CN112711766B

CN112711766B - Image transmission system based on scrambling block compressed sensing, encryption method and decryption method

Info

Publication number: CN112711766B
Application number: CN202110005734.9A
Authority: CN
Inventors: 王兰; 杨兵; 石熙; 韦鹏程; 佘远俊; 张霖; 彭亚飞
Original assignee: Chongqing Ecological Environment Monitoring Center; Chongqing University of Education
Current assignee: Chongqing Ecological Environment Monitoring Center; Chongqing University of Education
Priority date: 2021-01-05
Filing date: 2021-01-05
Publication date: 2022-09-16
Anticipated expiration: 2041-01-05
Also published as: CN112711766A

Abstract

The application provides an image transmission system based on scrambling block compressed sensing, an encryption method and a decryption method, original images are transformed to a frequency domain (a sparse coefficient matrix is obtained) through wavelet transform, and a key k is generated through Logistic-Tent chaotic mapping ₁ And constructing a scrambling matrix to scramble the sparse system matrix to obtain the scrambling matrix, then partitioning the scrambling matrix, and measuring each block. Quantizing the obtained measured value by a quantizer to obtain an integer value; key k is formed by utilizing Logistic-Tent chaotic mapping ₂ Carrying out confusion operation on the whole numerical value to obtain a confusion sequence; generating a key k by utilizing Logistic-Tent chaotic mapping ₃ Performing diffusion operation to obtain a final ciphertext; sending the cipher text to the image receiving equipment, and sending the key k ₁ Key k ₂ And a secret key k ₃ Shared with the image receiving device.

Description

Image transmission system based on scrambling block compressed sensing, encryption method and decryption method

Technical Field

The application relates to the technical field of image processing, in particular to an image transmission system based on scrambling block compressed sensing, and an encryption and decryption method.

Background

With the rapid development of information technology and network technology, the collection, processing, transmission and storage of images are attracting wide attention in many fields such as military security, medical processing and network transmission. In practical application, in order to reduce data transmission amount and ensure data safe transmission, compression and encryption processing are generally required, while most of the existing image encryption schemes are designed to be sensitive encryption, so that the decrypted data quality is low, even when a part of encrypted data is lost, the decrypted data cannot be correctly decrypted, and the compression operation is not considered. Most transmission channels are not safe and are easy to be attacked, and how to safely transmit images and resist the robustness of various attacks becomes an important problem in the field of image processing and information security.

The CS (Compressive Sensing) theory is an emerging research hotspot in the recent international, and the framework thereof has the characteristics of simultaneous compression, sampling and encryption, and can ensure the security of information to a certain extent. There is some preliminary discussion about security of compressed sensing. For example, it is demonstrated in some existing literature that although CS does not meet the perfect security defined by shannon, computational guarantees can be provided for confidentiality; some documents indicate that a compressed sensing symmetric cryptosystem formed by iteratively updating a measurement matrix can achieve perfect security in an information theory sense; the literature also proves that perfect safety can be realized by introducing energy constancy of measured values when a primary random Gaussian matrix is used as a measurement matrix for compressed sensing; alternatively, indistinguishable security can be achieved by updating the measurement matrix with the unitary matrix and the bidirectional keystream. Therefore, compressed sensing is a security that can achieve image transmission.

The CS theory indicates that sampling the signal at a frequency much lower than that determined by the Nyquist-Shannon sampling theorem under certain conditions can still ensure accurate recovery of the original signal, and is just suitable for robust transmission of images in resource-constrained environments. For example, some documents indicate that when the measurement matrix follows a gaussian distribution, the energy of each measurement is approximately equal, i.e., the measurements have a 'democratic' (democracy) property. It is considered that the reconstruction process of compressed sensing has better robustness to noise, making it a "robust encryption" technology for promising multimedia data, and even if additional noise is introduced into the encrypted data, the original signal can be recovered with high fidelity, which is extremely suitable for the reconstruction requirement of partially lost data after the image in the resource-limited or non-peer-to-peer network is transmitted through an insecure channel.

At present, scholars at home and abroad have conducted partial research on image robustness encryption. An image robust encryption algorithm based on compressed sensing is designed in foreign documents, packet loss attack can be resisted, but a measurement matrix is used as a key, so that the transmission quantity is large, and the transmission load is increased; an algorithm for image encryption based on compressed sensing is also proposed in the literature, but the histogram distribution of the algorithm is uneven, the pixel correlation is more remarkable, and the algorithm does not guarantee enough security. And a robust encryption algorithm of a multi-focus image based on compressed sensing, which is proposed for the multi-focus image, has better robustness against attack, but is mainly directed for the multi-focus image, and the application range is limited.

While domestic research mainly uses image robust coding algorithms mostly. Such as: a robust SAR image coding transmission scheme emphasizes coding efficiency, but does not consider the security of image robust transmission; for another example, based on an image encryption algorithm of compressed sensing and real-time dynamic scrambling, the robustness of resisting shearing attack is simply analyzed, but the PSNR value (Peak Signal To Noise Ratio) of a recovered image still needs To be improved; or the robustness of resisting noise is analyzed based on the design of an image encryption scheme of parallel compressed sensing and chaotic mapping.

In summary, most of the existing encryption algorithms based on compressed sensing do not specially aim at the transmission problems of resisting noise attack, shearing attack, statistical attack and plaintext attack selection in an insecure channel, and especially, the research of considering security and robustness of a ciphertext in the transmission process is not considered.

Disclosure of Invention

The embodiment of the application aims to provide an image transmission system based on scrambling block compressed sensing, an encryption method and a decryption method, so as to reduce channel bandwidth and ensure image safe and robust transmission.

In order to achieve the above object, embodiments of the present application are implemented as follows:

in a first aspect, an embodiment of the present application provides an image encryption method based on compressed sensing of a scrambling block, which is applied to an image transmission device, and includes:

transforming the original image wavelet to a frequency domain by using DWT as a sparse basis psi to obtain a sparse coefficient matrix;

obtaining scrambling matrix R and key k by using Logistic-Tent chaotic mapping system ₁ And determining a scrambled image according to the original image and the scrambling matrix R, wherein the secret key k ₁ Is (r) ₁ ，z ₁ )，r ₁ Control parameter for this chaotic mapping, z ₁ The chaos initial value of the chaos mapping is obtained;

dividing the scrambled image into M sizes of

To obtain corresponding M scrambled image blocks P _i (x) And, for each of said scrambled image blocks P _i (x) Performing compressed sensing measurement to obtain each scrambled image block P _i (x) Compressed perceptual measurement y of _i ；

For each of the compressed perceptual measurements y _i Quantizing it to an integer value Z _i ；

Utilizing the Logistic-Tent chaotic mapping system to map the integer value Z _i Performing aliasing operation to obtain an aliased sequence

And a secret key k ₂ ，

The key k ₂ Is (r) ₂ ，z ₂ )，r ₂ Control parameter for this chaotic mapping, z ₂ The chaos initial value of the chaos mapping is obtained;

utilizing the Logistic-Tent chaotic mapping system to map the confusion sequence

Performing diffusion operation to obtain a pseudo-random sequence V and a secret key k ₃ Said secret key k ₃ Is (r) ₃ ，z ₃ )，r ₃ Control parameter for this chaotic mapping, z ₃ The chaos initial value of the chaos mapping is obtained;

carrying out key stream conversion on the pseudorandom sequence V to obtain a key stream sequence K (i), and carrying out key stream conversion on the pseudorandom sequence V according to the key stream sequence K (i) and the confusion sequence

Determining the ciphertext C _i ；

The ciphertext C _i Sending the key k to an image receiving device ₁ The key k ₂ And said key k ₃ Sharing to the image receiving apparatus so that the image receiving apparatus bases on the ciphertext C _i The key k ₁ The key k ₂ And said key k ₃ And reconstructing the original image by combining a preset image decryption method, wherein the image decryption method is the reverse process of the image encryption method.

In the embodiment of the application, the original image is transformed to the frequency domain by using wavelet transform (to obtain a sparse coefficient matrix), and the sparse coefficient matrix is subjected to chaotic mapping by using a Logistic-Tent chaotic mapping system to obtain a scrambling matrix and a key k ₁ (the control parameters and the chaos initial value of the chaos mapping) further determine a scrambled image, then divide the scrambled image to obtain corresponding M scrambled image blocks, and then perform compressed sensing measurement on each scrambled image block. Firstly, the pixels of the whole image are reordered (namely scrambled), the spatial correlation of adjacent pixel blocks can be eliminated, the simultaneous sampling and compression can be realized by utilizing a compressed sensing theory, the data transmission quantity can be reduced, and the efficiency can be improved. The image is firstly subjected to wavelet transformation to a frequency domain, and then the image frequency domain coefficients are scrambled, so that the sparsity of a sampling object tends to be uniform, the RIP performance of compressed sensing can be effectively relaxed, and the improvement of the image reconstruction quality can be facilitated. Therefore, the scrambled block compressed sensing is adopted for measurement, the data transmission quantity can be effectively reduced, the transmission efficiency is guaranteed, and meanwhile the data transmission quantity is used as the first layer of encryption. Then, quantization processing (quantizing into integer value) is carried out on the compressed sensing measured value, and confusion operation is carried out on the integer value by utilizing a Logistic-Tent chaotic mapping system to obtain a confusion sequence and a key k ₂ Namely the control parameters and the chaos initial value of the chaos mapping; and then, carrying out diffusion operation on the confusion sequence by using a Logistic-Tent chaotic mapping system to obtain a pseudorandom sequence and a secret key k ₃ Namely the control parameters and the chaos initial value of the chaos mapping; then, carrying out key stream conversion on the pseudorandom sequence to obtain a key stream sequence, and determining a ciphertext according to the key stream sequence and the confusion sequence; sending the ciphertext to an image receiving device, and sending a secret key k ₁ Key k ₂ And a secret key k ₃ Shared with the image receiving device. The Logistic-Tent mapping is utilized to encrypt the quantization value by adopting a confusion-diffusion mechanism, the chaotic range of mapping is wider, the chaotic performance of mapping is better, the security of data transmission can be ensured by constructing a key stream, and statistical attack is resisted, so that the security is further ensured. Through the analysis in various aspects such as the spatial comparison of the compressed and encrypted images and the reconstructed images under different sampling rates, the analysis of the relation between the sampling rate and the packet loss rate, the comparison of compression performance, the analysis of key space, the analysis of pixel correlation, the analysis of robustness for resisting packet loss, shearing and noise attack, the comprehensive comparison analysis and the like, the scheme proves that the image is subjected to the analysis in various aspects such asSecurity, effectiveness and robustness of transmission over an unsecured channel after encryption. The decryption reconstruction process is realized by utilizing an inverse process, comprises inverse quantization and inverse confusion-diffusion operation, and can adopt a GRSR reconstruction algorithm to obtain high-performance reconstruction of an image and ensure transmission robustness. Experimental simulation results and comparative analysis show that the PSNR value of a reconstructed image of an original image is 20.4dB at a sampling rate of 0.05; the PSNR value of the reconstructed image also reaches 22.24dB under the packet loss rate of 90 percent; the reconstructed image still retains the main information and is visually acceptable under a 256 × 256 cropping attack. Therefore, the scheme has high compression performance, can resist common attacks such as brute force attack, statistical attack, packet loss attack, shearing attack, noise attack and the like, has high robustness, and has wide applicability to practical application scenes under various resource-limited conditions. The data acquisition, the effective transmission and the reduction of the calculation load are realized, and the safe and robust transmission of the image can also be realized.

With reference to the first aspect, in a first possible implementation manner of the first aspect, the chaotic mapping is performed on the sparse coefficient matrix by using a Logistic-Tent chaotic mapping system to obtain a scrambling matrix R and a key k ₁ The method comprises the following steps:

generating a pseudo-random sequence p1 by using the Logistic-Tent chaotic mapping system, and carrying out the chaotic mapping of the time on a control parameter r ₁ And chaos initial value z ₁ As a key k ₁ ＝(r ₁ ，z ₁ )；

For the pseudo-random sequence p ₁ Iterating h + MxN times, and discarding the previous h values;

setting a value of each element of the N × N matrix to zero;

for the pseudo-random sequence p ₁ Sorting in ascending order, and sorting R (p) ₂ (m), m) is set to 1 to obtain a reordered sequence p ₂ The scrambling matrix R is thus obtained, where m ∈ {1, 2, … N }.

With reference to the first aspect, in a second possible implementation manner of the first aspect, the scrambling image block P is a block of a block _i (x) Performing compressed sensing measurement to obtain each scrambled mapImage block P _i (x) Compressed perceptual measurement y of _i The method comprises the following steps:

for each of said scrambled image blocks P _i (x) And independently measuring through a measurement matrix to obtain each scrambled image block P _i (x) The compressed perceptual measurement value yi of (a), the measurement matrix is:

y _i ＝φP _i (x)φ ^T ，

wherein, the first and the second end of the pipe are connected with each other,

representing the scrambled image block P _i (x) Compressed perceptual measurement of; p _i (x)＝vec(x)×R；

Representing scrambled image blocks P _i (x) By selecting the Hadamard matrix

Front of a Hadamard matrix of size

Obtaining a row;

or, the measurement matrix is:

wherein the content of the first and second substances,

is a Kronecker product operator; vec (y) _i ) Denotes y _i Line order vectorization of, vec (P) _i (x) ) represents P _i (x) Vectorizing the line order of (c);

or, the measurement matrix is:

or, the measurement matrix is:

in this implementation, the measurement matrix in the compressed sensing measurement of the scrambled image block may be represented as a structural random matrix, which is almost irrelevant to all other orthogonal matrices and theoretically has exactly the same sensing characteristics as the random observation matrix.

With reference to the first aspect, in a third possible implementation manner of the first aspect, the compression perception measurement value y is obtained by applying a compression perception measurement value to each of the compressed perception measurement values y _i Quantizing it to an integer value Z _i The method comprises the following steps:

for each of the compressed perceptual measurements y _i Quantizing the data by a preset quantization formula to obtain a corresponding integer value Z _i The preset quantization formula is as follows:

Z _i ＝round(δ _i-1 +y _i )，

wherein Z is _i Representing the compressed perceptual measurement y _i Quantized integer value, δ representing the compressed perceptual measurement y _i Error residual value of (2), initial residual value delta ₀ Round (a) denotes returning the integer value closest to a.

In this implementation, the compressed sensing measurement is quantized in such a way that it can fit into the distribution of most of the measurements, and the error residual of the previous measurement is added to the quantization of the next measurement with a diffusion effect.

With reference to the first aspect, in a fourth possible implementation manner of the first aspect, the using the Logistic-Tent hybridChaotic mapping system for said integer value Z _i Performing aliasing operation to obtain an aliased sequence

And a secret key k ₂ The method comprises the following steps:

utilizing the Logistic-Tent chaotic mapping system to carry out the control parameter r of the chaotic mapping ₂ And chaos initial value z ₂ As a key k ₂ ＝(r ₂ ，z ₂ )；

For the integer value Z _i Iteration n ₀ + MXN times, discarding the first N ₀ Values to generate a sequence

The sequence b ═ b (n) ₀ +1)，b(n ₀ +2)，…，b(n ₀ +M×N)]Obtaining new sequences in ascending order

Searching

In the sequence of

Form an index sequence by the corresponding index values

For the index sequence

By transforming in the following way:

wherein z is _i ＝vec(Z _i ) Is denoted by Z _i Is denoted as z _i ；

To pair

Obtaining the confusion sequence after recombination

With reference to the first aspect, in a fifth possible implementation manner of the first aspect, the confusion sequence is mapped by using the Logistic-Tent chaotic mapping system

Performing diffusion operation to obtain a pseudo-random sequence V and a secret key k ₃ The method comprises the following steps:

utilizing the Logistic-Tent chaotic mapping system to carry out the control parameter r of the chaotic mapping ₃ And chaos initial value z ₃ As a key k ₃ ＝(r ₃ ，z ₃ )；

For the confusion sequence

Iteration n ₁ + MXN times, discarding the first N ₁ Values to form the pseudorandom sequence V ═ V (n) ₁ +1)，V(n ₁ +2)，…，V(n ₁ +M×N)]。

With reference to the first aspect, in a sixth possible implementation manner of the first aspect, the performing key stream transformation on the pseudorandom sequence V to obtain a key stream sequence k (i), and performing key stream transformation according to the key stream sequence k (i) and the confusion sequence

Determining the ciphertext C _i The method comprises the following steps:

converting the pseudo-random sequence V into a keystream sequence K (i) having a value of [0, 255] using the following equation:

K(i)＝mod(floor(V(i)×2 ¹⁴ )，256)；

applying the following formula to the obfuscated sequence

Performing logical XOR to obtain the ciphertext C _i ：

Wherein, C _i For the ciphertext, C ₀ Is a seed, C ₀ ∈[0，255]；C _i-1 Representing a previous encrypted integer value;

representing a current integer value of the obfuscated sequence; k _i Representing a key stream element.

In a second aspect, an embodiment of the present application provides an image decryption method based on scrambled block compressed sensing, which is applied to an image receiving device, and is configured to decrypt and reconstruct an original image processed by an image encryption method based on scrambled block compressed sensing according to any one of the first aspect or possible implementation manners of the first aspect, where the image decryption method includes:

receiving the ciphertext C transmitted by the image transmitting apparatus _i And obtaining the secret key k shared by the image transmission device ₁ The key k ₂ And said key k ₃ ；

Using said key k ₃ For the ciphertext C _i Performing inverse transformation of the diffusion operation to obtain the pseudorandom sequence V, and performing the key stream transformation on the pseudorandom sequence V to obtain the key stream sequence K (i);

processing the keystream sequence K (i) by the following formula to obtain the obfuscated sequence

Wherein, the

K _i 、C _i 、C _i-1 Representing the decrypted value, the keystream element value, the current encrypted value, and the previous encrypted value, respectively;

according to said secret key k ₂ And the confusion sequence

Reducing the integer value Z by combining the confusion operation process of the Logistic-Tent chaotic mapping system _i ；

For the integer value Z _i Obtaining a compressed sensing measurement value y after inverse quantization _i Then, the GRSR algorithm is utilized to pass the secret key k ₁ Creating a measurement matrix versus compressed perceptual measurement y _i Reconstructing to obtain the sparse coefficient matrix;

and reconstructing the sparse coefficient matrix into the original image by utilizing inverse wavelet transform.

In the embodiment of the application, the ciphertext and the key which are encrypted and transmitted by the image encryption method based on scrambling block compressed sensing are decrypted and reconstructed in the mode, so that the quality of the restored original image can be well ensured.

In a third aspect, an embodiment of the present application provides an image transmission system based on compressed sensing of scrambled blocks, including an image transmission device and an image reception device,

the image transmission device is configured to execute the image encryption method based on the scrambled block compressed sensing according to the first aspect or any one of possible implementation manners of the first aspect;

the image receiving device is configured to execute the image decryption method based on the compressed sensing of the scrambled block according to the second aspect.

In order to make the aforementioned objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.

Fig. 1 is a bifurcation diagram of Logistic mapping.

FIG. 2 is a diagram of a fork of the Skaew Tent map.

FIG. 3 is a bifurcation diagram of the Logistic-Tent mapping.

FIG. 4 is a Lyapunov index diagram of a Logistic-Tent map.

Fig. 5 is a schematic diagram of an image transmission system based on compressed sensing of scrambled blocks according to an embodiment of the present application.

Fig. 6 is an overall flowchart of implementing secure image transmission based on compressed sensing of a scrambled block according to an embodiment of the present application.

Fig. 7 is a flowchart of an image encryption method based on compressed sensing of scrambled blocks according to an embodiment of the present application.

Fig. 8 is a flowchart of an image decryption method for compressed sensing of scrambled blocks according to an embodiment of the present application.

Fig. 9 is a spatial contrast diagram of an original image, an encrypted image, and a reconstructed image at different compression rates according to an embodiment of the present application.

Fig. 10 is an encrypted image and a histogram distribution thereof according to an embodiment of the present application.

Fig. 11 is a schematic diagram of a sensitivity experiment result of the encryption phase provided in the embodiment of the present application.

Fig. 12 is a diagram illustrating a sensitivity test result of a decryption stage according to an embodiment of the present application.

Fig. 13 is a schematic diagram of a pixel correlation provided in the embodiment of the present application.

Fig. 14 is a schematic diagram of a cropping attack and an image reconstruction result provided in an embodiment of the present application.

Fig. 15 is a schematic diagram of noise interference and image reconstruction results provided in the embodiment of the present application.

Fig. 16 is a schematic diagram of gaussian noise interference and image reconstruction results provided in the embodiment of the present application.

Icon: 100-image transmission system based on compressed sensing of scrambled blocks; 110-an image transfer device; 120-image receiving device.

Detailed Description

The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.

To facilitate understanding of the present solution, a brief introduction is made to the Logistic-Tent mapping and the compressive sensing theory.

The Logistic-Tent mapping is formed by combining two classical one-dimensional chaotic mappings, namely the Logistic mapping and the Sview Tent mapping. The Logistic map is defined as:

z _n+1 ＝αz _n (1-z _n )， (1)

the Skaw Tent map is defined as:

initial state value z ₀ E (0, 1), control parameter alpha e [3.75, 4 ∈]，μ∈(0，1)。

The Logistic-Tent mapping is described as follows:

initial state value z of the system ₀ Belongs to (0, 1), and the control parameter r belongs to [0, 4 ]]. The Logistic-Tent mapping has a larger chaotic space than the Logistic mapping and the Sview Tent mapping, and the generated chaotic sequence is more uniformly distributed.

Referring to fig. 1 to 4, fig. 1 is a bifurcation diagram of a logic map, fig. 2 is a bifurcation diagram of a Skew Tent map, fig. 3 is a bifurcation diagram of a logic-Tent map, and fig. 4 is a Lyapunov index diagram of the logic-Tent map.

From the three chaotic bifurcation diagrams in fig. 1 to fig. 3, it can be seen that the cascaded Logistic-Tent mappings are uniformly distributed in the control parameter range, and from fig. 4, it can also be seen that the Lyapunov exponent of the Logistic-Tent mappings is a positive number in the whole control parameter (0, 4), which indicates that the Logistic-Tent mappings have a larger key space.

The compressed sensing theory breaks the limitations of the Nyquist/Shannon sampling theorem, and when the sampling rate is much less than Nyquist sampling, a sparse signal can be reconstructed using few measurements. That is, for K sparse signals or images, compressed sensing can accurately recover the original signal or image from M measurements that are much less than N samples, and therefore, image processing based on compressed sensing with simultaneous sampling and compression can reduce computation and transmission costs.

One-dimensional signal x ∈ R ^N Generally non-sparse, the sparse representation can be performed by the sparse transform matrix Ψ:

x＝Ψθ， (4)

where θ is a sparse coefficient, if θ has only k non-zero entries, it can be called k sparse, and Ψ is an N × N orthogonal transform matrix. The measurement process uses a measurement matrix phi that is not coherent with the sparse basis psi to obtain a linear measurement y, namely:

y＝φx， (5)

where φ is an M N measurement matrix, i.e.:

y＝φΨθ， (6)

then, the approximate value of the sparse coefficient theta can be recovered by solving the following non-convex optimization problem, and finally, the original signal x can be obtained through orthogonal basis transformation.

min||θ|| ₀ s.t.y＝φx＝φΨθ， (7)

l ₀ The optimization problem is an NP (Non-deterministic problem of Polynomial complexity), and therefore, in the technical solution in the embodiment of the present application, a GRSR (Sparse Gradient Projection) algorithm is used for Reconstruction.

Referring to fig. 5, fig. 5 is a schematic diagram of an image transmission system 100 based on compressed sensing of scrambling blocks according to an embodiment of the present disclosure. In the embodiment, the image transmission system 100 based on compressed sensing of the scrambled block can be used for encrypted transmission of images to reduce channel bandwidth and ensure safe and robust transmission of images.

For example, the image transmission system 100 based on the compressed sensing of the scrambled blocks may include an image transmission device 110 and an image reception device 120. And the image transmission device 110 may be a terminal, the image encryption method based on the compressed sensing of the scrambling block is executed by the terminal; of course, the image transmission device 110 may also be a server, for example, a server interacting with a terminal, the terminal may send the image to the server, and the server needs to transmit the encrypted image to the image receiving device 120 via an unsecure channel, in which case, the image encryption method based on the compressed sensing of the scrambling block is performed by the server. Similarly, the image receiving device 120 may be a terminal or a server, and the image receiving device 120 is embedded with a program for executing an image decryption method based on scrambling block compressed sensing to decrypt an image, thereby implementing image secure and robust transmission of the image.

Referring to fig. 6, fig. 6 is an overall flowchart of implementing image secure transmission based on scrambling block compressed sensing according to an embodiment of the present application.

In this embodiment, the encryption process for the original image is the upper half, and the decryption reconstruction process is the lower half. The encryption process may include pixel scrambling, blocking, compression sampling, measurement value quantization, encryption, and the like, a stack of original images is compressed and encrypted, and the decryption reconstruction process may include decryption, inverse quantization, reconstruction, and the like, so as to decrypt and reconstruct the transmitted data to obtain the original images. The present scheme will be described in detail later with the image transmitting apparatus 110 performing the scrambled block compression perception-based image transmission method and the image receiving apparatus 120 performing the scrambled block compression perception-based image decryption method, respectively.

Referring to fig. 7, fig. 7 is a flowchart of an image encryption method based on compressed sensing of a scrambling block according to an embodiment of the present application. In this embodiment, the method for encrypting the image by scrambling block compressed sensing may include: step S11, step S12, step S13, step S14, step S15, step S16, step S17, and step S18.

For example, in order to securely transmit an image, the image transmission apparatus may acquire an original image to be transmitted by encryption.

After obtaining the original image, the image transmission apparatus may perform step S11.

Step S11: and transforming the original image wavelet to a frequency domain by using DWT as a sparse basis psi to obtain a sparse coefficient matrix.

In this embodiment, the image transmission apparatus may Wavelet-transform the original image into the frequency domain using DWT (Discrete Wavelet transform) as the sparse basis Ψ, resulting in a sparse coefficient matrix.

Resulting in a sparse coefficient matrix, the image transmission apparatus may perform step S12.

Step S12: carrying out chaotic mapping on the sparse coefficient matrix by using a Logistic-Tent chaotic mapping system to obtain a scrambling matrix R and a key k ₁ And determining a scrambled image according to the original image and the scrambling matrix R, wherein the secret key k ₁ Is (r) ₁ ，z ₁ )，r ₁ Control parameter for this chaotic mapping, z ₁ Is the chaos initial value of the chaos mapping.

In this embodiment, the image transmission device may perform chaotic mapping on the sparse coefficient matrix by using a Logistic-Tent chaotic mapping system to obtain a scrambling matrix R and a key k ₁ 。

For example, the image transmission device may generate a pseudo-random sequence p by using a Logistic-Tent chaotic mapping system ₁ And the control parameter r of the chaotic mapping is carried out ₁ And chaos initial value z ₁ As a key k ₁ ＝(r ₁ ，z ₁ ). For pseudo-random sequence p ₁ Iteration h + mxn times can be performed, discarding the previous h values, where h > 0, for improving the sensitivity of the initial value.

Then, each element of the N matrix can be divided into two or moreThe value is set to zero (i.e. initialized) for the pseudo-random sequence p ₁ Sorting R (p) in ascending order (although other sorting schemes may be used, the sorting scheme is not limited thereto), and ₂ (m), m) is set to 1 to obtain a reordered sequence p ₂ This results in a scrambling matrix R, where m ∈ {1, 2, … N }.

Obtaining a scrambling matrix R and a key k ₁ Then, the image transmission device may multiply the original image by the scrambling matrix R to obtain a scrambled image with an encryption effect, and the image decryption may be implemented by multiplying the scrambled image by an inverse permutation matrix (i.e., an inverse matrix of the scrambling matrix R).

After the scrambled image is obtained, the image transmission apparatus may execute step S13.

Step S13: dividing the scrambled image into M sizes of

In this embodiment, the image transmission apparatus may divide the scrambled image into M pieces of size

To obtain corresponding M scrambled image blocks P _i (x)。

Illustratively, the scrambled image is divided into M sizes

The ith scrambled image block (i.e., the non-overlapping sub-block) may be defined as P _i (x)，

P _i (x)＝vec(x)×R， (8)

Where vec (x) represents the row order vectorization of x.

Obtaining M scrambled image blocks P _i (x)Thereafter, the image transmission apparatus may scramble the image blocks P for each _i (x) Performing compressed sensing measurement to obtain each scrambled image block P _i (x) Compressed perceptual measurement y of _i 。

Illustratively, for each scrambled image block P _i (x) Each scrambled image block P can be obtained by independent measurement through the measurement matrix _i (x) Compressed perceptual measurement y of _i 。

For example, the measurement matrix may be a simple random linear projection:

y _i ＝φP _i (x)φ ^T ， (9)

wherein the content of the first and second substances,

representing scrambled image blocks P _i (x) Compressed perceptual measurement of;

representing scrambled image blocks P _i (x) The Hadamard matrix can be selected

Front of a Hadamard matrix of size

And (6) obtaining the line.

Since such a two-dimensional separable sensing operator described in equation (9) can be considered a case of a conventional column-based CS measurement operator, it is assumed that

Can be decomposed into

Then, the measurement matrix in equation (9) can be equivalent to:

wherein the content of the first and second substances,

is a Kronecker product operator; vec (y) _i ) Denotes y _i Line order vectorization of, vec (P) _i (x) ) represents P _i (x) Is vectorized.

Furthermore, equation (10) may represent the scrambled image block CS measurement and thus may be equivalently represented as the entire image CS measurement, i.e. the measurement matrix is:

as can be seen from the scrambling matrix R described above,

thus, further, the measurement matrix may be:

thus, the measurement matrix in the measurement scheme proposed for the entire image can be represented as a structurally random matrix

Almost irrelevant to all other orthogonal matrices and theoretically having exactly the same sensing characteristics as the random observed matrix.

The measured value y can be obtained through the sparse transformation and the measurement process, and meanwhile, the image can be regarded as being simultaneously compressed, sampled and encrypted by the first layer, so that the data security is enhanced while the data quantity is reduced.

Obtaining each scrambled image block P _i (x) By compression ofPerception measurement value y _i Thereafter, the image transmission apparatus may perform step S14.

Step S14: for each of the compressed perceptual measurements y _i Performing quantization processing on the data to obtain an integer value Z _i 。

Since the measured values obtained by compressed sensing sampling are generally real values, and the transmission channel is generally for a limited number of precision in practical applications, the image transmission apparatus in this embodiment can utilize the quantizer to transmit all the measured values y _i Quantized to an integer value Z _i 。

Illustratively, for each compressed perceptual measurement y _i The image transmission device may quantize the image data by a preset quantization formula to obtain a corresponding integer value Z _i . For example, the preset quantization formula may be:

Z _i ＝round(δ _i-1 +y _i )， (14)

wherein Z is _i Representing a measurement y on compressed sensing _i Quantized integer value, δ representing the compressed perceptual measurement y _i Error residual value of, initial residual value delta ₀ Round (a) denotes the integer value returned to the nearest a. Thereby, the compressed sensing measured value is subjected to

Integer value obtained after quantization

The compressed sensing measurement value is quantized in such a way, so that the quantized integer value can adapt to the distribution interval of most measurement values, and the error residual value of the previous measurement value is added to the quantization of the next measurement value to have a diffusion effect.

Obtaining all compressed sensing measurement values y _i Quantized integerValue Z _i Thereafter, the image transfer apparatus may perform step S15.

Step S15: utilizing the Logistic-Tent chaotic mapping system to map the integer value Z _i Performing aliasing operation to obtain an aliased sequence

And a secret key k ₂ ，

The key k ₂ Is (r) ₂ ，z ₂ )，r ₂ Control parameter for this chaotic mapping, z ₂ The chaos initial value of the chaos mapping is obtained.

When the compressive sensing measurement matrix is used as a secret key, the compressive sensing framework can be regarded as an encryption scheme, but the security of the compressive sensing framework cannot meet the requirements of practical application, so that the security of image transmission is further ensured through encryption operation in the embodiment.

In this embodiment, the image transmission device may utilize a Logistic-Tent chaotic mapping system to perform the control parameter r of the chaotic mapping of this time ₂ And chaos initial value z ₂ As a key k ₂ ＝(r ₂ ，z ₂ ) (ii) a For integer values Z _i Can iterate n ₀ + MXN times, the first N may be discarded to prevent transient effects ₀ Values to generate a sequence:

the sequence b is ═ b (n) ₀ +1)，b(n ₀ +2)，…，b(n ₀ +M×N)]The new sequences are obtained in ascending order:

then, the image transfer apparatus can search

In the sequence of

Forming an index sequence by using the corresponding index values:

for index sequences

May be transformed by:

wherein z is _i ＝vec(Z _i ) Is denoted by Z _i Is denoted as z _i 。

Image transfer apparatus pair

Recombination to obtain a confusion sequence

By adopting Logistic-Tent mapping, compared with single Skaew Tent mapping, the chaos range is wider, and the chaos performance is better.

Obtaining a confusion sequence

And a secret key k ₂ Thereafter, the image transfer apparatus may perform step S16.

Step S16: utilizing the Logistic-Tent chaotic mapping system to map the confusion sequence

To carry outA diffusion operation to obtain a pseudorandom sequence V and a secret key k ₃ Said secret key k ₃ Is (r) ₃ ，z ₃ )，r ₃ Control parameter for this chaotic mapping, z ₃ The chaos initial value of the chaos mapping is obtained.

In order to further ensure that the encryption method of the scheme can resist statistical attack, the image transmission equipment can further map the confusion sequence through Logistic-Tent

A diffusion operation is performed.

In this embodiment, the image transmission device may utilize a Logistic-Tent chaotic mapping system to perform the control parameter r of the chaotic mapping of this time ₃ And chaos initial value z ₃ As a key k ₃ ＝(r ₃ ，z ₃ ) And, for obfuscated sequences

Iteration n ₁ + M × N times, the first N may be discarded to prevent transient effects ₁ Values to form a pseudo-random sequence:

V＝[V(n ₁ +1)，V(n ₁ +2)，…，V(n ₁ +M×N)]， (20)

and encrypting the quantization value by adopting a scrambling-diffusing mechanism through Logistic-Tent mapping, so that the security and robustness of image encryption can be further improved.

Obtaining a pseudorandom sequence V and a secret key k ₃ Thereafter, the image transfer apparatus may perform step S17.

Step S17: carrying out key stream conversion on the pseudorandom sequence V to obtain a key stream sequence K (i), and carrying out key stream conversion on the pseudorandom sequence V according to the key stream sequence K (i) and the confusion sequence

Determining the ciphertext C _j 。

In this embodiment, the image transmission device may perform key stream transformation on the pseudorandom sequence V to obtain a key stream sequence k (i).

Illustratively, the pseudorandom sequence V may be converted into a keystream sequence k (i) having a value of [0, 255] using the following equation:

K(i)＝mod(floor(V(i)×2 ¹⁴ )，256)， (21)

of course, this can be expressed by the following ways, which are not limited herein:

K(i)←floor(V(i)×2 ¹⁴ )mod255， (22)

the image transfer device may then be based on the keystream sequence K (i) and the obfuscated sequence

Determining the ciphertext C _i . Illustratively, the obfuscated sequence may be paired using the following formula

Performing logical XOR to obtain the ciphertext C _i ：

Wherein, C _i Is a ciphertext, C ₀ Is a seed, C ₀ ∈[0，255]；C _i-1 Representing a previous encrypted integer value;

representing a current integer value of the obfuscated sequence; k is _i Representing a keystream element.

Determining the ciphertext C _i Key k ₁ Key k ₂ And a secret key k ₃ Thereafter, the image transfer apparatus may perform step S18.

Step S18: the ciphertext C _i Sending the key k to an image receiving device ₁ The key k ₂ And said key k ₃ Sharing to the image receiving device so that the image receiving device is based on the ciphertext C _i The key k ₁ The key k ₂ And said key k ₃ In combination with presetsThe image decryption method of (2) reconstructs the original image, wherein the image decryption method is the inverse process of the image encryption method.

In this embodiment, the image transmission apparatus may transmit the ciphertext C _i Sending to the image receiving device and sending the key k ₁ Key k ₂ And a secret key k ₃ Sharing to the image receiving apparatus so that the image receiving apparatus is based on the ciphertext C _i Key k ₁ Key k ₂ And a secret key k ₃ And reconstructing the original image by combining a preset image decryption method (i.e., an image decryption method based on scrambling block compressed sensing), where the image decryption method is an inverse process of the image encryption method, and will be described in detail later.

Original images are transformed to a frequency domain (sparse coefficient matrix is obtained) by utilizing wavelet transform, and a Logistic-Tent chaotic mapping system is utilized to carry out chaotic mapping on a sparse coefficient matrix to obtain a scrambling matrix and a key k ₁ (the control parameters and the chaos initial value of the chaos mapping) further determine a scrambled image, then divide the scrambled image to obtain corresponding M scrambled image blocks, and then perform compressed sensing measurement on each scrambled image block. Firstly, the pixels of the whole image are reordered (namely scrambled), the spatial correlation of adjacent pixel blocks can be eliminated, the simultaneous sampling and compression can be realized by utilizing a compressed sensing theory, the data transmission quantity can be reduced, and the efficiency can be improved. The image is firstly subjected to wavelet transformation to a frequency domain, and then the image frequency domain coefficients are scrambled, so that the sparsity of a sampling object tends to be uniform, the RIP performance of compressed sensing can be effectively relaxed, and the improvement of the image reconstruction quality can be facilitated. Therefore, the scrambled block compressed sensing is adopted for measurement, the data transmission quantity can be effectively reduced, the transmission efficiency is guaranteed, and meanwhile the data transmission quantity is used as the first layer of encryption. Then, quantization processing (quantizing into integer value) is carried out on the compressed sensing measured value, and confusion operation is carried out on the integer value by utilizing a Logistic-Tent chaotic mapping system to obtain a confusion sequence and a key k ₂ Namely the control parameters and the chaos initial value of the chaos mapping; and then, carrying out diffusion operation on the confusion sequence by using a Logistic-Tent chaotic mapping system to obtain a pseudorandom sequence and a secret key k ₃ The control parameters and the chaos initial value of the chaos mapping are obtained; then, carrying out key stream conversion on the pseudorandom sequence to obtain a key stream sequence, and determining a ciphertext according to the key stream sequence and the confusion sequence; sending the ciphertext to an image receiving device, and sending a secret key k ₁ Key k ₂ And a secret key k ₃ Shared with the image receiving device. The Logistic-Tent mapping is utilized to encrypt the quantization value by adopting a confusion-diffusion mechanism, the chaotic range of mapping is wider, the chaotic performance of mapping is better, the security of data transmission can be ensured by constructing a key stream, and statistical attack is resisted, so that the security is further ensured.

For a detailed description of the decryption and reconstruction process of an image, please refer to fig. 8, and fig. 8 is a flowchart of an image decryption method based on compressed sensing of a scrambling block according to an embodiment of the present application. In the present embodiment, the image decryption method of scrambled block compressed sensing is applied to an image receiving apparatus and may include step S21, step S22, step S23, step S24, step S25, and step S26.

In the present embodiment, the ciphertext C is transmitted at the image transmission apparatus _i Shared secret key k ₁ Key k ₂ And a secret key k ₃ Thereafter, the image receiving apparatus may perform step S21.

Step S21: receiving the ciphertext C transmitted by the image transmitting apparatus _i And obtaining the secret key k shared by the image transmission device ₁ The key k ₂ And said key k ₃ 。

In the present embodiment, the image receiving apparatus can receive the ciphertext C transmitted by the image transmitting apparatus _i And obtaining a key k shared by the image transfer apparatus ₁ Key k ₂ And a secret key k ₃ 。

After that, the image receiving apparatus may perform step S22.

Step S22: using said key k ₃ For the ciphertext C _i And performing inverse transformation of the diffusion operation to obtain the pseudorandom sequence V, and performing the key stream transformation on the pseudorandom sequence V to obtain the key stream sequence K (i).

In this embodiment, the image receiving apparatus may utilize the inverse of the diffusion operation, utilizing the key k ₃ For ciphertext C _i And carrying out inverse transformation of diffusion operation to obtain a pseudorandom sequence V. The pseudo-random sequence V is then converted into a keystream sequence k (i) by equation (21) or equation (22).

Then, the image receiving apparatus may perform step S23.

Step S23: applying the following formula to the keystream sequence K (i) to obtain the obfuscated sequence

Wherein, the

K _i 、C _i 、C _i-1 Representing the decrypted value, the keystream element value, the current encrypted value, and the previous encrypted value, respectively.

In this embodiment, the image receiving device may process the key stream sequence k (i) using the following formula to obtain an obfuscated sequence

Wherein the content of the first and second substances,

Obtaining a confusion sequence

Thereafter, the image receiving apparatus may perform step S24.

Step S24: according to said secret key k ₂ And the confusion sequence

Combining the confusion operation process of the Logistic-Tent chaotic mapping system, and reducing to obtain the integer value Z _i 。

In this embodiment, the image receiving apparatus may be based on the key k ₂ And confusion sequences

Reducing to obtain an integer value Z by combining the confusion operation process of the Logistic-Tent chaotic mapping system _i 。

For example, the image receiving device may first use the key k ₂ Iterative Logistic-Tent mapping n ₀ + mxn times, and then by steps in the aliasing operation:

sequencing the obtained sequences in an ascending order to obtain a new sequence; then, the image receiving apparatus may search for the index value corresponding to the element in the previous sequence in the obtained next sequence to obtain an index sequence:

then through the index sequence

For the confusion sequence

Inverse scrambling and reduction to obtain quantized integer value Z _i 。

To obtain an integer value Z _i Thereafter, the image receiving apparatus may perform step S25.

Step S25: for the integer value Z _i Obtaining a compressed sensing measurement value y after inverse quantization _i Then, the GRSR algorithm is utilized to pass the secret key k ₁ Creating a measurement matrix versus compressed perceptual measurement y _i And reconstructing to obtain the sparse coefficient matrix.

In bookIn an embodiment, the image receiving apparatus may correct the integer value Z by inverse quantization _i Processing to obtain a compressed sensing measurement value y _i . The image receiving device may then use the GRSR algorithm, via key k ₁ Creating a measurement matrix versus compressed perceptual measurement y _i And reconstructing to obtain a sparse coefficient matrix.

After obtaining the sparse coefficient matrix, the image receiving apparatus may perform step S26.

Step S26: and reconstructing the sparse coefficient matrix into the original image by utilizing inverse wavelet transform.

In the present embodiment, the image receiving apparatus can reconstruct the sparse coefficient matrix into the original image using the inverse wavelet transform.

In order to verify the effects (validity, robustness, security and the like) of the image encryption method and the image decryption method in the image transmission system based on the compressed sensing of the scrambled block provided by the embodiment of the application, the following experiment proves.

In this embodiment, the grayscale images with the sizes of 256 × 256 and 512 × 512 are selected respectively through experiments, and the GRSR algorithm is used as the reconstruction algorithm. The experimental environment is a personal computer implementation algorithm of an Intel Core i5 CPU, an 8GB memory and a Windows 1064 bit operating system, the size of a block in compressed sensing measurement is 32 multiplied by 32, and a key k ₁ 、k ₂ 、k ₃ Parameter (r) mapped by three pairs of Logistic-Tent ₁ ，z ₁ )、(r ₂ ，z ₂ )、(r ₃ ，z ₃ ) Configured to measure, perform obfuscation and diffusion operations, respectively. Will r (i.e. r) ₁ 、r ₂ 、r ₃ ) Set to a 15-bit fractional number, initial value z ₀ Set to a 15-bit fractional number.

Analysis of image encryption results: the experiment selects the spatial contrast of the original image, the encrypted image and the reconstructed image at different compression rates with a lens of 512 × 512 and a house of 256 × 256, and the result is shown in fig. 9. When the sampling rate is 0.75, it means that the compression-sampled image is 75% of the original image. The quality of the reconstructed image is measured by adopting the peak signal-to-noise ratio PSNR, and the higher the value of the quality, the better the image quality is. Its unit is dB. The formula is as follows:

wherein, the mean square error between the original image and the decrypted image is represented by MSE, and the expression is as follows:

it can be seen from fig. 9 that the highest PSNR value of the reconstructed image can reach 40.7325. It can also be seen that the reconstructed image retains most of the features of the original image, and the quality of the decrypted image is still acceptable to some extent at different sampling rates, which indicates that the algorithm herein has a better recovery effect, and at the same time, has better compression capability and is beneficial to transmission and storage.

Analysis of compression performance: in this embodiment, a 512 × 512 lena image is selected and sampled at a sampling rate of 0.05 to 0.95, and the distribution trend of PSNR values after reconstruction is shown in table 1, where PSNR values of reconstructed images increase with increasing sampling rate. As can be seen from table 1, the PSNR values of the reconstructed images exceed 30dB when the sampling rate exceeds 0.35. The PSNR values for which 256 × 256 lena images were selected for compression performance comparison in this scheme and other methods (method 1: visual security image encryption scheme based on parallel compressed sensing; method 2: synchronous compressed encrypted image encoding scheme based on parallel compressed sensing) are listed in table 2. As can be seen from table 2, the reconstruction quality of the algorithm proposed herein is improved by 5.69dB compared to the best result of method 1, and is improved by 5.35 to 10.57dB compared to the reconstruction quality of method 2 under the same compression rate. Illustrating that the algorithm proposed herein outperforms these methods in compression performance.

Table 1: PSNR value of reconstructed images at different sampling rates

Table 2: compression Performance comparison with

methods

1 and 2

Histogram analysis: the frequency of the image pixel intensity value can be displayed through an image histogram, and for a meaningful ordinary image, the histogram distribution is always uneven because the pixel value distribution of the ordinary image is relatively concentrated. An effective image encryption algorithm should generate an encrypted image with a uniform histogram. In fig. 10, (a), (e), (b), and (f) are the original images lena and peppers, respectively, and the corresponding histogram distributions, and in fig. 10, (c), (g), (d), and (h) are the encrypted images and the histogram distributions thereof, respectively. The fluctuation range of the histogram of the plaintext image is large and is distributed unevenly; the image histograms after encryption are uniformly distributed, and the difference between the encrypted image and the plaintext image is huge. This demonstrates that the method in this embodiment is able to resist a certain degree of statistical attack.

And (3) key space analysis: in the image encryption method based on scrambling block compressed sensing provided by this embodiment, three pairs of keys k are used ₁ 、k ₂ 、k ₃ Has a floating point number precision of 10 ^-15 Precision of floating point number of chaos initial value is 10 ^-15 The key space size can be calculated as:

keyspace＝(10 ¹⁵ ×10 ¹⁵ ) ³ ＝10 ⁹⁰ ≈2 ³⁰⁰ ， (27)

and 2 ¹⁰⁰ The key space can better resist brute force attack, so that the key space of the scheme can be theoretically enough to resist brute force attack.

Key sensitivity analysis: the key sensitivity means that the wrong key and the correct key have extremely small changes to cause the incorrect encryption or decryption, and the better the key sensitivity is, the better the effect of resisting the differential attack is.

The result of the sensitivity experiment in the encryption stage is shown in fig. 11, and the differential image of the correct key and the incorrect key is completely disordered, which indicates that the scheme has sensitivity to the encryption key.

Among them, in fig. 11:

(a) is an original image;

(b) is ciphertext encrypted using the correct key (z ═ 0.234857728820643);

(c) is ciphertext encrypted using the error key (z ═ 0.234857728820644);

(d) are differential images.

The results of the sensitivity experiments in the decryption phase are shown in fig. 12: the correct key can be used for normal decryption, and the wrong key can not be used for decryption, so that the algorithm has sensitivity to the decryption key.

Among them, in fig. 12:

(e) is an encrypted image;

(f) decrypting the correct key (r is 3.997636563976482, z is 0.215663864979742) to obtain an image;

(g) decrypting the resulting image for the error key (r ═ 3.997636563976483); (h) the resulting image is decrypted for the wrong key (z ═ 0.215663864979743).

Therefore, the scheme is sensitive to the key and can resist differential attack.

Pixel correlation analysis: the analysis attack of the cryptographic algorithm by using the essential attribute of high correlation among the pixels of the natural image is called as statistical attack, in order to resist the statistical attack, the correlation coefficient of the encrypted image is much weaker than that of the original image, and the lower the correlation coefficient among the pixels of the encrypted image, the better the effect of resisting the statistical attack. 8000 pixels are randomly selected as samples from the original image, the measured image and the encrypted image for pixel correlation in the present embodiment.

The first line in fig. 13 represents the correlation distribution between adjacent pixels in the plaintext image in the horizontal, vertical, and diagonal directions; the second row represents the correlation distribution between adjacent pixels of the measured image after compressed perceptual measurement; line 3 shows the correlation distribution between adjacent pixels of the encrypted image of the proposed encryption algorithm. As can be seen from fig. 13, the correlation coefficient of the plaintext image exhibits a concentrated distribution; and the correlation of the measurement image in the horizontal direction and the diagonal direction is reduced to some extent; but there is still a high correlation in the vertical direction; the correlation distribution of the encrypted image shows that the points of the image are distributed in a discrete and uniform manner, which indicates that the correlation among the pixels is low. The scheme is shown to be capable of resisting statistical attack to a certain extent.

And (3) analyzing robustness of packet loss resistance: the image is compressed and perceptually sampled to obtain a measurement value y with a length of M, which can be divided into a plurality of packets at equal intervals. Each packet carries a similar amount of information to the original image, since the importance of the measured values is approximately equal. Assuming m measurements per packet, there are a total

And (5) packaging. The receiving end will update the sampling rate according to the number of received packets, and the packet loss rate is indicated as PLR, which can be up to 30% in practical cases [33 ]]. The sampling rate is denoted SR, i.e. SR ═ M/N. Assuming SR ═ α (0 < α < 1), PLR ≦ β (0 ≦ β ≦ 0.3), when α ≦ 0.75 and β ≦ 0.2, the measured value M ═ N0.75 ≦ 512 × 0.75 ≦ 196608, M/100 ═ 1966 packets, the number of dropped packets 1966 × 0.2 ≦ 393, the packets received by the receiving end 1966-. If the packet loss rate is not considered, the amount of reduction is 65536. The real sampling rate is close to alpha (1-beta) through the analysis, and meanwhile, the transmission of the data volume can be reduced through compressed sensing sampling, and the load of the network can be reduced. That is, the amount of the specific reduction in the practical application is affected by the sampling rate and the packet loss rate.

Robust analysis of shear resistance: when data is subjected to malicious shearing attack in a transmission channel, the loss of the information block can influence the content of a reconstructed image, but the compressed sensing sampling quantization is carried out on the image, the measured values have democratic property, and the energy of each measured value is approximately equal, so that the algorithm can resist the shearing attack theoretically.

The encrypted images of lena were subjected to clipping attack experiments with 20 × 20, 30 × 30, 50 × 50, 100 × 100, 128 × 128, and 256 × 256 pixel blocks, respectively, and the reconstructed images thereof are shown in fig. 14 (a) to (f). When the cropping size is 256 × 256, the reconstructed image is still visually acceptable, in line with theoretical reasoning.

Robust analysis of noise immunity: in insecure channel transmission, the ciphertext image is also susceptible to interference of various noises, and has a large influence on the quality of the decrypted image. Fig. 15(a), (b), (c), and table 3 show reconstructed images obtained by adding salt and pepper noises with intensities of 0.01, 0.05, and 0.10 to the ciphertext image of lena, and their PSNR values, respectively. Experiments show that when the intensity of the salt and pepper noise reaches 0.1, the reconstructed image still retains the main information of the original image and is visually acceptable, and the PSNR value still reaches 13.78dB, so that the method has certain robustness to the salt and pepper noise.

Table 3: PSNR (Peak Signal to noise ratio) value of reconstructed image subjected to salt and pepper noises with different intensities

The encrypted image is susceptible to gaussian noise, which is added to the ciphertext image in the form of equation (28).

G′＝G+σW， (28)

Where G' denotes a ciphertext image to which noise is added, G denotes an encrypted image, W denotes gaussian noise data, and σ denotes a gaussian noise intensity coefficient.

Reconstructed images obtained by adding gaussian noise having σ of 1, σ of 5, σ of 15, and σ of 20 to the ciphertext image of lens are shown in (a) to (d) of fig. 16. The result shows that the reconstructed image has certain distortion with the increase of the noise intensity sigma, but the main information of the reconstructed image can still be seen visually when sigma is 20, which shows that the algorithm has better robustness to Gaussian noise.

And (3) comprehensive analysis: according to the scheme, the compressed sensing of the scrambling block realizes efficient and rapid transmission and storage through simultaneous sampling, compression and encryption, has a good recovery effect, can well resist common attacks such as brute force attack, statistical attack, packet loss attack, shearing attack and noise attack while ensuring the transmission efficiency, and has robustness. Therefore, the scheme has better innovation in comprehensive performance and better applicability in practical application scenes under various resource-limited conditions.

In summary, the embodiment of the present application provides an image transmission system, an encryption method and a decryption method based on scrambling block compressed sensing, an original image is transformed to a frequency domain (to obtain a sparse coefficient matrix) by using wavelet transform, and a Logistic-Tent chaotic mapping system is used to perform chaotic mapping on the sparse coefficient matrix to obtain a scrambling matrix and a key k ₁ (the control parameters and the chaos initial value of the chaos mapping) further determine a scrambled image, then divide the scrambled image to obtain corresponding M scrambled image blocks, and then perform compressed sensing measurement on each scrambled image block. Firstly, the pixels of the whole image are reordered (namely scrambled), the spatial correlation of adjacent pixel blocks can be eliminated, the simultaneous sampling and compression can be realized by utilizing a compressed sensing theory, the data transmission quantity can be reduced, and the efficiency can be improved. The image is firstly subjected to wavelet transformation to a frequency domain, and then the image frequency domain coefficients are scrambled, so that the sparsity of a sampling object tends to be uniform, the RIP performance of compressed sensing can be effectively relaxed, and the improvement of the image reconstruction quality can be facilitated. Therefore, the scrambled block compressed sensing is adopted for measurement, the data transmission quantity can be effectively reduced, the transmission efficiency is guaranteed, and meanwhile the data transmission quantity is used as the first layer of encryption. Then, quantization processing (quantizing into integer value) is carried out on the compressed sensing measured value, and confusion operation is carried out on the integer value by utilizing a Logistic-Tent chaotic mapping system to obtain a confusion sequence and a key k ₂ Namely the control parameters and the chaos initial value of the chaos mapping; and then, carrying out diffusion operation on the confusion sequence by using a Logistic-Tent chaotic mapping system to obtain a pseudorandom sequence and a secret key k ₃ Namely the control parameters and the chaos initial value of the chaos mapping; then, carrying out key stream conversion on the pseudorandom sequence to obtain a key stream sequence, and determining a ciphertext according to the key stream sequence and the confusion sequence; sending the ciphertext to an image receiving device, and sending a secret key k ₁ Key k ₂ And a secret key k ₃ Shared with the image receiving device. Applying a confusion-diffusion mechanism to the quantization value by using Logistic-Tent mappingEncryption is carried out, the chaotic range of mapping is wider, the chaotic performance of mapping is better, and the security of data transmission can be ensured by constructing a key stream, so that statistical attack is resisted, and the security is further ensured. Through the analysis in various aspects such as the spatial comparison of the compressed and encrypted images and the reconstructed images under different sampling rates, the analysis of the relation between the sampling rate and the packet loss rate, the comparison of compression performance, the analysis of key space, the analysis of pixel correlation, the analysis of robustness for resisting packet loss, shearing and noise attack, the comprehensive comparison analysis and the like, the safety, effectiveness and robustness of the transmission through an unsafe channel after the images are encrypted are proved. The decryption reconstruction process is realized by utilizing an inverse process, comprises inverse quantization and inverse confusion-diffusion operation, and can adopt a GRSR reconstruction algorithm to obtain high-performance reconstruction of an image and ensure transmission robustness. Experimental simulation results and comparative analysis show that the PSNR value of a reconstructed image of an original image is 20.4dB at a sampling rate of 0.05; the PSNR value of the reconstructed image also reaches 22.24dB under the packet loss rate of 90 percent; the reconstructed image still retains the main information and is visually acceptable under a 256 × 256 cropping attack. Therefore, the scheme has high compression performance, can resist common attacks such as brute force attack, statistical attack, packet loss attack, shearing attack, noise attack and the like, has high robustness, and has wide applicability to practical application scenes under various resource-limited conditions. The data acquisition, the effective transmission and the reduction of the calculation load are realized, and the safe and robust transmission of the image can also be realized.

In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.

The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An image encryption method based on scrambling block compressed sensing is characterized by being applied to an image transmission device and comprising the following steps:

performing wavelet transformation on an original image to a frequency domain by using DWT as a sparse basis psi to obtain a sparse coefficient matrix;

generating key k by using Logistic-Tent chaotic mapping system ₁ Constructing a scrambling matrix R, and determining a scrambled image according to the original image and the scrambling matrix R, wherein a secret key k ₁ Is (r) ₁ ，z ₁ )，r ₁ Control parameter for this chaotic mapping, z ₁ The chaos initial value of the chaos mapping is obtained;

dividing the scrambled image into M sizes of

And a secret key k ₂ ，

utilizing the Logistic-Tent chaotic mapping system to perform alignment on the confusion sequence

Determining the ciphertext C _i ；

The ciphertext C _i Sending the key k to an image receiving device ₁ The key k ₂ And said key k ₃ Sharing to the image receiving device so that the image receiving device is based on the ciphertext C _i The key k ₁ The key k ₂ And said key k ₃ Reconstructing the original image by combining a preset image decryption method, wherein the image decryption method is the reverse process of the image encryption method;

wherein for each of said scrambled image blocks P _i (x) Performing compressed sensing measurement to obtain each scrambled image block P _i (x) Compressed perceptual measurement y of _i The method comprises the following steps:

for each of said scrambled image blocks P _i (x) And independently measuring through a measurement matrix to obtain each scrambled image block P _i (x) Compressed perceptual measurement y of _i The measurement matrix is:

y _i ＝φP _i (x)φ ^T ，

wherein the content of the first and second substances,

Representing scrambled image blocks P _i (x) By selecting the Hadamard matrix

Front of a Hadamard matrix of size

Obtaining a row;

or, the measurement matrix is:

is a Kronecker product operator; vec (y) _i ) Denotes y _i Order vectorization of (c), vec (P) _i (x) ) represents P _i (x) Vectorizing the order of (a);

or, the measurement matrix is:

or, the measurement matrix is:

2. the image encryption method based on scrambling block compressed sensing of claim 1, wherein the sparse coefficients are mapped by using a Logistic-Tent chaotic mapping systemCarrying out chaotic mapping on the matrix to obtain a scrambling matrix R and a secret key k ₁ The method comprises the following steps:

generating a pseudo-random sequence p by using the Logistic-Tent chaotic mapping system ₁ And the control parameter r for the chaotic mapping is obtained ₁ And chaos initial value z ₁ As a key k ₁ ＝(r ₁ ，z ₁ )；

For the pseudo-random sequence p ₁ Iterating for h + NXN times, and discarding the previous h values;

setting a value of each element of the N × N matrix to zero;

3. The method according to claim 1, wherein said compressed sensing for each of said compressed sensing measures y _i Quantizing it to an integer value Z _i The method comprises the following steps:

Z _i ＝round(δ _i-1 +y _i )，

wherein, Z _i Representing the compressed perceptual measurement y _i Quantized integer value, δ representing the compressed perceptual measurement y _i Error residual value of, initial residual value delta ₀ Round (a) denotes the integer value returned to the nearest a.

4. The scrambled block compressed perception-based image encryptor of claim 1The method is characterized in that the integer value Z is mapped by using the Logistic-Tent chaotic mapping system _i Performing aliasing operation to obtain an aliased sequence

And a secret key k ₂ The method comprises the following steps:

The sequence b is ═ b (n) ₀ +1)，b(n ₀ +2)，…，b(n ₀ +M×N)]Obtaining new sequences in ascending order

Searching

In the sequence of

Form an index sequence by the corresponding index values

For the index sequence

Is transformed by:

wherein z is _i ＝vec(Z _i ) Is represented by Z _i Is denoted as z _i ；

To pair

Obtaining the confusion sequence after recombination

5. The image encryption method based on scrambling block compressed sensing of claim 1, wherein the obfuscating sequence is subjected to the Logistic-Tent chaotic mapping system

utilizing the control parameter r of the Logistic-Tent chaotic mapping system ₃ And chaos initial value z ₃ As a key k ₃ ＝(r ₃ ，z ₃ )；

For the obfuscated sequence

6. The image encryption method based on compressed sensing of scrambled blocks according to claim 1, wherein said transforming said pseudorandom sequence V into a key stream sequence K (i), and obtaining a key stream sequence K (i) according to said key stream sequence K (i) and said obfuscated sequence

Determining the ciphertext C _i The method comprises the following steps:

K(i)＝mod(floor(V(i)×2 ¹⁴ )，256)；

applying the following formula to the obfuscated sequence

Performing logical XOR to obtain the ciphertext C _i ：

representing a current integer value of the obfuscated sequence; k _i Representing a keystream element.

7. An image decryption method based on scrambled block compressed sensing, which is applied to an image receiving device and used for decrypting and reconstructing an original image processed based on the image encryption method based on scrambled block compressed sensing of any one of claims 1 to 6, and the image decryption method comprises:

Using said key k ₃ For the ciphertext C _i Performing inverse transformation of the diffusion operation to obtain the pseudorandom sequence V, and performing the keystream transformation on the pseudorandom sequence V to obtain the keystream sequenceK(i)；

Processing the keystream sequence K (i) by obtaining the obfuscated sequence by

Wherein, the

according to said secret key k ₂ And the confusion sequence

8. An image transmission system based on compressed sensing of scrambling blocks is characterized by comprising an image transmission device and an image receiving device,

the image transmission device is used for executing the image encryption method based on the scrambled block compressed sensing of any one of claims 1 to 6:

the image receiving device is configured to execute the image decryption method based on the compressed sensing of scrambled blocks according to claim 7.