherwise return to step 2.1; Step 2.4: Extract pixel matrices (P ₁ , P ₂ , ..., P _T ) of T subimages, and convert the i-th row of T pixel matrices into Gödel code numbers S _i ^t , where i represents the i-th pixel matrix row, t represents the t-th sub-image, t is between 1 and T, and S _i ^t represents the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image; Step 2.5: According to S _i ^t obtained in Step 2.4, use Lagrangian interpolation at the same time Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵; Step 2.6: Obtain T (t, H(t)) coordinate points according to the additional verification mark H(t) of the t-th sub-image, find out the constant term of the polynomial, and use Lagrangian interpolation Get the flag‵ to be matched; Step 2.7: Compare the flag‵ value to be matched with the flag value of the original image, if flag‵ and flag are not equal, return to step 2.1; if flag‵=flag, determine B‵=B, and enter step 2.8; Step 2.8: Restore B‵ from interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^{- 1} = C ^-1 B C ^-1 = C ^-1 CAC C ^-1 , to obtain the original image. 2. A kind of picture storage method based on multi-cloud according to claim 1, is characterized in that, described step 1.4 comprises the following steps: Step 1.4.1: Construct the conversion polynomial according to Gi, Among them: mod p is the polynomial modulus, p is a large prime number, j is a variable with a value from 1 to T-1, a _j means (a ₁ , a ₂ ,..., a _T-1 ), x ^j means The j-th power of x is calculated to obtain the value of group c (Fi(1),...,Fi(N)), and then convert these Gödel code numbers into the pixel value of the i-th row to obtain the pixel of the i-th row, And get N r×c row pixel matrix (P ₁ , P ₂ ,..., P _N ); wherein, the system randomly generates T-1 numbers (a ₁ , a ₂ , ..., a _T-1 ), provide coefficients for creating polynomials, and P is the modulus of a large prime number; Step 1.4.2: Construct a flag polynomial according to flag j is a variable whose value ranges from 1 to T-1, a _j represents (a ₁ , a ₂ ,..., a _T-1 ), x ^j represents the jth power of x, and the calculated H(t) is distributed Give the tth subgraph as an additional verification mark, and the value of t is (1, 2, ..., N); the calculated result is the additional verification mark of each subgraph. 3. A multi-cloud based image storage method according to claim 1 or 2, characterized in that: the values of N and T in the step 1.2 are respectively N=5 and T=3. 4. A picture storage system based on multiple clouds, comprising a picture storage module and a picture recovery module; The picture storage module includes: The first extraction module: used to extract the pixel matrix A of the original image, add a unique identification flag to the pixel matrix, and save the flag value of the picture; calculate the pixel matrix B after interference, B=C×A×C, and the system saves C ^{- 1} , where matrix C is an elementary transformation matrix of the same size as pixel matrix A, and C ^-1 is the inverse matrix of matrix C; Parameter construction module: used to convert the original image into N subimages, and construct a parameter T, where T represents the minimum number of subimages that can restore the original image, N and T are both positive numbers and T≤N; Coding module: used to perform Gödel encoding on the i-th row of the disturbed pixel matrix B, the converted Gödel encoding number is Gi, and traverse each row of the pixel matrix; where: if the size of the image pixel matrix is r×c, The value of i is (1,2,3,...,c), i, r and c are positive integers; Polynomial construction module: used to construct a polynomial according to Gi and flag, the polynomial constructed by Gi obtains pixel matrices (P ₁ , P ₂ , ..., P _N ) of N subimages, and generates pixel matrices (P ₁ , P ₂ , ... ..., P _N ) constitute a subgraph; meanwhile, the polynomial constructed by flag gets an additional verification mark, and adds additional verification mark information for the subgraph; Allocation module: used to add secondary marks to each sub-image, and then distribute the marked sub-images randomly and evenly to multiple clouds; Image recovery modules include: selection module: used to select subgraphs from multiple clouds, Verification module: perform secondary mark verification on the selected sub-graph, if the sub-graph mark verification is passed, keep the current sub-graph and enter the judgment module, otherwise, discard the sub-graph and return to the selection module; Judgment module: judge whether the number of subgraphs reaches T; if yes, enter the second extraction module, otherwise return to the selection module; The second extraction module: used to extract the pixel matrix (P ₁ , P ₂ , ..., P _T ) of T subimages, and convert the i-th row of the T pixel matrix into a Gödel coded number S _i ^t , where i represents a pixel In the i-th row of the matrix, t represents the t-th sub-image, and t is between 1 and T, so S _i ^t represents the number of Gödel codes converted from the pixels in the i-th row of the pixel matrix of the t-th sub-image; Restoration module: used to use Lagrangian interpolation at the same time according to ^{the Si t} _obtained by the extraction module Among them: t is an integer, indicating the t-th picture, j is an integer, indicating that the j-th picture in the sub-image is obtained, mod p is the modulo p, and p is a large prime number; to restore the Gödel code of the interference pixel matrix B‵ Count Gi‵, convert the calculated Gi‵ to Gödel encoding to obtain the pixel in the i-th row of the pixel matrix, and perform the above operation on each row of the T subimages to obtain a complete restored interference pixel matrix B‵; Matching module: According to the additional verification mark H(t) of the t-th sub-image, T (t, H(t)) coordinate points are obtained, the constant term of the polynomial is obtained, and Lagrangian interpolation is used Get the flag‵ to be matched; Comparison module: used to compare the flag‵ value to be matched with the flag value of the original image, if flag‵ and flag are not equal, return to the selection module; if flag‵=flag, determine B‵=B, and enter the calculation module; Calculation module: used to restore B‵ to interference; use C ^-1 to restore the original image pixel matrix A, where C ^-1 is the inverse matrix of the elementary transformation matrix C of the pixel matrix A, and finally calculate A=C ^-1 B‵ C ^-1 ＝C ^-1 BC ^-1 ＝C ^-1 CAC C ^-1 , to obtain the original image.