An image encryption method based on parallel compressed sensing and secret sharing

Abstract

The present invention discloses an image encryption method based on parallel compressed sensing and secret sharing. First, a measurement matrix with good performance is used as a key to compress the image in parallel, which not only realizes encryption, but also reduces the size of the image, and has lower storage and computational complexity. Secondly, block Arnold transform encryption is introduced for non-square matrix images to make the image appear messy, thereby realizing encryption of the image after parallel compression. Then, in order to further improve the reliability and confidentiality of the system and prevent the secrets from being too concentrated, the (k,n)-threshold secret sharing technology is used to process the secret image after the block Arnold transform, which not only realizes the encryption of the secret image, but also disperses the risk and tolerates the intrusion. Finally, Zigzag obfuscation is used to process the shadow image generated by the secret sharing technology, interfere with the position of the element in the shadow image, and realize the encryption of the shadow image.

Description

Technical Field

[0001] The present invention relates to the technical field of image encryption, and in particular to an image encryption method based on parallel compressed sensing and secret sharing. Background Art

[0002] In the era of information explosion, as the amount of stored data increases exponentially, there are more and more storage servers, and storage pressure continues to rise. This not only increases the high cost of storage, but also this traditional storage method also has great risks in terms of the security and reliability of data storage.

[0003] Traditional compressed sensing considers sampling of one-dimensional signals. For multi-dimensional signals, if they are reshaped into one-dimensional signals, the required size of the measurement matrix will increase significantly, which will significantly increase the storage and computational complexity.

[0004] To solve this problem, the existing technology reshapes the multidimensional signal into a two-dimensional signal, and then uses the same measurement matrix to sample and reconstruct it column by column. This method is called parallel compressed sensing, which has lower storage and computational complexity. The measurement matrix plays a connecting role in parallel compressed sensing. It not only guarantees the sampling quality, but also determines the hardware implementation of compressed sampling.

[0005] However, parallel compressed sensing in a resource-constrained environment with very little sampling makes it difficult to reconstruct a good quality image using existing reconstruction algorithms, such as: Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), Subspace Pursuit (SP), etc. Therefore, the present invention proposes an image encryption scheme that can adjust the size of the shadow image according to different application scenarios and make a trade-off between storage burden and reconstructed image quality according to different scenarios. Summary of the invention

[0006] Aiming at the technical problem that it is difficult for existing parallel compressed sensing methods to reconstruct high-quality images with very few samples in a resource-constrained environment, the present invention proposes an image encryption method based on parallel compressed sensing and secret sharing. On the basis of the Arnold transform of the measured value image, the secret sharing technology is introduced. The secret of the proposed scheme can adjust the size of the shadow image according to different application scenarios, and at the same time, a trade-off can be made between the storage burden and the quality of the reconstructed image according to different scenarios. Finally, in order to protect the security of the shadow image, Zigzag obfuscation is introduced to process the shadow image, and the encryption of the shadow image is realized.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] An image encryption method based on parallel compressed sensing and secret sharing comprises the following steps:

[0009] S1, using the measurement matrix as a key to compress the image in parallel to obtain a measurement value matrix image;

[0010] S2, using block Arnold transformation to scramble the parallel compressed measurement value matrix image, the pixel positions of the image are rearranged to obtain a secret image;

[0011] S3, using secret sharing technology to process the secret image after the block Arnold transformation to obtain a shadow matrix image;

[0012] S4. Use Zigzag confusion to process the shadow matrix image, interfere with the position of the element in the shadow matrix image, and obtain the shadow encrypted matrix image.

[0013] Furthermore, the parallel compression process in step S1 is as follows:

[0014] Let α be the compression ratio, satisfying 0<α<1. For an N×N-dimensional image X, an N×1-dimensional column vector x i represents the i-th column of image X, and the measurement process of parallel compressed sensing is expressed as:

[0015] y i =Φx i (1)

[0016] Where i = 1, 2, ..., N, Φ is a measurement matrix of αN × N dimensions, and the corresponding measurement value matrix Y = [y1, y2, ..., y N ];

[0017] The logistic mapping equation is as follows:

[0018] z n+1 =μz n (1-z n ) (2)

[0019] Wherein, μ is the chaotic parameter of the chaotic system, 3.5699456<μ≤4;

[0020] For the Logistic map, set the initial value z0, chaotic parameter μ, sampling distance d, and then get the chaotic sequence z(l), where l = αN 2 , the sequence z(l) is arranged column by column into the following αN×N dimensional matrix Φ:

[0021]

[0022] For a flat image X:

[0023] Y=ΦX (4)

[0024] Among them, Y is the corresponding αN×N dimensional measurement value matrix.

[0025] Furthermore, the scrambling process in step S2 is as follows:

[0026] For the αN×N dimension measurement value matrix image, the hash function is applied to calculate the three parameters a, b, n of the key image, and p = gcd(αN, N). The measurement value matrix Y is divided into Blocks, each block is p×p dimensional, and each block is encrypted by equation (5):

[0027]

[0028] Finally, each encrypted block is combined to obtain the secret image A, where n is the number of iterations of the Arnold transform, and a and b are the parameters of the Arnold transform.

[0029] Furthermore, step S3 uses secret sharing technology to process the secret image after the block Arnold transformation as follows:

[0030] For two positive integers m, t (1≤m, t≤αN2), if mt=αN 2 , the secret image A is reshaped into an m×t-dimensional matrix B by column, and for each row k (1≤k≤m) of the matrix B, a polynomial is given:

[0031] s k (x) = s k,0 +s k,1 x+…+s k,t-1 x t-1 , (6)

[0032] where s k,0 ,s k,1 ,…,s k,t-1 Corresponding to each element in the kth row; for a given x, equation (6) is used to obtain a set of m values ​​s1(x), s2(x), …s m (x); for two positive integers M1, N1, and m = M1N1, if the array s(x) is reshaped column by column into a matrix S(x) of dimension M1×N1, a shadow matrix S(x) is obtained; if n different x1, x2, …, x are selected n , we get n different shadow matrices S(x1),S(x2),…,S(x n), denoted as S1,S2,…,S n .

[0033] Furthermore, the Zigzag obfuscation encryption process in step S4 is as follows:

[0034] Apply the hash function to calculate the three parameters a, b, n of the key image, where n is the number of iterations of Zigzag confusion, (a, b) is the starting position of Zigzag confusion, and the shadow matrices S1, S2, …, S n Encrypt through Zigzag confusion to obtain the shadow encryption matrix Z1, Z2, …, Z n .

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The image encryption method based on parallel compressed sensing and secret sharing provided by the present invention, first, uses a good performance measurement matrix as a key to compress the image in parallel, and the parallel compressed sensing uses the same measurement matrix to sample and reconstruct column by column, which not only realizes encryption, but also reduces the size of the image, and has lower storage and computational complexity. Secondly, for non-square matrix images, block Arnold transform encryption is introduced, and the pixel positions of the image will be rearranged, making the image appear messy, thereby realizing the encryption of the image after parallel compression. Then, in order to further improve the reliability and confidentiality of the system and prevent the secrets from being too concentrated, the (k,n)-threshold secret sharing technology is used to process the secret image after the block Arnold transform, which not only realizes the encryption of the secret image, but also disperses the risk and tolerates the intrusion. Finally, Zigzag obfuscation is used to process the shadow image generated by the secret sharing technology, interfere with the position of the element in the shadow image, and realize the encryption of the shadow image. The method of the present invention is applied to distributed storage, especially in a resource-constrained environment. The size of the shadow image can be adjusted according to different application scenarios. At the same time, a trade-off can be made between the storage burden and the quality of the reconstructed image according to different scenarios. This not only realizes image encryption and improves security and reliability, but also reduces the storage space of the image and improves transmission efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0038] Figure 1A flowchart of an image encryption process and a decryption process based on parallel compressed sensing and secret sharing provided in an embodiment of the present invention.

[0039] Figure 2 A schematic diagram of a Zigzag path provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to better understand the technical solution, the method of the present invention is described in detail below with reference to the accompanying drawings.

[0041] The image encryption method based on parallel compressed sensing and secret sharing provided by the embodiment of the present invention has the following process: Figure 1 As shown, the specific steps include:

[0042] S1. Use the measurement matrix as a key to compress the image in parallel to obtain a measurement value matrix image.

[0043] Specifically, the parallel compression process in step S1 is as follows:

[0044] Let α be the compression ratio, satisfying 0<α<1. For an N×N-dimensional image X, an N×1-dimensional column vector x i represents the i-th column of image X, and the measurement process of parallel compressed sensing is expressed as:

[0045] y i =Φx i (1)

[0046] Where i = 1, 2, ..., N, Φ is a measurement matrix of αN × N dimensions, and the corresponding measurement value matrix Y = [y1, y2, ..., y N ];

[0047] In the present invention, for the Logistic mapping, the initial value z0, the chaotic parameter μ, and the sampling distance d are set, and then the chaotic sequence z(l) is obtained, where l = αN 2 , the sequence z(l) is arranged column by column into the following αN×N dimensional matrix Φ:

[0048]

[0049] For a flat image X:

[0050] Y=ΦX (3)

[0051] Among them, Y is the corresponding αN×N dimensional measurement value matrix.

[0052] About Logistic Mapping:

[0053] A chaotic system refers to a deterministic system with seemingly random irregular motions, whose behavior is uncertain, non-repeatable and unpredictable, i.e., chaotic phenomena. Chaos is an inherent characteristic of nonlinear dynamic systems and a common phenomenon in nonlinear systems.

[0054] The Logistic map is a relatively simple one-dimensional chaotic system that can generate random numbers with better performance.

[0055] The logistic mapping equation is as follows:

[0056] z n+1 =μz n (1-z n ) (4)

[0057] Where z0∈(0,1], μ∈(0,4] are the initial value and parameter of the chaotic system respectively. It is worth noting that the Logistic map is not necessarily in a chaotic state, which is related to the value of μ. When 3.5699456<μ≤4, the values ​​generated by continuous iterations of the Logistic system will be in a pseudo-random state, that is, a chaotic state.

[0058] S2. Use block Arnold transformation to scramble the parallel compressed measurement value matrix image, and rearrange the pixel positions of the image to obtain a secret image.

[0059] The image can be regarded as a two-dimensional matrix. The Arnold transform is used to scramble the N×N dimensional square matrix image. After the Arnold transform, the pixel positions of the image will be rearranged, making the image appear messy, thereby achieving the scrambling and encryption effect of the image. The Arnold transform of the N×N dimensional square matrix image is defined as:

[0060]

[0061] Where a, b are parameters and n is the number of iterations.

[0062] Specifically, in step S2 of the present invention, the scrambling process is as follows:

[0063] For the αN×N dimension measurement value matrix image, the hash function is applied to calculate the three parameters a, b, n of the key image, and p = gcd(αN, N). The measurement value matrix Y is divided into Blocks, each block is p×p dimensional, and each block is encrypted by equation (5):

[0064] Finally, each encrypted block is combined to obtain the secret image A, where n is the number of iterations of the Arnold transform, and a and b are the parameters of the Arnold transform.

[0065] S3. Using secret sharing technology, the secret image after block Arnold transformation is processed to obtain a shadow matrix image.

[0066] The Shamir(t,n)-threshold secret sharing scheme consists of two stages:

[0067] 1) Secret share generation phase:

[0068] Let U = {P1, P2, ..., P n} is a set of n participants. The distributor first randomly selects t integers, denoted as s0, s1, …, s t-1 , and then create a t-1 degree polynomial:

[0069] s(x)=s0+s1x+…+s t-1 x t-1 (6)

[0070] Let the secret s = s(0), and finally select n different integers x1, x2, ..., x n Give each of the n participants and calculate the secret share s(x i ), send s(x i ) to the corresponding participant P i , where i=1,2,…,n.

[0071] 2) Secret reconstruction stage:

[0072] A subset of t(t≤n) participants The secret s can be reconstructed. Each participant discloses his or her secret share to all other participants. Participants with t secret shares can reconstruct the secret s through the Lagrange interpolation formula:

[0073]

[0074] in

[0075] Specifically, in the present invention, step S3 uses secret sharing technology to process the secret image after block Arnold transformation (secret share generation stage) as follows:

[0076] For two positive integers m, t (1≤m, t≤αN 2 ), if mt=αN 2 , the secret image A is reshaped into an m×t-dimensional matrix B by column, and for each row k (1≤k≤m) of the matrix B, a polynomial is given:

[0077] s k (x) = s k,0 +s k,1 x+…+sk,t-1 x t-1 (8)

[0078] where s k,0 ,s k,1 ,…,s k,t-1 Corresponding to each element in the kth row; for a given x, equation (8) is used to obtain a list containing m values ​​s1(x), s2(x), …s m (x); for two positive integers M1, N1, and m = M1N1, if the array s(x) is reshaped column by column into a matrix S(x) of dimension M1×N1, a shadow matrix S(x) is obtained; if n different x1, x2, …, x are selected n , we get n different shadow matrices S(x1),S(x2),…,S(x n ), denoted as S1,S2,…,S n .

[0079] S4. Use Zigzag confusion to process the shadow matrix image, interfere with the position of the element in the shadow matrix image, and obtain the shadow encrypted matrix image.

[0080] Zigzag confusion can be seen as Figure 2 A form of the Zigzag path shown in Figure 1. Zigzag obfuscation means that the pixels of each block are rearranged in a Zigzag path within the block, which is related to the selection of the starting pixel. Generally speaking, there is a strong correlation between adjacent pixels in an image. After Zigzag obfuscation, adjacent pixels are also shuffled within the image block, thereby interfering with the position of the elements in the matrix and achieving image encryption.

[0081] In the present invention, the Zigzag obfuscation encryption process in step S4 is as follows:

[0082] Apply the hash function to calculate the three parameters a, b, n of the key image, where n is the number of iterations of Zigzag confusion, (a, b) is the starting position of Zigzag confusion, and the shadow matrices S1, S2, …, S n Encrypt through Zigzag confusion to obtain the shadow encryption matrix Z1, Z2, …, Z n .

[0083] The decryption process of an image is the opposite of the encryption process of an image. Figure 1 As shown, the specific process of image decryption is described as follows.

[0084] A (t,n)-secret sharing scheme is one in which at least t secret shares can recover the secret, while less than t secret shares cannot recover the secret.

[0085] Step 1: t shadow encryption matrices Decryption of the inverse Zigzag obfuscation.

[0086] Apply the hash function to calculate the three parameters a, b, n of the key image, where n is the number of iterations of the inverse Zigzag obfuscation and (a, b) is the starting position of the inverse Zigzag obfuscation. Perform inverse Zigzag confusion to obtain t restored shadow matrices in

[0087] Step 2: Secret reconstruction phase.

[0088] make is a set of t shadow matrices, where t M1×N1 shadow matrices can be reshaped column by column into t m×1 arrays. For 1≤i≤m, the i-th element of each array can be expressed as Where 1≤l≤m. Then we can get t values ​​such that:

[0089]

[0090] Solving this system of equations, since the coefficient matrix is ​​non-singular, we can obtain the unique solution s i,0 ,s i,1 ,…,s i,t-1 , which is the i-th row of the matrix B'. Therefore, the m×t-dimensional matrix B' is reshaped column by column into an αN×N-dimensional matrix A'.

[0091] Step 3: Decryption of the matrix A' by block inverse Arnold transform.

[0092] Apply the hash function to calculate the three parameters a, b, n of the key image, where n is the number of iterations of the inverse Arnold transform and a and b are the parameters of the inverse Arnold transform. Perform a block inverse Arnold transform on the matrix A' to obtain a measurement value matrix Y' of the same dimension.

[0093] Step 4: Compressed reconstruction of the measurement matrix Y'.

[0094] Through the initial value z0 of the public Logistic map, the chaotic parameter μ, the sampling distance d, and then the chaotic sequence z(l) is obtained, and the αN×N-dimensional measurement matrix Φ is constructed. Then, the orthogonal matching pursuit (OMP) algorithm is selected to solve the l0-minimization problem, and the solution is recorded as X'.

[0095] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An image encryption method based on parallel compressed sensing and secret sharing, characterized in that: The following steps are involved: S1, using the measurement matrix as a key to compress the image in parallel to obtain a measurement value matrix image; S2, using block Arnold transformation to scramble the parallel compressed measurement value matrix image, the pixel positions of the image are rearranged, and a secret image is obtained; S3, using secret sharing technology to process the secret image after the block Arnold transformation to obtain a shadow matrix image; S4. Use Zigzag confusion to process the shadow matrix image, interfere with the position of the element in the shadow matrix image, and obtain the shadow encrypted matrix image.

2. The image encryption method based on parallel compressed sensing and secret sharing according to claim 1, characterized in that: The parallel compression process in step S1 is as follows: Let α be the compression ratio, satisfying 0<α<1. For an N×N-dimensional image X, an N×1-dimensional column vector x i represents the i-th column of image X, and the measurement process of parallel compressed sensing is expressed as: y i =Φx i (1) Where i = 1, 2, ..., N, Φ is a measurement matrix of αN × N dimensions, and the corresponding measurement value matrix Y = [y1, y2, ..., y N ]; The logistic mapping equation is as follows: z n+1 =μz n (1-z n ) (2) Wherein, μ is the chaotic parameter of the chaotic system, 3.5699456<μ≤4; For the Logistic map, set the initial value z0, chaotic parameter μ, sampling distance d, and then get the chaotic sequence z(l), where l = αN 2 , the sequence z(l) is arranged column by column into the following αN×N dimensional matrix Φ: For a flat image X: Y=ΦX (4) Among them, Y is the corresponding αN×N dimensional measurement value matrix.

3. The image encryption method based on parallel compressed sensing and secret sharing according to claim 2 is characterized in that: The scrambling process in step S2 is as follows: For the αN×N dimension measurement value matrix image, the hash function is applied to calculate the three parameters a, b, n of the key image, and p = gcd(αN, N). The measurement value matrix Y is divided into Blocks, each block is p×p dimensional, and each block is encrypted by equation (5): Finally, each encrypted block is combined to obtain the secret image A, where n is the number of iterations of the Arnold transform, and a and b are the parameters of the Arnold transform.

4. The image encryption method based on parallel compressed sensing and secret sharing according to claim 3 is characterized in that: Step S3 uses secret sharing technology to process the secret image after block Arnold transformation as follows: For two positive integers m, t (1≤m, t≤αN 2 ), if mt=αN 2 , the secret image A is reshaped into an m×t-dimensional matrix B by column, and for each row k (1≤k≤m) of the matrix B, a polynomial is given: s k (x)=s k,0 +s k,1 x+…+s k,t-1 x t-1 , (6) where s k,0 ,s k,1 ,…,s k,t-1 Corresponding to each element in the kth row; for a given x, equation (6) is used to obtain a set of m values ​​s1(x), s2(x), …s m (x); for two positive integers M1, N1, and m = M1N1, if the array s(x) is reshaped column by column into a matrix S(x) of dimension M1×N1, a shadow matrix S(x) is obtained; if n different x1, x2, …, x are selected n , we get n different shadow matrices S(x1),S(x2),…,S(x n ), denoted as S1,S2,…,S n .

5. The image encryption method based on parallel compressed sensing and secret sharing according to claim 4 is characterized in that: The Zigzag obfuscation encryption process in step S4 is as follows: Apply the hash function to calculate the three parameters a, b, n of the key image, where n is the number of iterations of Zigzag confusion, (a, b) is the starting position of Zigzag confusion, and the shadow matrices S1, S2, …, S n Encrypt through Zigzag confusion to obtain the shadow encryption matrix Z1, Z2, …, Z n .

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