Visually secure image encryption method based on semi-tensor product compressed sensing and DWT-HD-SVD embedding

Abstract

The present invention provides a visual security image encryption method based on half tensor product compressed sensing and DWT-HD-SVD embedding, comprising the following steps: generating parameters and initial values ​​of a two-dimensional chaotic system mapping according to plaintext image information; generating a measurement matrix according to the chaotic system, and optimizing the measurement matrix using singular value decomposition and column vector unitization; performing wavelet decomposition on the plaintext image to obtain a sparse image, and performing bidirectional cross zigzag scrambling on the sparse image to obtain an encrypted image; performing compression measurement on the encrypted image using the optimized measurement matrix to obtain a compressed image; performing HD decomposition and SVD decomposition on the carrier image and the compressed image at the same time, and embedding the compressed image into the carrier image to obtain the final cipher image. The visual security image generated by the method has higher information entropy, and it is difficult to obtain relevant information of the original image.

Description

Technical Field

[0001] The present invention relates to the technical fields of compressed sensing, image encryption and visual security, and in particular to a visual security image encryption method based on improved half-tensor product compressed sensing and DWT-HD-SVD embedding. Background Art

[0002] With the rapid development of network technology, massive amounts of image information are being rapidly generated and shared through the network. At the same time, unauthorized access and abuse issues have also emerged. As an important privacy protection technology, encryption technology has received widespread attention in recent years. Current image encryption technology usually combines other technologies to improve encryption security, such as chaos theory, DNA coding, optical transformation, cellular automata, etc. Although these technologies can prevent ciphertext data from being directly obtained, noise-like ciphertexts are more likely to expose the importance of the protected content and cannot ensure the visual security of the ciphertext. Therefore, how to improve the visual security of ciphertext so that it is not easily exposed during transmission has become an urgent problem to be solved in current encryption technology. Summary of the invention

[0003] In order to overcome the problems existing in the prior art, the present invention provides a visual security image encryption method based on half-tensor product compressed sensing and DWT-HD-SVD embedding, which generates a visual security image with higher information entropy, making it difficult to obtain relevant information of the original image.

[0004] The technical solution adopted by the present invention to solve the technical problem is: a visual security image encryption method based on half tensor product compressed sensing and DWT-HD-SVD embedding, comprising the following steps:

[0005] Generate the parameters and initial values ​​of the two-dimensional chaotic system mapping according to the plaintext image information;

[0006] Generate a measurement matrix according to the chaotic system, and optimize the measurement matrix using singular value decomposition and column vector normalization;

[0007] Perform wavelet decomposition on the plaintext image to obtain a sparse image, and perform bidirectional cross zigzag scrambling on the sparse image to obtain an encrypted image;

[0008] Use the optimized measurement matrix to perform compression measurement on the encrypted image to obtain a compressed image;

[0009] HD decomposition and SVD decomposition are performed on the carrier image and the compressed image at the same time, and the compressed image is embedded in the carrier image to obtain the final cipher image.

[0010] Furthermore, the parameters and initial values ​​of the two-dimensional chaotic system mapping are generated according to the plaintext image information, specifically: calculating the row sum S1, column sum S2 and diagonal sum S3 of the plaintext image matrix pixels, using hash functions 'MD2', 'MD5', 'SHA384', 'SHA512' for the row sum S1, column sum S2, diagonal sum S3 and a 256-bit external key K respectively, and using the 'SHA256' hash function again for the obtained result to generate a 256-bit sequence H;

[0011] H=SHA256(MD2(S1), MD5(S2), SHA384(S3), SHA512(K))

[0012] Divide the sequence H into 32 blocks, H = {h1, h2, ..., h32}, use the external key K and the sequence H to perform XOR to generate K',

[0013] K′={k′1,k′2,…k′ 32 )

[0014]

[0015] XOR the first 16 bits of K' to get key1, and XOR the last 16 bits to get key2. Use key1 and key2 as the initial values ​​of the chaotic system.

[0016]

[0017] Furthermore, a measurement matrix is ​​generated according to the chaotic system, specifically: the chaotic system parameter a=0.98, key1, key2 iterative mapping len+1000 times, then the first 1000 sequences are discarded to eliminate the transient effect of the chaotic mapping, and a chaotic sequence X with a length of len is obtained; X is then rewritten into a 256*256 matrix Φ, and then the matrix Φ is tensor-producted with a unit matrix of dimension 2 to expand it into a 512*512 measurement matrix M;

[0018]

[0019] Furthermore, the measurement matrix is ​​optimized using singular value decomposition and column vector unitization, specifically: SVD decomposition is performed on the measurement matrix M to obtain the diagonal elements ∑1 in the decomposed diagonal matrix ∑, the average value mean of the elements in ∑1 is taken, mean is assigned to the diagonal elements of ∑ to generate ∑′, SVD decomposition is performed on ∑′ to obtain the matrix M′, and M′ is unitized into a column vector to obtain the optimized measurement matrix M″, thereby further improving the independence of the column vectors.

[0020] Furthermore, the plaintext image is subjected to wavelet decomposition to obtain a sparse image, and the sparse image is subjected to bidirectional cross scrambling to obtain an encrypted image. Specifically, the plaintext image P is subjected to DWT sparseness, and then the obtained sparse matrix is ​​subjected to threshold processing, and the elements below the threshold TS are rewritten as 0 to obtain a matrix p', and the matrix p' is divided into blocks with a block size of 32*32. Two scrambling types are selected for the block matrix and bidirectional cross zigzag scrambling is performed, and then the overall matrix p' is scrambled again to obtain an encrypted image p". Use M" to perform compression measurement and quantization on p" to obtain a compressed image.

[0021] Furthermore, the bidirectional cross zigzag scrambling is specifically as follows: assuming that the matrix dimension is 2n*2n, the matrix is ​​divided into two parts along the diagonal line, and the two parts are scrambled in a forward and reverse zigzag manner respectively, and then the two parts are arranged in a cross combination method to generate a scrambled matrix. The matrix can also use the upper right corner and the lower left corner as the starting point for input and output, that is, the matrix is ​​divided into two parts along the anti-diagonal line, so 8 scrambling methods can be obtained in the end. The sparse image is divided into blocks, and each block is scrambled by a different scrambling method.

[0022] Furthermore, the carrier image is subjected to DWT thinning and then HD and SVD decompositions are performed in sequence. At the same time, the compressed secret image is subjected to HD and SVD decompositions, and the secret image is embedded in the carrier image. In this way, the final visually meaningful cipher image is obtained: an inverse transform is performed to obtain a visually secure cipher image C embedded with the secret image.

[0023] The beneficial effects of the present invention include: the visual security image obtained by the present invention has higher information entropy than the visual security image generated by the existing scheme, and it is difficult to obtain relevant information of the original image. At the same time, it has good plaintext sensitivity and key sensitivity and can resist various attacks. The decrypted image obtained by the present invention has higher quality and higher robustness than the decrypted image generated by the existing scheme, and can obtain better visual effects and more complete original image information.

[0024] Compared with the existing methods, the present invention has the following advantages:

[0025] 1. Perform semi-tensor product expansion on the low-dimensional measurement matrix generated by the two-dimensional chaotic system to obtain the measurement matrix, and perform singular value decomposition and column vector unit optimization on the obtained measurement matrix to obtain the optimized measurement matrix. This process not only reduces the memory burden, but also the optimized measurement matrix recovery effect is about 2db higher than the unoptimized process;

[0026] 2. The proposed DWT-HD-SVD embedding method performs HD decomposition and SVD decomposition on the carrier image and the cipher image at the same time, so that the cipher image embedded in the carrier image has higher visual security and robustness;

[0027] 3. An improved bidirectional cross zigzag scrambling is proposed, which can overcome some defects of traditional zigzag scrambling, such as the scrambling degree is not high enough and the first two elements and the last two elements of the sequence are always the same. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of a bidirectional cross zigzag scrambling method;

[0029] Figure 2 This is the overall encryption framework diagram;

[0030] Figure 3 To decrypt the framework diagram;

[0031] Figure 4 This is the encryption and decryption result graph;

[0032] Figure 5 PSNR and MSSIM values ​​of simulation results;

[0033] Figure 6 This is a comparison analysis diagram of the histogram before and after the carrier image;

[0034] Figure 7 is the NPCR of the decrypted image obtained using the correct key K and the incorrect key K1 K2;

[0035] Figure 8 It is the correlation coefficient graph of adjacent pixels of the ciphertext image;

[0036] Fig. 9 It is the plaintext correlation analysis diagram of the image;

[0037] Fig.10 This is a diagram showing the robustness of images under attack;

[0038] Fig.11 This is a comparison chart of PSNR values ​​before and after measurement matrix optimization. DETAILED DESCRIPTION

[0039] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0041] This paper proposes a visually secure image encryption method based on improved half-tensor product compressed sensing, bidirectional cross zigzag scrambling, and DWT-HD-SVD embedding. It mainly includes four parts. First, multiple hash algorithms are used to encrypt the original image and generate the parameters of the chaotic system to achieve the plaintext correlation sensitivity of the encrypted image; second, the original image is sparsed using DWT, and then the sparse image is scrambled using the improved bidirectional cross zigzag scrambling method; then, the measurement matrix in compressed sensing is optimized using SVD and column vector normalization to improve its reconstruction effect, and the image is compressed to obtain a secret image; finally, the secret image is embedded in an image with visual significance using the DWT-HD-SVD embedding method to obtain a visually secure cipher image. Simulation results and security analysis prove the effectiveness and security of the proposed algorithm.

[0042] Example 1

[0043] The chaotic map used in this embodiment is an improved two-dimensional Logistic chaotic map:

[0044]

[0045] The improved bidirectional cross zigzag pixel scrambling method used in this embodiment is:

[0046] Assume the matrix dimension is 2n*2n, divide the matrix into two parts along the diagonal, perform forward and reverse zigzag scrambling on the two parts, and then arrange the pixels in the two parts in a cross combination method to generate the scrambled matrix. The matrix can also use the upper right corner and the lower left corner as the starting point for input and output, that is, divide the matrix into two parts along the anti-diagonal line, so 8 scrambling methods can be obtained in the end.

[0047] The image to be encrypted is subjected to DWT sparse processing, and the sparse image is subjected to bidirectional cross zigzag scrambling. The measurement matrix generated by the improved two-dimensional Logistic chaotic system is optimized by SVD decomposition and column vector unitization. Then, the scrambled image is compressed and measured to obtain a compressed image. The compressed image is subjected to HD and SVD decomposition. At the same time, the carrier image is subjected to DWT-HD-SVD decomposition to embed the compressed image into the carrier image. The decryption process is the inverse process of the encryption process.

[0048] In this example, the external key Secretkey is set to:

[0049] 7f4e9f6847484a87826d30a76b6522479b3e6128df984ad0c91b1711c52176c1, TS=25, CR=0.25, alpha=0.05, reconstruction algorithm is SL0, sampling rate is set to 0.25. The chaotic map used is as described above.

[0050] Step 1: Calculate the row sum S1, column sum S2 and diagonal sum S3 of the original image matrix pixels, and use the hash functions 'MD2', 'MD5', 'SHA384', 'SHA512' for the row sum S1, column sum S2, diagonal sum S3 and the 256-bit external key K. Use the 'SHA256' hash function again for the above results to generate a 256-bit sequence H.

[0051] H=SHA256(MD2(S1), MD5(S2), SHA384(S3), SHA512(K))

[0052] Divide the hash value H into 32 blocks, H = {h1, h2, ..., h32}, and use the external key K and sequence H to perform XOR to generate K'.

[0053] K′={k′1,k′2,…k′ 32 )

[0054] XOR the first 16 bits of K' to get key1, and XOR the last 16 bits to get key2. Use key1 and key2 as the initial values ​​of the chaotic system.

[0055]

[0056]

[0057] Step 2: Perform DWT sparsification on the original image P, then perform threshold processing on the sparse matrix, rewrite the elements below the threshold TS to 0 to obtain p', divide the matrix after threshold processing into blocks with a block size of 32*32, select two scrambling types for the block matrix and perform bidirectional cross zigzag scrambling, and then scramble the entire matrix again to obtain p".

[0058] Step 3: Set the chaotic system parameter a=0.98, key1, key2 iterative mapping len+1000 times, then discard the first 1000 sequences to eliminate the transient effect of chaotic mapping, and obtain a chaotic sequence X with a length of len; then rewrite X into a 256*256 matrix Φ, and then perform a tensor product operation on the matrix Φ and the unit matrix with a dimension of 2 to expand it to a 512*512 measurement matrix M;

[0059]

[0060] Step 4: Perform SVD decomposition on the measurement matrix M to obtain the diagonal elements ∑1 in the decomposed diagonal matrix ∑, take the average value mean of the elements in ∑1, assign mean to the diagonal elements of ∑ to generate Σ′, and then perform SVD decomposition on Σ′ to obtain the matrix M'. The significance of this step is to improve the value of the minimum singular value to enhance the column independence of the measurement matrix;

[0061] M=UΣV T

[0062] Σ1=diag(δ1, δ2,...δr)δ1≥δ2≥...≥δ r >0

[0063] M′=U∑'V T

[0064] Among them, U, V T represents an orthogonal matrix.

[0065] Step 5: Normalize M' by column vector to obtain the optimized measurement matrix M", and further improve the independence of column vectors. Use M" to perform compression measurement quantization on p" to obtain the compressed image P".

[0066] Step 6: Perform HD-SVD decomposition on P″ to obtain Sw:

[0067] [P, H] = hess(P″)

[0068] [U W ,s W , V W ]=sVD(H)

[0069] Step 7: Perform DWT decomposition on the carrier image to obtain the LH part, and perform HD-SVD decomposition on the LH part to obtain HSw:

[0070] [LL,LH,HL,HH]=DWT(hostlmg)

[0071] [P, H] = hess (LH)

[0072] [HU W , Hs W , H.V. W ]=SVD(H)

[0073] Step 8: Embed Sw into HSw with an embedding strength of α.

[0074] HS′ W =HS W +αS W

[0075] In the above steps 6-8, P″ is the compressed cipher image, hostImg is the host image, Sw is the diagonal matrix after SVD decomposition of the encrypted image; Uw and Vw are orthogonal matrices; LL, LH, HL, and HH respectively represent the four parts of the host image after wavelet transformation; HUw, HSw, and HVw respectively represent the three matrices obtained after SVD decomposition of the LH part of the host image; HS′ W Represents the matrix after embedding the encrypted image.

[0076] Step 9: Perform inverse transformation to obtain a visually secure cipher image C embedded with the secret image;

[0077] H′=HU W HS′ W HV W

[0078] LH′=PH′P′

[0079] C=IDWT(LL, LH′, HL, HH);

[0080] IDWT refers to Inverse Discrete Wavelet Transform.

[0081] The present embodiment provides a visual security image encryption algorithm based on improved half-tensor product compressed sensing and DWT-HD-SVD embedding, which can achieve both image data security and appearance security. Simulation results show that the algorithm has high key sensitivity and can effectively resist brute force attacks. Adjacent pixel correlation and histogram analysis show that the algorithm has good security. In addition, the algorithm can also effectively resist chosen plaintext attacks and known plaintext attacks, noise attacks and data clipping attacks, and has good robustness. The present invention is simulated in MATLAB 2015a, and the operating environment is Win7Intel(R)CPU2.3GHz, ARM4.0GB, through Figure 5-10 The experimental results show that the encryption and decryption effects obtained in this example are better than those of other schemes.

[0082] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. A visually secure image encryption method based on semi-tensor product compressed sensing and DWT-HD-SVD embedding, characterized in that: The steps include: Generate the parameters and initial values ​​of the two-dimensional chaotic system mapping according to the plaintext image information; Generate a measurement matrix according to the chaotic system, and optimize the measurement matrix using singular value decomposition and column vector normalization; Perform wavelet decomposition on the plaintext image to obtain a sparse image, and perform bidirectional cross zigzag scrambling on the sparse image to obtain an encrypted image; Use the optimized measurement matrix to perform compression measurement on the encrypted image to obtain a compressed image; Perform HD decomposition and SVD decomposition on the carrier image and the compressed image at the same time, embed the compressed image into the carrier image to obtain the final cipher image; The method of generating parameters and initial values ​​of a two-dimensional chaotic system mapping according to plaintext image information is specifically as follows: calculating the row sum S1, column sum S2 and diagonal sum S3 of the plaintext image matrix pixels, using hash functions 'MD2', 'MD5', 'SHA384' and 'SHA512' for the row sum S1, column sum S2, diagonal sum S3 and a 256-bit external key K respectively, and using the 'SHA256' hash function again for the obtained result to generate a 256-bit sequence H; dividing the sequence H into 32 blocks, using the external key K and the sequence H to perform XOR to generate K', performing XOR on the first 16 bits of K' to obtain key1, performing XOR on the last 16 bits to obtain key2, and using key1 and key2 as initial values ​​of the chaotic system; The method of generating a measurement matrix according to a chaotic system is as follows: setting the chaotic system parameter a=0.98, iteratively mapping key1 and key2 for len+1000 times, and then discarding the first 1000 sequences to obtain a chaotic sequence X with a length of len; rewriting X into a 256*256 matrix Φ, and then performing a tensor product operation on the matrix Φ and a unit matrix with a dimension of 2 to expand it into a 512*512 measurement matrix M; The method of optimizing the measurement matrix by using singular value decomposition and column vector normalization is as follows: performing SVD decomposition on the measurement matrix M to obtain the diagonal elements ∑1 in the decomposed diagonal matrix ∑, taking the average value mean of the elements in ∑1, assigning mean to the diagonal elements of ∑ to generate ∑′, performing SVD decomposition on Σ′ to obtain the matrix M′, and performing column vector normalization on M′ to obtain the optimized measurement matrix M″; The method of performing wavelet decomposition on the plaintext image to obtain a sparse image, and performing bidirectional cross zigzag scrambling on the sparse image to obtain an encrypted image, specifically: performing DWT sparseness on the plaintext image P, and then performing threshold processing on the obtained sparse matrix, rewriting the elements below the threshold TS to 0 to obtain a matrix p', dividing the matrix p' into blocks, selecting two scrambling types for the block matrices and performing bidirectional cross zigzag scrambling, and then scrambling the overall matrix p' again to obtain an encrypted image p"; The bidirectional cross zigzag scrambling is specifically as follows: assuming that the matrix dimension is 2n*2n, the matrix is ​​divided into two parts, an upper part and an lower part, along a diagonal line, and the two parts are scrambled in a forward and reverse zigzag manner respectively, and then the two parts are arranged in a cross combination method to generate a scrambled matrix.

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