CN112887075B - Encryption method of similar full-connection network image based on plaintext correlation - Google Patents

Abstract

An encryption method for a fully connected network image based on plaintext correlation, relates to the technical field of image encryption, and solves the problem of poor encryption effect in existing image encryption methods. The convolution kernel is generated by the logistic chaotic system, and the original image is convolved, pooled and activated to obtain a matrix related to the plaintext, and the key is obtained by using this matrix. Using the obtained key, the nonlinear cross-coupled hyperchaotic system is iterated to obtain a pseudo-random number sequence. Then the original image is scrambled using pseudo-random, and the scrambling includes row cyclic shift and column cyclic shift. The scrambled image is then bit-level diffused using a fully connected-like network. Finally, XOR the diffused image with the pseudo-random number sequence to obtain the final password image.

Description

Encryption method of quasi fully connected network image based on plaintext correlation

technical field

The invention relates to the technical field of image encryption, in particular to an image encryption method based on a plaintext correlation-like fully connected network.

Background technique

With the development of image information acquisition and processing technology, image information security has received extensive attention. It has become a hot topic in information security and cryptography. Over the past few decades, encryption methods have played a vital role in hiding sensitive information transmitted over wireless or wired networks. Unauthorized people cannot reveal secret information from encrypted data. Encryption methods have been widely used in medical, military, remote sensing and other engineering fields. At present, image information security is mainly divided into two branches. One is the optical image encryption realized by optical technology, which encrypts the image during the image acquisition process. Its core technology is optical Fourier transform. The other is digital image encryption implemented by digital computers, which encrypts images during image storage. Its core method is called scrambling and diffusion. Traditional methods such as RSA, AES, DES, etc., are also used in the encryption process. But they do not produce optimal encryption results due to the high degree of redundancy and correlation in the image data. Chaotic systems are used to encrypt images to solve the above problems. In chaos-based image encryption, a chaotic system is usually used to generate a quasi-random chaotic sequence as the key stream for scrambling and diffusion in the encryption algorithm. In this mechanism, the initial value and control parameters of the chaotic system are one of the decisive factors for the security and complexity of the encryption method.

In recent decades, image encryption algorithms based on chaotic systems have appeared in large numbers. These encryption schemes can be classified into many categories, such as deoxyribonucleic acid (DNA)-based schemes, block-based schemes, schemes based on complex chaotic systems, schemes based on special algorithms, schemes based on new scrambled diffusion structures, etc.

SUMMARY OF THE INVENTION

In order to solve the problem of poor encryption effect in existing image encryption methods, the present invention provides a quasi-full-connection network image encryption method based on plaintext correlation.

A fully connected network image encryption method based on plaintext correlation, the method is realized by the following steps:

Step 1: Select a grayscale image with a size of M×N as the original plaintext image Image, calculate the average pixel value a of the original plaintext image Image, and perform precision processing on the average pixel value a to obtain the processed pixel value.

作为初值迭代混沌系统，生成长度为m的混沌序列X，X＝{x₁x₂x₃......x_m-1x_m}；Step 2, convert the pixel value

As an initial value iterative chaotic system, a chaotic sequence X with length m is generated, X={x ₁ x ₂ x ₃ ...... x _m-1 x _m };

The chaotic sequence X is used to calculate the sequence Y= _{ y ₁ , y ₂ , y ₃ , y ₄ ,... nuclear operation;

的矩阵，MCNN；并将生成的矩阵MCNN的每个值映射到0到

的整数中,映射矩阵MCNN2的每个元素记为

After performing n convolution and pooling on the original plaintext image Image, the final generated size is

matrix, MCNN; and map each value of the resulting matrix MCNN to 0 to

In the integers of , each element of the mapping matrix MCNN2 is denoted as

后获得中间变量h₁，h₂，h₃，h₄，通过所述中间变量h₁，h₂，h₃，h₄计算混沌系统参数μ和λ，以及混沌系统的初始值x₀和y₀，计算规则如下式所示：Step 3. Calculate the mapping matrix MCNN2 obtained in step 2, and calculate

After obtaining the intermediate variables h ₁ , h ₂ , h ₃ , h ₄ , the chaotic system parameters μ and λ are calculated through the intermediate variables h ₁ , h ₂ , h ₃ , h ₄ , and the initial values of the chaotic system x ₀ and y ₀ , the calculation rule is as follows:

Where μ′ ₀ , λ′ ₀ , x′ ₀ , y′ ₀ are the given initial values;

Step 4: Obtain a chaotic sequence by adopting a nonlinear cross-coupling hyper-chaotic system, and the nonlinear cross-coupling hyper-chaotic system is represented by the following formula:

In the formula, x _j and y _j represent the value of the j-th state variable of the nonlinear cross-coupled hyperchaotic system, x _j-1 and y _j-1 are the values of the j-1-th state variable, and δ is the chaotic system control parameter;

Step 5. Use μ and λ in step 3 as the control parameters of the nonlinear cross-coupled hyperchaotic system, x ₀ , y ₀ as the initial values of the nonlinear cross-coupled hyper-chaotic system, iterate M×N times, and the generation length is M The chaotic sequences X′ and Y′ of ×N are as follows:

Step 6: Starting from the td-th element of the chaotic sequence X' generated in step 5, intercept the M' sequence with a length of M, starting from the td-th element of the chaotic sequence Y' generated in step 5, intercept N with a length of N ' sequence, sort the M' and N' sequences from small to large respectively, and obtain the index sequences INDM and INDN of M' and N' respectively;

Step 7. Use the index sequence INDM to perform row cyclic shift on the original plaintext image Image, if the gth element of the index sequence INDM is odd, then the gth row corresponding to the gth row is shifted to the left by the odd value, if the index sequence INDM has an odd value If the value of g elements is even, then the corresponding g-th row will be cyclically shifted to the right by the even-valued bit, and after the row cyclic shift is completed, the matrix Image1 will be obtained;

Use the index sequence INDN to perform a column cyclic shift on the matrix Image1. If the value of the h-th element of the index sequence INDN sequence is odd, the odd-valued bit will be cyclically shifted up corresponding to the h-th column. If the value of the h-th element of the index sequence INDN sequence is an odd number If it is an even number, the even value bit is cyclically shifted down corresponding to the hth column, and after the column cyclic shift is completed, the matrix Image2 is obtained;

Step 8: Using the chaotic sequence X' with a length of M×N generated in step 5, map each element value of the X' sequence to between 0 and 7, generate a sequence XR, and divide the sequence XR into 1 blocks, Each block has 8 elements, expressed as:

XR=XR ₁ XR ₂ XR ₃ ......XR _b-1 XR _b

Among them, b represents the block number, b=1, 2, ... l;

Step 9. Transform the single-layer fully-connected neural network to generate a single-layer fully-connected network. The single-layer fully-connected network has eight inputs and eight outputs to generate a random arrangement of elements in each row from 1 to 8. Matrix W, adopts matrix W and the XR sequence described in step 8 to generate a new sequence of eight bits as the weight of the transformed network;

Step 10. Convert the Image2 obtained in Step 7 into a one-dimensional matrix P, and divide the one-dimensional matrix P into l blocks, each with 8 elements, P=P ₁ P ₂ P ₃ P ₄ ......P _{b -1} P _b ;

The eight-bit binary representation is used for the _Pi , which is represented by the following formula:

Take P _b as the input of the fully connected network in turn, and use the XR _b sequence to cyclically shift the matrix W in step 9; the value of the e-th element of the XR _b sequence is s, and if s is an odd number, set the e-th element corresponding to the W matrix The row is shifted to the left by s elements. If s is an even number, the e-th row corresponding to the W matrix is circularly shifted to the right by s elements, and the matrix obtained after this operation is used as the weight of the fully connected network;

According to the value on the w _c sequence of each row, select each binary number of the input P _b in turn, and then put each selected binary number on each element to be output;

Finally, the eight-bit binary number of each output element is represented by a decimal number, and then the value obtained by each decimal number calculated by the activation function s-box is used as the output value of the fully connected network; each time a P _b is input, it is A PC _b is output, and all elements of the matrix P are processed by a fully connected network to obtain a one-dimensional matrix PC;

之间；生成长度为M×N的序列YR，将序列YR分割为长度分别为M×N/2的序列YR₁和YR₂；Step 11. Map the chaotic sequence Y′ generated in step 5 to 0 to

between; generate a sequence YR with a length of M×N, and divide the sequence YR into sequences YR ₁ and YR ₂ with a length of M×N/2 respectively;

The one-dimensional matrix PC={pc _t } generated in step 10 is XORed with the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t }, which is expressed as:

In the formula, XOR is the XOR function, and the matrix PC1 is obtained after the XOR;

Step 12: Convert the matrix PC1 into an M×N matrix, and the generated matrix PC2 is the final encrypted image.

Beneficial effects of the present invention: the plaintext correlation-based fully connected network image encryption method proposed by the present invention. The convolution kernel is generated by the logistic chaotic system, and the original image is convolved, pooled and activated to obtain a matrix related to the plaintext, and the key is obtained by using this matrix. Using the obtained key, the nonlinear cross-coupled hyperchaotic system is iterated to obtain a pseudo-random number sequence. Then the original image is scrambled using pseudo-random, and the scrambling includes row cyclic shift and column cyclic shift. The scrambled image is then bit-level diffused using a fully connected-like network. Finally, XOR the diffused image with the pseudo-random number sequence to obtain the final password image.

Simulation experiments show that the invention has a larger key space, can resist various attacks and has better security, and can be applied to actual image communication.

Description of drawings

Fig. 1 is a flow chart of encryption process in the method for encrypting network image based on plaintext correlation in full connection according to the present invention;

Fig. 2 is a flow chart of decryption process in the method for encrypting a network image based on a plaintext correlation-like fully connected network according to the present invention;

Fig. 3 is an effect diagram of encryption and decryption using the plaintext correlation-like fully-connected network image encryption method of the present invention: Fig. 3(a) is the original image of the "ship"; Fig. 3(b) is Fig. 3(b) The encrypted image of a); wherein Fig. 3(c) is the decrypted image of Fig. 3(a).

Fig. 4 is the histogram analysis of the method for encrypting and decrypting images based on the plaintext correlation-like fully connected network according to the present invention: Fig. 4(a) is the histogram of Fig. 3(a); Fig. 4(b) is the histogram of Fig. 3 (c) Histogram.

Detailed ways

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, the present embodiment will be described in conjunction with FIG. 1 and FIG. 2 . Based on a method for encrypting a fully connected network image related to plaintext, the method is implemented by the following steps:

Step 1. Select a grayscale image with a size of M×N as the original plaintext image Image.

Step 2: Calculate the average pixel value a of the plaintext image Image described in Step 1, as shown in the following formula (1):

代表灰度等级，M和N分别代表原始图像的高和宽。The sum() in the formula is the summation function, Image(:) is all the pixels of the original image Image,

represents the gray level, and M and N represent the height and width of the original image, respectively.

由公式(2)所示：Step 3: Perform precision processing on the average pixel value a obtained in Step 2 to obtain

It is shown by formula (2):

where floor() is a rounding down function.

作为初值迭代混沌系统，生成长度为m的混沌序列X，X＝{x₁x₂x₃......x_m-1x_m}。Step 4. The obtained step 3

As the initial value iterative chaotic system, a chaotic sequence X of length m is generated, X={x ₁ x ₂ x ₃ ...... x _m-1 x _m }.

Step 5. Use the chaotic sequence X generated in step 4 to calculate the sequence Y={y ₁ , y ₂ , y ₃ , y ₄ , ...... y _n }, each element in Y is used as a convolution kernel, The convolution operation is performed with the original image, and the calculation method of the convolution kernel is shown in formula (3):

为卷积核的大小。reshape函数是把截取的X的序列，转换成

行和

列。in,

is the size of the convolution kernel. The reshape function converts the intercepted sequence of X into

line and

List.

First, use the element y ₁ in Y to perform a convolution operation with the original image Image, as shown in formula (4):

I _1,1 =conv2(Image,y ₁ ) (4)

where conv2() is the convolution function.

Pool the convolutional matrix using the average pooling function:

I _1,2 =averagePooling(I _1,1 ) (5)

Among them, averagePooling() is the average pooling function.

Execute formulas (4) and (5) in turn in a loop to calculate the result of convolution pooling. As shown in formula (6):

where i=2,3...n,

The formulas for calculating the size of the generated matrix after each convolution and pooling are (7) and (8), respectively:

和

分别为第i次卷积和池化后的矩阵的高和宽；in,

and

are the height and width of the matrix after the i-th convolution and pooling, respectively;

的矩阵，记为MCNN。并将生成的MCNN矩阵的每个值映射到0到

的整数,映射函数由公式(9)所示：After performing n convolutions and pooling on the input original plaintext Image, the final generated size is

The matrix of , denoted as MCNN. and map each value of the resulting MCNN matrix to 0 to

, the mapping function is given by equation (9):

Convert MCNN1 to a one-dimensional matrix, as shown in formula (10):

Record each element of MCNN2 as

后获得中间变量h₁，h₂，h₃，h₄，计算过程由公式(11)所示：Step 6. Calculate the MCNN2 matrix obtained in step 5. By calculating

After obtaining intermediate variables h ₁ , h ₂ , h ₃ , h ₄ , the calculation process is shown by formula (11):

Step 7: Calculate the parameters μ and λ of the chaotic system, and the initial values x ₀ and y ₀ of the chaotic system through h ₁ , h ₂ , h ₃ , and h ₄ in step 6. The calculation rules are shown in formula (12):

Where μ′ ₀ , λ′ ₀ , x′ ₀ , y′ ₀ are given initial values.

Step 8. Use the nonlinear cross-coupling hyper-chaotic system to obtain the chaotic sequence. The chaotic system is represented by formula (13):

Among them, x _j and y _j represent the value of the jth state variable of the nonlinear cross-coupled hyperchaotic system. x _j-1 and y _j-1 are the values of the j-1 th state variable. δ is the control parameter of the chaotic system.

Step 9. Use μ and λ in Step 7 as the control parameters of the nonlinear cross-coupled hyperchaotic system, x ₀ , y ₀ as the initial values of the nonlinear cross-coupled hyper-chaotic system, iterate M×N times, and the generation length is M The chaotic sequences X′ and Y′ of ×N are shown in formula (14):

Step 10. Starting from the td-th element of the X' sequence generated in Step 9, intercept the M' sequence of length M, which is represented by formula (15):

M'=X'(td:td+M-1) (15)

Starting from the td-th element of the Y' sequence generated in step 9, the N' sequence of length N is intercepted, which is represented by formula (16):

N'=Y'(td:td+N-1) (16)

Sort the M' and N' sequences from small to large, respectively, to obtain the index sequences INDM and INDN of M' and N', and the sorting is represented by formula (17):

Step 11. Use the INDM sequence to perform a row cyclic shift on the original image. If the value of the gth element of the INDM sequence is an odd number, the odd value position will be cyclically shifted to the left corresponding to the gth row. If the value of the gth element of the INDM sequence is an odd number If it is an even number, the corresponding g-th row will be shifted to the right by the even-valued bits, and the matrix Image1 will be obtained after the row cyclic shift is completed.

Step 12. Use the INDN sequence to cyclically shift the columns and rows of the matrix Image1. If the value of the hth element of the INDN sequence is an odd number, the odd value will be shifted up corresponding to the hth column. If the value of the hth element of the INDN sequence is an odd number, The even number will be cyclically shifted down corresponding to the hth column, and the matrix Image2 will be obtained after the column cyclic shift is completed. h=1,2,3,4,...N;

Step 13: Use the chaotic sequence X′ with a length of M×N generated in step 9. Map each element value of the X' sequence to a value between 0 and 7, as shown by Equation (18):

XR=mod(floor(X′×10 ^x , 8) (18)

Divide the sequence XR into l blocks, each with 8 elements, expressed by formula (19):

XR=XR ₁ XR ₂ XR ₃ ......XR _b-1 XR _b (19)

Among them, b represents the block number, b=1, 2, ... l;

Step 14. Transform the single-layer fully-connected neural network. The fully-connected neural network is the most basic neural network structure. Every node in the neural network except the input layer is connected to all nodes in the previous layer. . The transformed network has 8 inputs and 8 outputs, and generates a matrix W whose elements in each row are randomly arranged from 1 to 8. The c-th row w _c of W is shown by formula (20):

w _c = randperm(8) (20)

where randperm(8) is to generate a random sequence of 1 to 8.

Use W and the XR sequence described in step 13 to generate a new sequence of 8 bits as the weight of the network, and use an improved s-box algorithm as the activation function of the network. A single-layer fully-connected network is generated by transforming the single-layer fully-connected neural network, and the network is used to diffuse the image at the bit level;

Step 15: Convert the Image2 obtained in step 12 into a one-dimensional matrix, and the conversion formula is (21):

P=reshape(Image2, 1, M*N) (21)

Divide P into l blocks, each with 8 elements, represented by formula (22):

P=P ₁ P ₂ P ₃ P ₄ ......P _b-1 P _b (22)

Step 16: Use the 8-bit binary representation of _Pi described in Step 15, as shown by formula (23):

Take P _b as the input of the fully connected network in turn. The matrix W of step fourteen is cyclically shifted using the XR _b sequence in turn. The value of the e-th element of the XR _b sequence is s. If s is an odd number, the e-th row corresponding to the W matrix is shifted to the left by s elements. If s is an even number, the j-th row corresponding to the W matrix is rotated to the right by s elements. , and use the matrix obtained after this operation as the weight of the fully connected network.

According to the value of each row w _c sequence, select each binary digit of input P _b in turn, and then put each selected digit on each element to be output. Finally, the 8-bit binary number of each output element is represented by a decimal number, and then each decimal number is calculated by the activation function s-box to obtain the value as the output value of the fully connected network. Each time a P is input, a PC _b is output, and all elements of P are processed by a fully connected network to obtain a one-dimensional matrix PC.

之间。由公式(24)表示：Step seventeen, map the Y' sequence generated in step eight to 0 to

between. It is represented by formula (24):

Step 18: Divide the sequence YR of length M×N in step 17 into sequences YR ₁ and YR ₂ of length M×N/2, which are represented by formula (25):

Step 19, use the one-dimensional matrix PC={pc _t } generated in step 16 and the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t } generated in step 18 to perform XOR, according to formula (26) shown:

where XOR is the exclusive OR function. The PC1 matrix obtained after XORing.

Step 20: Convert the PC1 matrix generated in Step 19 into a matrix of size M×N, as shown by formula (27):

PC2=reshape(PC1, M, N) (27)

The converted matrix PC2 is the final encrypted image.

In this embodiment, it also includes a decryption step, specifically:

Step 21: Use μ, λ, x ₀ , y ₀ in step 7 and δ of the given initial value to obtain pseudo-random sequences INDM, INDN, XR, YR ₁ and YR ₂ .

Step 22, use the matrix W generated in step 14.

Step 23: Convert the encrypted image PC2 obtained in step 20 into a one-dimensional matrix, the method is as formula (28):

PC1=reshape(PC2, 1, M×N) (28)

Step 24: Perform XOR operation on the one-dimensional matrix PC1={PC1 _jt } obtained in step 23 and the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t } generated in step 21, method As shown in formula (29):

The PC matrix is obtained after XORing.

Step 25: Divide the PC matrix obtained in step 24 into l blocks, each of which has 8 elements, represented by formula (30):

PC = PC ₁ PC ₂ PC ₃ PC ₄ ..., ... PC _t-1 PC _t (30)

Wherein, t represents the block number, t=1, 2, . . . l.

In step 26, the PC _t obtained in step 25 is sequentially input into the fully connected network described in step 14, and the inverse operation is performed. Input each element of PC _t into the inverse fully connected network in turn, first use each value of PC _t as an 8-bit binary representation, and use the XR _i sequence to modify the value of w _c in each row of the W matrix, according to the value of w _c The number of corresponding positions of the input PC _t is selected, and finally a _Pb sequence of 8 elements is generated. The P matrix is obtained by processing all elements of the PC through an inverse fully connected network.

Step 27: Convert the P matrix obtained in step 24 into a matrix of M×N size, as shown by formula (31):

Image2=reshape(P, M, N) (31)

Step 28: Perform an inverse cyclic shift operation on the Image2 matrix and the INDM and INDN sequences obtained in step 27. First perform the inverse column cyclic shift to obtain the Image1 matrix, and then obtain the Image matrix through the inverse row cyclic shift. The Image matrix is the resulting decrypted image.

1 to 4, this embodiment is an example of the encryption method based on the plaintext correlation-like fully connected network image described in the specific embodiment 1:

Step 1. Select a grayscale image with a size of 512×512 as the original plaintext image Image. As shown in Figure 3(a).

Step 2: Calculate the average pixel value a of the plaintext image Image described in Step 1, as shown in the following formula (1):

a=sum(Image(:))/((2 ⁸ -1)×512×512) (1)

In the formula, sum() is the summation function, Image(:) is all the pixels of the original image Image, n represents the gray level, and M and N represent the height and width of the original image, respectively.

由公式(2)所示：Step 3: Perform precision processing on the average pixel value a obtained in Step 2 to obtain

It is shown by formula (2):

where floor() is a rounding down function.

作为初值迭代混沌系统，生成长度为1000的混沌序列X，X＝{x₁x₂x₃......x₉₉₉x₁₀₀₀}。混沌系统由公式(3)所示：Step 4. The obtained step 3

As an initial value iterative chaotic system, a chaotic sequence X with a length of 1000 is generated, X={x ₁ x ₂ x ₃ ...... x ₉₉₉ x ₁₀₀₀ }. The chaotic system is represented by formula (3):

x(i+1)=u×x(i)×(1-x(i)) (3)

Among them, u is a control parameter, and in this embodiment, u=3.99. x _i is the chaotic state variable value of the i-th chaotic system of the chaotic system, and x _i+1 is the i+1-th chaotic state variable value of the chaotic system.

Step 5. Use the chaotic sequence X generated in step 4 to calculate the sequence Y={y ₁ , y ₂ , y ₃ , y ₄ , ...... y _n }, each element in Y is used as a convolution kernel, The convolution operation is performed with the original image, and the calculation method of the convolution kernel is shown in formula (4):

The sizes of the convolution kernels in this embodiment are 11×11 and 12×12, respectively.

Convolve with the original image Image using the elements in Y in turn, as shown in formula (5):

I _{i, 1} =conv2(Image, y _i ) (5)

where conv2() is the convolution function.

Pool the convolutional matrix using the average pooling function:

I _{i, 2} = averagePooling(I _{i, 1} ) (6)

Among them, averagePooling() is the average pooling function.

where i=1, 2, ... 5, and execute formulas (5), (6) in sequence,

The formulas for calculating the size of the generated matrix after each convolution and pooling are (7) and 8(), respectively:

和

分别为第i次卷积和池化后的矩阵的高和宽。in

and

are the height and width of the matrix after the i-th convolution and pooling, respectively.

After 5 times of convolution, pooling and activation of the input original plaintext Image, a matrix of size 6 × 6 is finally generated, which is recorded as MCNN. And map each value of the generated MCNN matrix to an integer from 0 to 255, the mapping function is shown by formula (9):

MCNN1=mod(floor(MCNN/10 ²⁰ ), 2 ⁸ ) (9)

Convert MCNN1 to a one-dimensional matrix, as shown in formula (10):

MCNN2=reshape(MCNN1, 1, 36) (10)

Denote each element of MCNN2 as {k ₁ k ₂ k ₃ ......k ₃₆ }

Step 6: Calculate the MCNN2 matrix obtained in step 5, and obtain intermediate variables h ₁ , h ₂ , h ₃ , h ₄ by calculating k ₁ k ₂ k ₃ ...... k ₃₆ , the calculation process is determined by the formula ( 11) shown:

Step 7: Calculate the parameters μ and λ of the chaotic system, and the initial values x ₀ and y ₀ of the chaotic system through h ₁ , h ₂ , h ₃ , and h ₄ in step 6. The calculation rules are shown in formula (12):

Wherein, in this embodiment, μ′ ₀ =3.0, λ′ ₀ =4.5, x′ ₀ =0.4, and y′ ₀ =0.5.

Step 8. Use the nonlinear cross-coupling hyper-chaotic system to obtain the chaotic sequence. The chaotic system is represented by formula (13):

Among them, x _j and y _j represent the value of the jth state variable of the nonlinear cross-coupled hyperchaotic system. x _j-1 and y _j-1 are the values of the j-1 th state variable. δ is the control parameter of the chaotic system, and δ=9.999 in this embodiment.

Step 9. Use μ and λ obtained in Step 7 as the control parameters of the nonlinear cross-coupling hyperchaotic system, x ₀ , y ₀ as the initial values of the nonlinear cross-coupling hyper-chaotic system, and iterate 512×512 times to generate a length of are the chaotic sequences X′ and Y′ of 512×512, as shown in formula (14):

Step 10. Starting from the 3000th element of the X' sequence generated in step 9, intercept the M' sequence of length M, which is represented by formula (15):

M'=X'(3000:3000+512-1) (15)

Starting from the 5000th element of the Y' sequence generated in step 9, intercept the N' sequence of length N, which is represented by formula (16):

N'=Y'(5000:5000+512-1) (16)

Sort the M' and N' sequences from small to large, respectively, to obtain the index sequences INDM and INDN of M' and N', and the sorting is represented by formula (17):

Step 11. Use the INDM sequence to perform a row cyclic shift on the original image. If the i-th element value of the INDM sequence is an odd number, the corresponding i-th row will be cyclically shifted to the left by the odd value bit. If the INDM sequence's first element value is If the number is even, the even-valued bits will be shifted to the right of the i-th row, and the matrix Image1 will be obtained after the row cyclic shift is completed.

Step 12. Use the INDN sequence to perform a column-row cyclic shift on the matrix Image1. If the i-th element value of the INDN sequence is an odd number, the odd-valued bit will be cyclically shifted up corresponding to the i-th column. If the i-th element value of the INDN sequence is an odd number, The even number will be cyclically shifted down the even-valued bits corresponding to the first column, and the matrix Image2 will be obtained after the column cyclic shift is completed.

Step 13, use the chaotic sequence X' with a length of 512×512 generated in step 9. Map each element value of the X' sequence to a value between 0 and 7, as shown by Equation (18):

XR=mod(floor(X′×10 ⁴ , 8) (18)

Divide the sequence XR into 512×512/8 blocks, each block has 8 elements, which is represented by formula (19):

XR=XR ₁ XR ₂ XR ₃ ... XR _i ... XR ₃₂₇₆₇ XR ₃₂₇₆₈ (19)

Step 14. Transform the single-layer fully-connected neural network. The fully-connected neural network is the most basic neural network structure. Every node in the neural network except the input layer is connected to all nodes in the previous layer. . Generate a matrix W of size 8 × 8 in which each row of elements is randomly arranged from 1 to 8, and the c-th row w _c of W is given by formula (20):

w _c = randperm(8) (20)

where randperm(8) is to generate a random sequence of 1 to 8.

The transformed network has 8 inputs and 8 outputs. Use W and the XR sequence described in step 13 to generate a new sequence of 8 bits as the weight of the network, and use an improved s-box algorithm as the activation function of the network. A single-layer fully-connected network is generated by transforming a single-layer fully-connected neural network, and the network is used to diffuse images at the bit level;

Step 15: Convert the Image2 obtained in step 12 into a one-dimensional matrix, and the conversion formula is (21):

P=reshape(Image2, 1, 512×512) (21)

Divide P into 512×512/8 blocks, each with 8 elements, represented by formula (22):

P=P ₁ P ₂ P ₃ P ₄ ...P _i ...P ₃₂₇₆₇ P ₃₂₇₆₈ (22)

Step 16: Use 8-bit binary representation of P _b described in Step 15, as shown by formula (23):

Take P _b as the input of the fully connected network in turn. The matrix W of step fourteen is cyclically shifted using the XR _b sequence in turn. The value of the b-th element of the XR _b sequence is s. If s is an odd number, the i-th row corresponding to the W matrix is shifted to the left by s elements; if s is an even number, the c-th row corresponding to the W matrix is rotated to the right by s elements. , and use the matrix obtained after this operation as the weight of the fully connected network. According to the value of each row w _c sequence, select each binary digit of input P _b in turn, and then put each selected digit on each element to be output. Finally, the 8-bit binary number of each output element is represented by a decimal number, and then each decimal number is calculated by the activation function s-box to obtain the value as the output value of the fully connected network. Each time a P _b is input, a PC _b is output, and all elements of P are processed by a quasi-fully connected network to obtain a one-dimensional matrix PC.

Step 17: Map the Y' sequence generated in step 8 to between 0 and 255. It is represented by formula (24):

YR=mod(floor(Y′×10 ⁴ , 2 ⁸ )) (24)

Step 18: Divide the sequence YR with a length of 512×512 in Step 17 into sequences YR ₁ and YR ₂ with a length of 512×512/2, which are represented by formula (25):

Step 19, use the one-dimensional matrix PC={pc _t } generated in step 16 and the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t } generated in step 18 to perform XOR, according to formula (26) shown:

where XOR is the exclusive OR function. The PC1 matrix obtained after XORing.

Step 20: Convert the PC1 matrix generated in Step 19 into a matrix of size 512×512, as shown by formula (27):

PC2=reshape(PC1, 512, 512) (27)

The converted matrix PC2 is the final encrypted image.

Decryption steps:

Step 21: Use μ, λ, x ₀ , y ₀ in step 7 and δ of the given initial value to obtain pseudo-random sequences INDM, INDN, XR, YR ₁ and YR ₂ .

Step 22, use the matrix W generated in step 14.

Step 23: Convert the encrypted image PC2 obtained in step 20 into a one-dimensional matrix, the method is as formula (28):

PC1=reshape(PC2, 1, M×N) (28)

Step 24: Perform XOR operation on the one-dimensional matrix PC1={PC1 _t } obtained in step 23 and the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t } generated in step 21, method As shown in formula (29):

The PC matrix is obtained after XORing.

Step 25: Divide the PC matrix obtained in step 24 into l blocks, each of which has 8 elements, represented by formula (30):

PC = PC ₁ PC ₂ PC ₃ PC ₄ ..., ... PC _t-1 PC _t (30)

Wherein, t represents the block number, t=1, 2, . . . l.

In step 26, the PC _t obtained in step 25 is sequentially input into the fully connected network described in step 14, and the inverse operation is performed. Input each element of PC _t into the inverse fully connected network in turn, first use each value of PC _t as an 8-bit binary representation, and use the XR _b sequence to modify the value of w _c in each row of the W matrix, according to the value of w _c Select the number of corresponding positions of the input PC _t , and finally generate a _Pb sequence of 8 elements. The P matrix is obtained by processing all elements of the PC through an inverse fully connected network.

Step 27: Convert the P matrix obtained in step 24 into a matrix of M×N size, as shown by formula (31):

Image2=reshape(P, M, N) (31)

Step 28: Perform an inverse cyclic shift operation on the Image2 matrix and the INDM and INDN sequences obtained in step 27. First perform the inverse column cyclic shift to obtain the Image1 matrix, and then obtain the Image matrix through the inverse row cyclic shift. The Image matrix is the resulting decrypted image.

Claims (5)

1. the encryption method based on the relevant class fully connected network image of plaintext, it is characterized in that: this method is realized by the following steps: Step 1: Select a grayscale image with a size of M×N as the original plaintext image Image, calculate the average pixel value a of the original plaintext image Image, and perform precision processing on the average pixel value a to obtain the processed pixel value.

Step 2, convert the pixel value

As the initial value iterative chaotic system, a chaotic sequence X with length m is generated, X={x ₁ x ₂ x ₃ ...... x _m-1 x _m }; The chaotic sequence X is used to calculate the sequence Y= _{ y ₁ , y ₂ , y ₃ , y ₄ ,... nuclear operation; After performing n convolution and pooling on the original plaintext image Image, the final generated size is

matrix, MCNN; and map each value of the resulting matrix MCNN to 0 to

In the integers of , each element of the mapping matrix MCNN2 is denoted as

Step 3: Calculate the mapping matrix MCNN2 obtained in step 2, and calculate

After obtaining the intermediate variables h ₁ , h ₂ , h ₃ , h ₄ , the chaotic system parameters μ and λ are calculated through the intermediate variables h ₁ , h ₂ , h ₃ , h ₄ , and the initial values of the chaotic system x ₀ and y ₀ , the calculation rule is as follows:

Where μ′ ₀ , λ′ ₀ , x′ ₀ , y′ ₀ are the given initial values; Step 4: Obtain a chaotic sequence by adopting a nonlinear cross-coupling hyper-chaotic system, and the nonlinear cross-coupling hyper-chaotic system is represented by the following formula:

In the formula, x _j and y _j represent the value of the j-th state variable of the nonlinear cross-coupled hyperchaotic system, x _j-1 and y _j-1 are the values of the j-1-th state variable, and δ is the chaotic system control parameter; Step 5. Use μ and λ in step 3 as the control parameters of the nonlinear cross-coupled hyperchaotic system, x ₀ , y ₀ as the initial values of the nonlinear cross-coupled hyper-chaotic system, iterate M×N times, and the generation length is M The chaotic sequences X′ and Y′ of ×N are as follows:

Step 6: Starting from the td-th element of the chaotic sequence X' generated in step 5, intercept the M' sequence with a length of M, starting from the td-th element of the chaotic sequence Y' generated in step 5, intercept N with a length of N ' sequence, sort the M' and N' sequences from small to large respectively, and obtain the index sequences INDM and INDN of M' and N' respectively; Step 7. Use the index sequence INDM to perform row cyclic shift on the original plaintext image Image, if the gth element of the index sequence INDM is odd, then the gth row corresponding to the gth row is shifted to the left by the odd value, if the index sequence INDM has an odd value If the value of g elements is even, then the corresponding gth row will be cyclically shifted to the right by the even-valued bit, and after the row cyclic shift is completed, the matrix Image1 will be obtained; Use the index sequence INDN to perform a column cyclic shift on the matrix Image1. If the value of the h-th element of the index sequence INDN sequence is odd, the odd-valued bit will be cyclically shifted up corresponding to the h-th column. If the value of the h-th element of the index sequence INDN sequence is an odd number If it is an even number, the even value bit is cyclically shifted down corresponding to the hth column, and after the column cyclic shift is completed, the matrix Image2 is obtained; Step 8: Using the chaotic sequence X' with a length of M×N generated in step 5, map each element value of the X' sequence to between 0 and 7, generate a sequence XR, and divide the sequence XR into 1 blocks, Each block has 8 elements, expressed as: XR=XR ₁ XR ₂ XR ₃ ......XR _b-1 XR _b Among them, b represents the block number, b=1, 2, ... l; Step 9. Transform the single-layer fully-connected neural network to generate a single-layer fully-connected network. The single-layer fully-connected network has eight inputs and eight outputs to generate a random arrangement of elements in each row from 1 to 8. Matrix W, adopts matrix W and the XR sequence described in step 8 to generate a new sequence of eight bits as the weight of the transformed network; Step 10. Convert the Image2 obtained in Step 7 into a one-dimensional matrix P, and divide the one-dimensional matrix P into l blocks, each with 8 elements, P=P ₁ P ₂ P ₃ P ₄ ......P _{b -1} P _b ; The eight-bit binary representation is used for the _Pi , which is represented by the following formula:

Take P _b as the input of the fully connected network in turn, and use the XR _b sequence to cyclically shift the matrix W in step 9; the value of the e-th element of the XR _b sequence is s. If s is an odd number, set the e-th element corresponding to the W matrix. The row is shifted to the left by s elements. If s is an even number, the e-th row corresponding to the W matrix is circularly shifted to the right by s elements, and the matrix obtained after this operation is used as the weight of the fully connected network; According to the value on the w _c sequence of each row, select each binary number of the input P _b in turn, and then put each selected binary number on each element to be output; Finally, the eight-bit binary number of each output element is represented by a decimal number, and then the value obtained by each decimal number calculated by the activation function s-box is used as the output value of the fully connected network; each time a P _b is input, it is A PC _b is output, and all elements of the matrix P are processed by a fully connected network to obtain a one-dimensional matrix PC; Step 11. Map the chaotic sequence Y′ generated in step 5 to 0 to

between; generate a sequence YR with a length of M×N, and divide the sequence YR into sequences YR ₁ and YR ₂ with a length of M×N/2 respectively; The one-dimensional matrix PC={pct} generated in step 10 is XORed with the sequence of YR ₁ ={yr _1t } and YR ₂ ={yr _2t }, which is expressed as:

In the formula, XOR is the XOR function, and the matrix PC1 is obtained after the XOR; Step 12: Convert the matrix PC1 into an M×N matrix, and the generated matrix PC2 is the final encrypted image. 2. the encryption method based on the relevant class fully connected network image of plaintext according to claim 1, it is characterized in that: in step 2, the calculation method of convolution kernel is represented by following formula as:

In the formula,

is the size of the convolution kernel; reshape is the interception function; First, use the element y ₁ in Y to perform a convolution operation with the original plaintext image Image, which is expressed as: I _1,1 =conv2(Image,y ₁ ) where conv2() is the convolution function; The convolutional matrix is pooled using the average pooling function: I _1,2 =averagePooling(I _1,1 ) Among them, averagePooling() is the average pooling function; Execute the above two formulas in turn, and then calculate the result of the convolution pooling, as follows:

Among them, i=2, 3...n, I _i,1 , is the result of the ith convolution, I _i,2 , is the result of the ith pooling, I _i-1,2 , represents the ith - The result after 1 pooling; The formulas for calculating the size of the generated matrix after each convolution and pooling are as follows:

In the formula,

and

are the height and width of the matrix after the i-th convolution, respectively;

and

are the height and width of the matrix after the i-th pooling, respectively; After performing n convolutions and pooling on the input original plaintext image Image, the final generated size is

the matrix of MCNN; and map each value of the resulting MCNN matrix to 0 to

Between integers of , the mapping function is expressed as:

Convert the matrix MCNN1 to a one-dimensional matrix MCNN2, as follows:

Denote each element of the one-dimensional matrix MCNN2 as

3. The encryption method based on plaintext correlation class fully connected network image according to claim 1, is characterized in that: the intermediate variables h ₁ , h ₂ , h ₃ , h ₄ described in step 3, the calculation process is:

4. The encryption method based on plaintext correlation-like fully connected network images according to claim 1, characterized in that: the lengths described in step 11 are respectively M×N/2 sequences YR ₁ and YR ₂ , by the following The formula is expressed as:

5. the encryption method based on the relevant class fully connected network image of plaintext according to claim 1, is characterized in that: also comprises decryption step, is specially: Step A. Use μ, λ, x ₀ , y ₀ in step 3 and δ of a given initial value to obtain pseudo-random sequences NINDM, NINDN, NXR, NYR ₁ according to the same method as step 6, step 8 and step 11 and NYR ₂ ; Step B, use the matrix W that step 9 generates; The encrypted image PC2 that generates in step 12 is converted into one-dimensional matrix PC1, and the following formula is: PC1=reshape(PC2, 1, M×N) Step C, perform XOR operation on the one-dimensional matrix PC1={PC1 _t } obtained in step B and YR ₁ ={yr _1t } and YR ₂ ={yr _2t } sequence generated in step A to obtain matrix PC; Step D, the obtained matrix PC is divided into 1 blocks, each block has 8 elements, and the following formula is used to express as: PC = PC ₁ PC ₂ PC ₃ PC ₄ ..., ... PC _b-1 PC _b Step E, input PC _b to the class fully connected network of step 9 successively, and carry out inverse operation; Input each element of PC _b into the inverse fully connected network in turn, first use each value of PC _b as an 8-bit binary representation, and use the XR _b sequence to modify the value of w _c in each row of the W matrix, according to the value of w _c Select the number of the corresponding positions of the input PC _b , and finally generate a P _b sequence of 8 elements; after all the elements of the PC are processed by the inverse class fully connected network, the matrix P is obtained; Step F, convert the obtained matrix P into a matrix Image2 of M×N size; Step G. Perform an inverse cyclic shift operation on the obtained matrix Image2 and the NINDM and NINDN sequences in step A, first perform an inverse column cyclic shift to obtain the Image1 matrix, and then obtain an Image matrix through an inverse row cyclic shift, Image The matrix is the decrypted image.

Images