Method of Chebyshev Toeplitz Chaotic Sensing Matrix for CSE

Abstract

The present invention provides a method for a Chebyshev Toeplitz chaotic sensing matrix for CSE, characterized in that it includes an encryption process and a decryption process; the encryption process includes: image sparse representation, Arnold scrambling operator, compressed sensing operator, bilateral diffusion operator and chaotic scrambling operator; the decryption process is the reverse operation of the encryption process; that is, the encryption process and the decryption process are inversely proportional; the image encryption performed by the present invention through compressed sensing can not only protect information security, but also greatly reduce memory and calculation complexity, and is easy to implement on hardware, the Toeplitz matrix is ​​used to compress and sample the perturbed image to reduce the transmission bandwidth and data volume, and finally, the bilateral diffusion operator and the chaotic encryption operator are used to disturb and expand the image pixels, the pixel position and pixel value of the compressed image are changed, and the encrypted image is finally obtained; the algorithm not only improves the image transmission efficiency, but also introduces higher security, and is suitable for popularization and application.

Description

Technical Field

[0001] The invention belongs to the technical field of plaintext image processing, in particular to a method for a Chebyshev Toeplitz chaotic sensing matrix of a CSE. Background Art

[0002] At present, with the rapid development of computer technology and multimedia technology, a large part of the information transmitted and stored in the network is disseminated and stored in the form of digital images. These digital images are related to all aspects of people's lives, from food, clothing, housing and transportation to national security. The image content is likely to involve personal privacy, commercial secrets, national defense security and other fields, which requires that the images can be transmitted and stored safely and effectively. How to ensure the security and reliability of digital images has become a hot topic.

[0003] In recent years, people have used cryptography to effectively protect image information. However, due to the rapid development of cryptanalysis and cracking technologies, some previously secure encryption algorithms, such as DES and AES, have been cracked. The development of cryptanalysis and cracking technologies requires new technologies to improve the security of encryption algorithms to adapt to the needs of the information security era, and therefore poses severe challenges to cryptography.

[0004] Scholars have conducted in-depth research on image encryption schemes based on chaotic systems. However, with the improvement of cryptanalysis and cracking technology, the use of chaos-based image encryption methods alone is no longer sufficient to resist some special attacks. Therefore, it is necessary to introduce new encryption technologies combined with chaotic systems to improve the security and reliability of image encryption schemes.

[0005] In recent years, compressed sensing (CS) has gained people's attention, and algorithms that apply CS to the field of image encryption have also appeared one after another. An optical image encryption scheme based on CS and Arnold transform has been proposed, which uses CS to encrypt and compress plaintext images, and uses Arnold transform to scramble the compressed encrypted images. In order to make it more secure, double random phase encoding is applied to obtain ciphertext images, which makes the encrypted images more secure and the data volume is greatly reduced, but the algorithm is independent of the plaintext image. Someone proposed a two-dimensional CS image encryption method, which simultaneously realizes the compression and encryption of images from two directions, greatly reducing the amount of ciphertext data.

[0006] In summary, the existing image encryption algorithms have achieved good performance in the field of information security, but there are still the following problems:

[0007] ① Currently, many encryption schemes use 1D chaotic mapping to encrypt images. Although it has a simple structure and is easy to implement, its algorithm security level is low;

[0008] ② Many encryption schemes are irrelevant to plaintext images, which makes the scheme unable to resist chosen plaintext attacks and reduces the security of the scheme;

[0009] ③ Most image encryption algorithms based on compressed sensing use chaotic systems to construct random observation matrices. In order to improve the quality of compression and reconstruction, some algorithms also perform sparse transformations on the images. However, this does not break through the limitations of sampling rate and sparsity in compressed sensing. In addition, the use of random observation matrices that are independent of image features makes it impossible to dynamically adapt to image features during image compression, resulting in the loss of key information.

[0010] ④ The traditional reconstruction algorithm has poor reconstruction efficiency and quality. Some algorithms have defects in the scrambled diffusion encryption used after compression encryption.

[0011] ⑤Some image encryption algorithms based on hyperchaos have emerged one after another. In , a hyperchaotic image encryption scheme using pixel-level scrambling and bit-level scrambling was proposed. This scheme uses a five-dimensional multi-wing hyperchaotic system to generate the key stream of the scrambling and diffusion process, and then performs pixel-level scrambling and bit-level scrambling operations on the image, and then diffuses the scrambled image to obtain the ciphertext image. Although the encryption scheme based on the hyperchaotic system has excellent encryption performance, its hardware implementation is relatively difficult.

[0012] ⑥ A chaotic color image encryption method based on DNA coding, which first divides the plaintext image into three components: R, G, and B. Then, the pixels of the three components are expanded bit by bit and DNA-encoded. Then, DNA addition is performed on the encoded DNA matrix, and the result is decoded. Finally, the three encrypted components are obtained by XOR operation with the sequence generated by the Logistic system and combined into the final ciphertext image. However, the algorithm uses fixed encoding and decoding rules to operate the pixels of the plaintext image, resulting in low security of the algorithm.

[0013] ⑦ An optical image encryption scheme based on CS and Arnold transform was proposed. They used CS to encrypt and compress the plaintext image, and used Arnold transform to scramble and compress the encrypted image. In order to make it more secure, double random phase encoding was applied to obtain the ciphertext image, which made the encrypted image more secure and the amount of data was greatly reduced, but the algorithm was independent of the plaintext image.

[0014] ⑧ Image scrambling method based on elementary cellular automata (ECA). In this article, ECA is used to scramble the image. This scheme has excellent scrambling performance and reduces the algorithm's ability to resist chosen plaintext attacks, but the key of this method is independent of the plaintext. Summary of the invention

[0015] In order to solve the above technical problems, the present invention provides a method of Chebyshev Toeplitz chaotic sensing matrix for CSE (compressed sensing encryption), uses sparse transformation to perform sparse processing on the plaintext image, and then uses cat face transformation (Arnold) to perturb the image pixels; uses chaos and compressed sensing technology to build an efficient transmission and encryption and decryption security environment, establishes a new digital image encryption algorithm research, solves the problems of low security and insufficient efficient transmission of image encryption in the prior art, and greatly improves the overall level of image encryption.

[0016] A method of Chebyshev Toeplitz chaotic sensor matrix for CSE, including encryption process and decryption process;

[0017] The encryption process includes: image sparse representation, cat face transformation (Arnold) scrambling operator, compressed sensing (CS) operator, bilateral diffusion operator and chaos scrambling operator;

[0018] The decryption process is the reverse operation of the encryption process; that is, the encryption process and the decryption process are inversely proportional;

[0019] Furthermore, the compressed sensing (CS) operator, the bilateral diffusion operator and the chaotic scrambling operator are based on the Chebyshev chaotic sequence generated by formula 1;

[0020] The μ-Chebyshev chaotic system is defined as:

[0021] z (i+1) =τ(z i )=cos(μ·arccos(z i )) Formula 1;

[0022] Where: z i =τ i (z0)(i∈N),z0 is a seed, and -1≤z0≤1,1<μ∈N + ;

[0023] Through iteration, a set of Chebyshev chaotic sequences is obtained

[0024] Said It has the following characteristics: mean Ε(z) = 0, variance δ 2 (z) = 0.5;

[0025] Let d∈N + express The sampling step size is , then the Chebyshev chaotic sequence The matrix z ini and the (i+d)th matrix z (i+d) Can be nearly independent;

[0026] Mathematically, let x∈R n represents the signal of interest; as prior information, x is usually k-sparse or compressible in the transform domain, that is, x = Bc, where B∈R n×n is an orthonormal basis or a frame, c∈R n is the corresponding k-sparse vector;

[0027] Let A∈R m×n (m<<n) and τ=(m / n) are the sensing matrix and measurement rate respectively; then, CS can be modeled as:

[0028] Let x be an image of size n×n; use the plaintext image x as a parameter to generate a key, and then use the secure hash algorithm SHA-256 to generate four sets of keys;

[0029] Furthermore, the encryption process includes:

[0030] Step 1: Image sparse representation: Use discrete wavelet transform (DWT) sparse basis B∈R n×n Sparse the original image and obtain the corresponding sparse coefficient matrix C∈R n×n ,

[0031] B -1 x=C,Formula 2;

[0032] As an example, the sparse basis B is one of Fourier transform or discrete cosine domain.

[0033] As an example, the sparse coefficients of the original image include: many zeros and a few large coefficients; therefore, the sparse representation of the image can greatly reduce the complexity of image processing;

[0034] As an example, the sparsification defined by Equation 2 is reversible.

[0035] Step 2: Arnold scrambling operator:

[0036] The sparse coefficient matrix C is subjected to the Arnold scrambling operator F. as , get the scrambled coefficient matrix;

[0037] The Arnold scrambling operator can be modeled as:

[0038] D=F as (C), Formula 3;

[0039] Where: D∈R n×n is the scrambling coefficient matrix;

[0040] As an example, Arnold scrambling, or cat face transformation, is used to evenly distribute the energy of an image and is particularly suitable for digital watermarking.

[0041] For the original image of order P, define the two-dimensional Arnold transform F as for:

[0042]

[0043] Where: (r, t) and (r', t') are the pixel positions of C and D respectively, r, t∈{0,1,2,…,P-1};

[0044] The Arnold scrambling operator can make the high-frequency information of C evenly distributed in the D space; experimental results show that the Arnold scrambling operator can reduce the block effect and obtain a better image CS effect;

[0045] Step 3: Compressed Sensing (CS) Operator:

[0046] Using the CS operator μ (1) , bilateral diffusion operator d (1) , Chaos Scrambling Operator And the generated sequence T1, construct a perception matrix CTsM,A∈R m×n ; Then use CTsM to sample and compress the scrambled coefficient matrix, which can be formalized as:

[0047] y=AD, formula 5;

[0048] Where: y∈R m×n , represents the measured value; the measurement rate is τ=(m / n);

[0049] Since the data dimension can be obtained from R n×n Reduce to R m×n ,Therefore, the proposed CSE scheme can achieve fairly good compression performance;

[0050] Where: m is the number of rows of the perception matrix, n is the number of columns of the perception matrix;

[0051] Step 4: Bilateral diffusion operator:

[0052] The bilateral diffusion operator includes: positive diffusion function F fd and the anti-diffusion function F cd , which are based on modular addition operations;

[0053] First, y∈R m×n Straighten it into a vector y' of size 1×mn;

[0054] Then, use F fd and F cd Acts on vector y';

[0055] The positive diffusion function F fd Modeled as: w = F fd (y′) Formula 6;

[0056] Specifically, for an element w in w j ,have

[0057]

[0058] in: represents the jth Chebyshev chaotic sequence generated th elements, j∈{1,2,3,…,mn}.

[0059] Furthermore, with F fd Similarly, the inverse diffusion function F cd for:

[0060] q=F cd (w) Formula 8;

[0061] Where: q is F fd Output:

[0062] Specifically, for an element q in q j ,have

[0063]

[0064] After the bilateral diffusion operator, it is difficult to obtain the information of the original image through the ciphertext image q, which can introduce high security;

[0065] Step 5: Chaos scrambling operator:

[0066] Using the chaotic scrambling operator F cs Scramble the ciphertext image q, defined as:

[0067] y s =F cs (q) = sort (Corr {vect (q), T3), Formula 10;

[0068] Where: y s is the final ciphertext image, sort(·) and vect(·) represent sorting and vectorization operations respectively, and the Corr(·) function is used to establish a one-to-one correspondence between q and the chaotic sequence T3.

[0069] Furthermore, the decryption process includes:

[0070] The reverse process of the encryption process.

[0071] Beneficial effects of the present invention:

[0072] The image encryption performed by the present invention through compressed sensing can not only protect information security, but also reduce the bandwidth and data volume of image transmission in the network, while also greatly reducing memory and calculation complexity, and is easy to implement on hardware.

[0073] The present invention proposes a Chebyshev Toeplitz chaotic sensing matrix for CSE, and uses the Toeplitz matrix to compress and sample the perturbation image to reduce the transmission bandwidth and data volume. Finally, the bilateral diffusion operator and the chaotic encryption operator are used to perturb and expand the image pixels, and the pixel position and pixel value of the compressed image are changed to finally obtain the encrypted image. The algorithm not only improves the image transmission efficiency, but also introduces higher security.

[0074] The proposed CSE not only improves the efficiency of image transmission, but also introduces the high security of chaotic systems. The designed CSE can not only avoid the traditional 1D chaotic mapping to achieve image encryption, but also avoid the shortcomings of some hyperchaotic image encryption algorithms that are relatively difficult to implement in hardware; multiple tests have proved the good encryption compression performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 The theoretical logic method framework diagram of the method of using the Chebyshev Toeplitz chaotic sensing matrix for CSE in the present invention.

[0076] Figure 2 The figure is a schematic diagram of the implementation effect of the method of the present invention for the Chebyshev Toeplitz chaotic sensing matrix of CSE. DETAILED DESCRIPTION

[0077] Below, reference Figure 1 to Figure 2 As shown in FIG. 1 , a method of a Chebyshev Toeplitz chaotic sensing matrix for CSE includes an encryption process and a decryption process;

[0078] The encryption process includes: image sparse representation, Arnold scrambling operator, compressed sensing (CS) operator, bilateral diffusion operator and chaotic scrambling operator;

[0079] The decryption process is the reverse operation of the encryption process; that is, the encryption process and the decryption process are inversely proportional;

[0080] Furthermore, the compressed sensing (CS) operator, the bilateral diffusion operator and the chaotic scrambling operator are based on the Chebyshev chaotic sequence generated by formula 1;

[0081] The μ-Chebyshev chaotic system is defined as:

[0082] z (i+1) =τ(z i )=cos(μ·arccos(z i )) Formula 1;

[0083] Where: z i =τ i (z0)(i∈N),z0 is a seed, and -1≤z0≤1,1<μ∈N + ;

[0084] Through iteration, a set of Chebyshev chaotic sequences is obtained

[0085] Said It has the following characteristics: mean Ε(z) = 0, variance δ 2 (z) = 0.5;

[0086] Let d∈N + express The sampling step size is , then the Chebyshev chaotic sequence The matrix z in i and the (i+d)th matrix z (i+d) Can be nearly independent;

[0087] Mathematically, let x∈R n represents the signal of interest; as prior information, x is usually k-sparse or compressible in the transform domain, that is, x = Bc, where B∈R n×n is an orthonormal basis or a frame, c∈R n is the corresponding k-sparse vector;

[0088] Let A∈R m×n (m<<n) and τ=(m / n) are the sensing matrix and measurement rate respectively; then, CS can be modeled as:

[0089] Let x be an image of size n×n; use the plaintext image x as a parameter to generate a key, and then use the secure hash algorithm SHA-256 to generate four sets of keys;

[0090] Furthermore, the encryption process includes:

[0091] Step 1: Image sparse representation: Use discrete wavelet transform (DWT) sparse basis B∈R n×n Sparse the original image and obtain the corresponding sparse coefficient matrix C∈R n×n ,

[0092] B-1 x=C,Formula 2;

[0093] As an example, the sparse basis B is one of Fourier transform or discrete cosine domain.

[0094] As an example, the sparse coefficients of the original image include: many zeros and a few large coefficients; therefore, the sparse representation of the image can greatly reduce the complexity of image processing;

[0095] As an example, the sparsification defined by Equation 2 is reversible.

[0096] Step 2: Arnold scrambling operator:

[0097] The sparse coefficient matrix C is subjected to the Arnold scrambling operator F. as , get the scrambled coefficient matrix;

[0098] The Arnold scrambling operator can be modeled as:

[0099] D=F as (C), Formula 3;

[0100] Where: D∈R n×n is the scrambling coefficient matrix;

[0101] As an example, Arnold scrambling, or cat face transformation, is used to evenly distribute the energy of an image and is particularly suitable for digital watermarking.

[0102] For the original image of order P, define the two-dimensional Arnold transform F as for:

[0103]

[0104] Where: (r, t) and (r', t') are the pixel positions of C and D respectively, r, t∈{0,1,2,…,P-1};

[0105] The Arnold scrambling operator can make the high-frequency information of C evenly distributed in the D space; experimental results show that the Arnold scrambling operator can reduce the block effect and obtain a better image CS effect;

[0106] Step 3: Compressed Sensing (CS) Operator:

[0107] Using the CS operator μ (1) , bilateral diffusion operator d (1) , Chaos Scrambling Operator And the generated sequence T1, construct a perception matrix CTsM,A∈R m×n; Then use CTsM to sample and compress the scrambled coefficient matrix, which can be formalized as:

[0108] y=AD, formula 5;

[0109] Where: y∈R m×n , represents the measured value; the measurement rate is τ=(m / n);

[0110] Since the data dimension can be obtained from R n×n Reduce to R m×n ,Therefore, the proposed CSE scheme can achieve fairly good compression performance;

[0111] Where: m is the number of rows of the perception matrix, n is the number of columns of the perception matrix;

[0112] Step 4: Bilateral diffusion operator:

[0113] The bilateral diffusion operator includes: positive diffusion function F fd and the anti-diffusion function F cd , which are based on modular addition operations;

[0114] First, y∈R m×n Straighten it into a vector y' of size 1×mn;

[0115] Then, use F fd and F cd Acts on vector y';

[0116] The positive diffusion function F fd Modeled as: w = F fd (y′) Formula 6;

[0117] Specifically, for an element w in w j ,have

[0118]

[0119] in: represents the jth Chebyshev chaotic sequence generated th elements, j∈{1,2,3,…,mn}.

[0120] Furthermore, with F fd Similarly, the inverse diffusion function F cd for:

[0121] q=F cd (w) Formula 8;

[0122] Where: q is F fd Output:

[0123] Specifically, for an element q in q j ,have

[0124]

[0125] After the bilateral diffusion operator, it is difficult to obtain the information of the original image through the ciphertext image q, which can introduce high security;

[0126] Step 5: Chaos scrambling operator:

[0127] Using the chaotic scrambling operator F cs Scramble the ciphertext image q, defined as:

[0128] y s =F cs (q) = sort (Corr {vect (q), T3), Formula 10;

[0129] Where: y s is the final ciphertext image, sort(·) and vect(·) represent sorting and vectorization operations respectively, and the Corr(·) function is used to establish a one-to-one correspondence between q and the chaotic sequence T3.

[0130] Furthermore, the decryption process includes:

[0131] The reverse process of the encryption process.

[0132] In order to better illustrate the design principle of the present invention, the following specific embodiments are given as examples:

[0133] Embodiment 1:

[0134] The decryption process includes: the encryption and decryption processes are opposite processes, and decryption can be performed according to the reverse process of encryption.

[0135] The present invention can greatly improve the security of the image encryption algorithm and avoid the low security level of the 1D chaotic system while inheriting the advantages of low complexity, simple structure and easy implementation. The present invention can take into account the excellent encryption performance of the hyperchaotic image encryption algorithm and has the characteristic of being easily implemented at the hardware level. The present invention can be superior to the security of the chaotic color image encryption method based on DNA coding. The present invention can avoid the disadvantage that the optical image encryption algorithm based on CS and Arnold transformation is independent of the plaintext image and resist plaintext attacks. The present invention can avoid the disadvantage that the image scrambling method based on elementary cellular automata (ECA) can reduce the ability to resist chosen plaintext attacks, but the key is independent of the plaintext. The CCSE proposed by the present invention not only improves the efficiency of image transmission, but also introduces the high security of the chaotic system. Based on the construction of efficient transmission and secure encryption and decryption based on chaos and compressed sensing technology, a new direction of digital image encryption algorithm is established.

[0136] The above are only preferred embodiments of the present invention. It should be understood that the description of the above embodiments is only used to help understand the method and core ideas of the present invention, and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, etc. made within the ideas and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method of a Chebyshev Toeplitz chaotic sensing matrix for CSE, characterized in that, The invention comprises an encryption process and a decryption process; the encryption process comprises: image sparse representation, Arnold scrambling operator, compressed sensing operator, bilateral diffusion operator and chaotic scrambling operator; the decryption process is the reverse operation of the encryption process; that is, the encryption process and the decryption process are inversely proportional; The encryption process includes: Step 1: Image sparse representation: Use discrete wavelet transform (DWT) sparse basis B∈R n×n Sparse the original image and obtain the corresponding sparse coefficient matrix C∈R n×n , B -1 x=C,Formula 2; Step 2: Arnold scrambling operator: The sparse coefficient matrix C is subjected to the Arnold scrambling operator F. as , and get the scrambling coefficient matrix; the Arnold scrambling operator can be modeled as: D=F as (C), Formula 3; where: D∈R n×n is the scrambling coefficient matrix; For the original image of order P, define the two-dimensional Arnold transform F as for: Where: (r, t) and (r', t') are the pixel positions of C and D respectively, r, t∈{0,1,2,…,P-1}; Step 3: Compressed Sensing (CS) Operator: Using the CS operator μ (1) , bilateral diffusion operator d (1) , Chaos Scrambling Operator And the generated sequence T1, construct a perception matrix CTsM,A∈R m×n ; Then use CTsM to sample and compress the scrambled coefficient matrix, which can be formalized as: y = AD, Formula 5; where: y∈R m×n , represents the measured value; the measurement rate is τ = (m / n); since the data dimension can be obtained from R n×n Reduce to R m ×n , so the proposed CSE scheme can achieve quite good compression performance; where: m is the number of rows of the perception matrix, n is the number of columns of the perception matrix; Step 4: Bilateral diffusion operator: The bilateral diffusion operator includes: positive diffusion function F fd and the anti-diffusion function F cd , which are based on modular addition operations; first, y∈R m×n Straighten it into a vector y' of size 1×mn; then, use F fd and F cd Acts on vector y'; The positive diffusion function F fd Modeled as: w = F fd (y′) Formula 6; Specifically, for an element w in w j ,have in: represents the jth Chebyshev chaotic sequence generated th elements, j∈{1,2,3,…,mn}; and F fd Similarly, the inverse diffusion function F cd for: q=F cd (w) Formula 8; Where: q is F fd Output: Specifically, for an element q in q j ,have After the bilateral diffusion operator, it is difficult to obtain the information of the original image through the ciphertext image q, which can introduce high security; Step 5: Chaos scrambling operator: Using the chaotic scrambling operator F cs Scramble the ciphertext image q, defined as: y s =F cs (q) = sort (Corr {vect (q), T3), Formula 10; Where: y s is the final ciphertext image, sort(·) and vect(·) represent sorting and vectorization operations respectively, and the Corr(·) function is used to establish a one-to-one correspondence between q and the chaotic sequence T3; The decryption process includes: a step flow opposite to the encryption process.

2. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: The compressed sensing (CS) operator, the bilateral diffusion operator and the chaotic scrambling operator are based on the Chebyshev chaotic sequence generated by formula 1; The μ-Chebyshev chaotic system is defined as: z (i+1) = τ(z i ) = cos(μ·arccos(z i )) Equation 1; Where: z i =τ i (z0)(i∈N),z0 is a seed, and -1≤z0≤1,1<μ∈N + ; Through iteration, a set of Chebyshev chaotic sequences is obtained 3. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 2, characterized in that: Said It has the following characteristics: mean Ε(z) = 0, variance δ 2 (z) = 0.5; Let d∈N + express The sampling step size is , then the Chebyshev chaotic sequence The matrix z in i and the (i+d)th matrix z (i+d) Almost independent.

4. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 3, characterized in that: Let x∈R n represents the signal of interest; as prior information, x is usually k-sparse or compressible in the transform domain, that is, x = Bc, where B∈R n×n is an orthonormal basis or a frame, c∈R n is the corresponding k-sparse vector; Let A∈R m×n (m<<n) and τ=(m / n) are the sensing matrix and measurement rate respectively; then, CS can be modeled as: Let x be an image of size n×n; use the plaintext image x as a parameter to generate a key, and then use the secure hash algorithm SHA-256 to generate four sets of keys.

5. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: The sparse basis B is one of Fourier transform or discrete cosine domain.

6. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: The sparse coefficients of the original image include: many 0s and a few large coefficients; the sparse representation of the image can greatly reduce the complexity of image processing.

7. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: The sparsification defined by Formula 2 is reversible.

8. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: Arnold scrambling, also known as cat face transformation, is used to evenly distribute the energy of an image and is particularly suitable for digital watermarking.

9. The method of Chebyshev Toeplitz chaotic sensing matrix for CSE according to claim 1, characterized in that: The Arnold scrambling operator makes the high-frequency information of C evenly distributed in the D space; the Arnold scrambling operator can reduce the block effect and obtain a better image CS effect.

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