CN116707754A - A digital image encryption method based on five-dimensional non-equilibrium point hyperchaos - Google Patents

Abstract

The invention discloses a digital image encryption method based on five-dimensional non-balance point hyperchaotic system, which relates to a digital image encryption method, wherein proper parameters and initial values are selected for the five-dimensional non-balance point hyperchaotic system, and a chaotic password generation module is realized to generate five random matrixes by a specific method so as to prepare for the diffusion and scrambling of the following D; forward diffusion treatment is carried out on the original plaintext image P, and the plaintext P is converted into a matrix R; scrambling is carried out on the matrix R, and the positions of the pixel points are replaced; and (3) marking the scrambled image as D, performing reverse diffusion treatment, and converting the matrix D into a matrix C to generate a ciphertext image. The encryption method solves the problems that the encryption process is simple, the encryption time is long, and the plaintext attack or the selective plaintext attack is difficult to resist in the existing method. The method has the advantages of sufficient security, confusion and strong attack resistance, high encryption speed and obvious advantage utilization value.

Description

A digital image encryption method based on five-dimensional non-equilibrium point hyperchaos

technical field

The invention relates to a digital image encryption method in the field of information security, in particular to a digital image encryption method based on five-dimensional non-equilibrium point hyperchaos.

Background technique

With the continuous development of technology and Internet transmission, the demand for information security in real life is becoming more and more urgent. At the same time, more and more attention has been paid to the security issues in the process of information storage and transmission. Due to the unique essential characteristics of the initial value sensitivity and unpredictability of the chaotic system, the chaotic system has great application value, one of which is very suitable for digital image encryption.

At present, the encryption method of digital image is not only time-consuming, but also difficult to meet the encryption requirements of modern digital image with large amount of data, high redundancy and high correlation between data points. Chaotic systems generally have lower dimensions and simpler dynamics, which lead to relatively predictable behavior. The attacker can deduce the key parameters or keys of the encryption by analyzing the dynamics of the system or by observing a small number of ciphertext and plaintext pairs, so as to crack the encryption. The dynamics of the five-dimensional non-equilibrium hyperchaotic system are very complex, with a high degree of chaos and randomness. This makes it difficult for attackers to predict the behavior of the system and keys, improving the security of encryption. Compared with the low-dimensional chaotic system, the five-dimensional non-equilibrium hyper-chaotic system is more unpredictable, which increases the difficulty of cracking.

Contents of the invention

The purpose of the present invention is to provide a digital image encryption method based on five-dimensional non-equilibrium point hyperchaos, which uses the random sequence of hyperchaotic hidden attractors to scramble and diffuse the plaintext to obtain ciphertext similar to random noise, This method improves the key sensitivity and has the advantages of high security, fast encryption speed, adaptability and flexibility, and anti-noise performance.

The technical scheme adopted in the present invention is as follows:

A digital image encryption method based on five-dimensional non-equilibrium point hyperchaos, the steps of the method are as follows:

Step 1, by selecting appropriate parameters and initial values for the five-dimensional non-equilibrium point hyperchaotic system, the chaotic password generation module generates five random matrices through a specific method to prepare for the subsequent diffusion and scrambling of D;

Step 1 is specifically implemented according to the following steps:

Step 1.1, take [x ₀ ,y ₀ ,z ₀ ,u ₀ ,v ₀ ] as the initial value of the five-dimensional non-equilibrium hyper-chaotic system, and take [0.1,0.1,-5,2.5,2], where the five-dimensional The non-equilibrium point hyperchaotic system (1) is as follows:

In system (1), b and c are the control parameters of the system, x, y, z, u, v are the state variables of the system, and the given plaintext gray image P has a size of M×N, and the Runge-Kutta algorithm is used to Iterate MN+r times, where r=r ₁ +r ₂ +r ₃ +r ₄ , remove the previous r values, and get a variable sequence {x _i },{y _i },{z _i },{ w _i },{v _i }, i=1,2,...MN;

Step 1.2, calculate the last digit of the sequence {x _i },{y _i },{z _i },{w _i },{v _i }, as follows:

The function of formula (2) is to limit the size of x _MN , y _MN , z _MN , w _MN , and v _MN to [-10,10];

Step 1.3, will As the initial value of system (1), iterate MN+r times, at this time, r=r ₅ +r ₂ +r ₃ +r ₄ , remove the previous r values, and obtain a variable sequence with length MN/>

Step 1.4, perform the following operations on the state sequence in the above steps to obtain five random matrices X, Y, Z, W, V, X, V for the forward diffusion module, Y, V for the reverse diffusion module, Z, W is used to scramble the module;

u=1,2,...M, v=1,2,...N. X, V are used for forward diffusion module, Y, V are used for reverse diffusion module, Z, W are used for scrambling module;

Step 2, perform forward diffusion processing on the original plaintext image P, and convert the plaintext P into a matrix R; Step 2 is specifically as follows

Follow the steps below to implement:

Step 2.1, convert P(1,j) into R(1,j), j=2,3,...N;

R(1,1)＝mod(P(1,1)+X(1,1)+V(1,1)+r ₁ +r ₃ +r ₅ ,256) (4)

R(1,j)=mod(P(1,j)+X(1,j)+R(1,j-1)+V(1,j),256) (5)

Step 2.2, converting P(i,1) into R(i,1), i=2,3,...M;

R(i,1)=mod(P(i,1)+X(i,1)+V(i,1)+R(i-1,1),256) (6)

Step 2.3, converting P(i,j) into R(i,j), i=2,3,...M, j=2,3,...N;

R(i,j)=mod(P(i,j)+X(i-1,j)+V(i,j)+R(i,j-1)+R(i-1,j), 256) (7)

Step 3, scrambling the matrix R, and replacing the pixel points in step 2;

Step 3 is specifically implemented according to the following steps:

Step 3.1, calculate the sum of all elements (excluding R(i,j)) in the row where R(i,j) is located, denoted as rs _i , namely

rs _i = sum(R(i,1:N))-R(i,j) (8)

Step 3.2, calculate the sum of all elements (excluding R(i,j)) in the column where R(i,j) is located, denoted as cs _j

cs _j = sum(R(1:M,j))-R(i,j) (9)

Step 3.3, Calculation Parameters value;

Step 3.4, according to step 3.1 to step 3.3, first scramble the element R(M,1:N-1), then scramble the element R(1:M-1,N), and then from top to bottom from left to right Shuffle the element R(1:M-1,1:N-1), and finally shuffle the element R(M,N);

Step 4, denote the image obtained after scrambling as D, perform reverse diffusion processing, convert matrix D to matrix C, and generate a ciphertext image;

Step 4 is specifically implemented according to the following steps:

Step 4.1, converting D(M,j) into C(M,j), j=N-1, N-2,...1;

C(M,N)=mod(D(M,N)+Y(M,N)+V(M,N)+r ₂ +r ₄ +r ₅ ,256) (12)

C(M,j)=mod(D(M,j)+Y(M,j)+V(M,j)+C(M,j+1),256) (13)

Step 4.2, converting D(i, N) into C(i, N), i=M-1, M-2,...1;

C(i,N)=mod(D(i,N)+Y(i,N)+V(i,N)+C(i+1,N),256) (14)

Step 4.3, D(i, j) is transformed into C(i, j), j=N-1, N-2...1, i=M-1, M-2,...1;

C(i,j)=mod(D(i,j)+Y(i,j)+V(i,j)+C(i+1,j)+C(i,j+1),256) (15)

Through the reverse diffusion process from step 4.1 to step 4.3, the ciphertext matrix C is obtained, that is, the encrypted image is obtained.

The obvious effect of the present invention is as follows:

(1) The present invention is an image encryption method based on a five-dimensional non-equilibrium hyper-chaotic system. The five-dimensional non-equilibrium hyper-chaotic system is a highly complex and unpredictable system with extremely high security. Its nonlinear dynamics and random nature make it difficult for attackers to crack or reverse engineer the algorithm, thereby protecting the confidentiality of the image.

(2) An image encryption method based on a five-dimensional non-equilibrium hyper-chaotic system of the present invention, the algorithm utilizes a five-dimensional hyper-chaotic system to encrypt images by introducing five state variables. The interaction and chaotic behavior among these variables lead to complex confusion among image pixels, making the encrypted image no longer have obvious correlation in visual and statistical properties, increasing the difficulty for attackers to decrypt.

(3) An image encryption method based on a five-dimensional non-equilibrium hyperchaotic system of the present invention generates five random matrices, one of which is reflected in forward and reverse diffusion, and each random matrix can be viewed The operation is to perturb and confuse the image in different dimensions. By introducing five random matrices, image pixels can be manipulated in a wider range of dimensions, increasing the difficulty and complexity of encryption.

(4) An image encryption method based on a five-dimensional non-equilibrium hyperchaotic system of the present invention can increase randomness, dimension and confusion, and provide higher security and ability to resist attacks. This method can strengthen the confidentiality of the image, making the encrypted image more secure and difficult to be cracked.

Description of drawings

In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the description of the specific embodiments or the prior art.

Fig. 1 is the image encryption flowchart of encryption method of the present invention;

Fig. 2 is the five-dimensional non-equilibrium hyperchaotic attractor graph of encryption method of the present invention;

Fig. 3 is a five-dimensional non-equilibrium hyperchaotic system circuit simulation diagram of the encryption method of the present invention;

Fig. 4 is " Baboon " encryption and decryption figure of encryption method of the present invention;

Fig. 5 is a histogram of the encryption method of the present invention;

Fig. 6 is a pixel correlation analysis diagram of the encryption method of the present invention;

Fig. 7 is a key sensitivity test diagram of the encryption method of the present invention.

Detailed ways

The technical solution of the present invention will be described in further detail below in conjunction with the accompanying drawings.

An image encryption method based on a five-dimensional non-equilibrium hyperchaotic system of the present invention, as shown in Figure 1, the specific implementation steps are as follows:

Step 1, by selecting appropriate parameters and initial values for the five-dimensional non-equilibrium point hyperchaotic system, the chaotic password generation module generates five random matrices through a specific method to prepare for the subsequent diffusion and scrambling of D;

Step 1 is specifically implemented according to the following steps:

Step 1.1, take [x ₀ ,y ₀ ,z ₀ ,u ₀ ,v ₀ ] as the initial value of the five-dimensional non-equilibrium hyper-chaotic system, and take [0.1,0.1,-5,2.5,2], where the five-dimensional The non-equilibrium point hyperchaotic system (1) is as follows:

In the system (1), b and c are the control parameters of the system, x, y, z, u, v are the state variables of the system, x=0, y=0 are obtained from 35x=0, x+y=0, and are substituted into 2y ² -xu-28.45, cannot satisfy the condition of equality, so the system (1) has no equilibrium point.

When the fixed parameter b=c=1 and the initial value is (0.1,0.1,-5,2.5,2), the partial phase locus diagrams of system (1) are shown in Fig. 2(a) and Fig. 2(b).

The fixed parameter b=1, the initial value selection (0.1,0.1,-5,2.5,2), when c=0.25, the five-dimensional non-equilibrium point hyperchaotic system (1) attractor type is shown in Figure 2(c) that is periodic attractor;

When c=0.15, the five-dimensional non-equilibrium point hyperchaotic system (1) attractor type is the four-period attractor in Figure 2(d);

When c=0.17, the attractor type of the five-dimensional non-equilibrium hyperchaotic system (1) is the quasi-periodic attractor in Figure 2(e);

When c=0.30, the five-dimensional non-equilibrium hyperchaotic system (1) attractor type is shown in Figure 2(f), which is the chaotic attractor;

When c=0.50, the attractor type of the five-dimensional non-equilibrium hyperchaotic system (1) is the hyperchaotic attractor in Figure 2(g);

The Lyapunov exponent and attractor type when c takes different values are shown in Table 1:

Table 1 Lyapunov exponent and attractor type when c takes different values

Using the system (1) shown above, the fixed parameters b=1, c=0.50, the initial value selection (0.1,0.1,-5,2.5,2), considering the given plaintext grayscale image P size is M×N , use the Runge-Kutta algorithm to iterate MN+r times, where r=r ₁ +r ₂ +r ₃ +r ₄ , remove the previous r values, and obtain a variable sequence {xi }, { _{y i of} length MN },{z _i },{w _i },{v _i }, i=1,2,...MN.

Step 1.2, calculate the last digit of the sequence {x _i },{y _i },{z _i },{w _i },{v _i }, as follows:

The function of formula (2) is to limit the sizes of x _MN , y _MN , z _MN , w _MN , and v _MN to [-10,10].

Step 1.3, will As the initial value of system (1), iterate MN+r times, at this time, r=r ₅ +r ₂ +r ₃ +r ₄ , remove the previous r values, and obtain a variable sequence with length MN/>

Step 1.4, perform the following operations on the state sequence in the above steps to obtain five random matrices X, Y, Z, W, V, X, V for the forward diffusion module, Y, V for the reverse diffusion module, Z, W is used to scramble modules.

u=1,2,...M, v=1,2,...N. X, V are for the forward diffusion module, Y, V are for the reverse diffusion module, and Z, W are for the scrambling module.

Step 2, perform forward diffusion processing on the original plaintext image P, and convert the plaintext P into a matrix R; Step 2 is specifically as follows

Follow the steps below to implement:

Step 2.1, convert P(1,j) into R(1,j), j=2,3,...N.

R(1,1)＝mod(P(1,1)+X(1,1)+V(1,1)+r ₁ +r ₃ +r ₅ ,256) (4)

R(1,j)=mod(P(1,j)+X(1,j)+R(1,j-1)+V(1,j),256) (5)

Step 2.2, convert P(i,1) into R(i,1), i=2,3,...M.

R(i,1)=mod(P(i,1)+X(i,1)+V(i,1)+R(i-1,1),256) (6)

Step 2.3, converting P(i,j) into R(i,j), i=2,3,...M, j=2,3,...N.

R(i,j)=mod(P(i,j)+X(i-1,j)+V(i,j)+R(i,j-1)+R(i-1,j), 256) (7)

Step 3, scrambling the matrix R, and replacing the pixel points in step 2;

Step 3 is specifically implemented according to the following steps:

Step 3.1, calculate the sum of all elements (excluding R(i,j)) in the row where R(i,j) is located, denoted as rs _i , namely

rs _i = sum(R(i,1:N))-R(i,j) (8)

Step 3.2, calculate the sum of all elements (excluding R(i,j)) in the column where R(i,j) is located, denoted as cs _j

cs _j = sum(R(1:M,j))-R(i,j) (9)

Step 3.3, Calculation Parameters value.

Step 3.4, according to step 3.1 to step 3.3, first scramble the element R(M,1:N-1), then scramble the element R(1:M-1,N), and then from top to bottom from left to right Scramble the elements R(1:M-1,1:N-1), and finally scramble the elements R(M,N).

Step 4, denote the image obtained after scrambling as D, perform reverse diffusion processing, transform matrix D into matrix C, and generate a ciphertext image.

Step 4 is specifically implemented according to the following steps:

Step 4.1, converting D(M,j) into C(M,j), j=N-1, N-2,...1.

C(M,N)=mod(D(M,N)+Y(M,N)+V(M,N)+r ₂ +r ₄ +r ₅ ,256) (12)

C(M,j)=mod(D(M,j)+Y(M,j)+V(M,j)+C(M,j+1),256) (13)

Step 4.2, convert D(i,N) into C(i,N), i=M-1, M-2,...1.

C(i,N)=mod(D(i,N)+Y(i,N)+V(i,N)+C(i+1,N),256) (14)

Step 4.3, D(i,j) is transformed into C(i,j), j=N-1, N-2...1, i=M-1, M-2,...1.

C(i,j)=mod(D(i,j)+Y(i,j)+V(i,j)+C(i+1,j)+C(i,j+1),256) (15)

Through the reverse diffusion process from step 4.1 to step 4.3, the ciphertext matrix C is obtained, that is, the encrypted image is obtained.

A kind of image encryption method based on five-dimensional non-equilibrium point hyperchaotic system of the present invention, carry out performance test and analysis, specifically include the following parts:

①Analysis of encryption and decryption effects

② Histogram analysis

③Information entropy analysis

④Adjacent pixel correlation analysis

⑤Key sensitivity analysis

⑥Operation efficiency analysis

In order to prove the universality of the present invention, the test images are all selected from the international standard test image library.

Analysis of encryption and decryption effects

Select the "Baboon" image (512×512) to do the encryption and decryption test, as shown in Figure 4; from Figure 4(b), it can be seen that the encrypted image information appears as noise without visual information, which well hides the original image information; the image decrypted with the correct key is exactly the same as the original image, as shown in Figure 4(c). It shows that the algorithm of the present invention can realize the encryption and decryption of the image, and it is feasible.

Histogram analysis

The histogram is used to analyze the frequency of each gray value in the digital image. The ideal histogram of the encrypted image should be flat. In Figure 5(a), the plaintext histogram is not flat, and in Figure 5(b) , the histogram of the encrypted image is flat. It can be seen that the ciphertext image obtained by the algorithm of the present invention can well hide useful information, and can also resist statistical attacks.

Information entropy analysis

The image corresponding to the flat histogram has larger information entropy. It reflects the uncertainty of image information, the greater the information entropy, the greater the uncertainty, and the less visible information, the higher the security. The mathematical formula of information entropy is as follows:

Among them, h(l) is the probability of occurrence of gray value l, and L is the number of gray levels of pixels. For a completely random image, if the number of gray levels is L=256, the theoretical value of its information entropy is H _l =8. Table 2 shows the test results of three image information entropy. It can be seen from Table 2 that the information entropy of the plaintext is quite different from H _i , and the information entropy of the encrypted image is close to H _i . Therefore, in the algorithm of the present invention, the visible information of the ciphertext is very little, and the security is extremely high.

Table 2 Information entropy test results

Adjacent Pixel Correlation Analysis

The degree of correlation between adjacent pixels can be used as an important index to evaluate the performance of the encryption algorithm, that is, to calculate the correlation coefficient between adjacent pixels. The adjacent pixels of the original image in the horizontal, vertical and diagonal directions have a strong correlation, and the adjacent pixels of the encrypted image should not have obvious correlation. The closer the absolute value of the correlation coefficient between adjacent pixels of the image is to 0, the better the performance of the encryption algorithm.

Assuming that N pairs of adjacent pixels are randomly selected from the survey image, the recorded gray value is

(u _i , v _i ), i=1,2,3...N Calculate the correlation coefficient r _xy of the image through the following formula:

For the test of the present invention, the calculation results of the correlation coefficients of adjacent pixels are shown in Table 3, and the related situation is shown in FIG. 6 . These images can qualitatively show that the encryption scheme has better performance and can effectively remove the correlation of adjacent pixels.

Table 3 Adjacent pixel correlation coefficient

Key Sensitivity Analysis

Make a small change to the original key to get a new key. Using two keys to obtain different ciphertext images respectively, by analyzing the difference between the two ciphertext images, it is judged whether the encryption algorithm has key sensitivity.

Qualitative analysis: To test the sensitivity of the key, use parameters b=1, c=0.50, select the initial value (0.1,0.1,-5,2.5,2), and select the key K1=[0.1 0.1 -5 2.5 2 123 205 131 74 33], K2 = [0.1+h 0.1 -5 2.52 123 205 131 74 33]. Encrypt and decrypt "Baboon". Figure 7(c) shows the image decrypted with the correct key, and Figure 7(f) shows the decrypted image with the correct key slightly altered.

Quantitative analysis: NPCR (pixel rate of change) and UACI (normalized average change intensity) are generally used to measure sensitivity. For any image size of M×N, it is recorded as R ₁ and R ₂ . The calculation formulas of NPCR and UACI are as follows :

For the test of the present invention, 8 groups of keys are randomly selected from the key space. Experiment 8 times, add an increment to a certain element in a group of keys each time, and the elements of each operation are different. Where x ₀ , y ₀ , z ₀ , u ₀ , v ₀ change by 1/h. Calculate the NPCR and UACI obtained from 8 experiments and calculate the average value. The results are shown in Table 4. From the results in Table 4, it can be seen that the values of NPCR and UACI are very close to the ideal values. Therefore, the image encryption algorithm of the present invention has strong anti-differential attack capability.

Table 4 Ciphertext sensitivity test results

Operational Efficiency Analysis

In order to measure the encryption and decryption operation efficiency of the present invention, the encryption test is performed on images of different sizes under the MATLAB environment, and the average time of encryption is taken 30 times, as shown in Table 5. It can be seen from Table 5 that the image encryption algorithm of the present invention is effective and very fast.

Table 5 Encryption and decryption average running time

The invention discloses an image encryption method based on a five-dimensional non-equilibrium hyperchaotic system, which uses a random sequence of five-dimensional hyperchaotic hidden attractors to scramble and diffuse plaintext to obtain ciphertext similar to random noise. The image encryption algorithm based on the five-dimensional non-equilibrium point hyperchaotic system of the present invention has high security, confusion and fast encryption speed, improves key sensitivity, is suitable for large-scale data, and has strong anti-attack ability. making this method a viable option for preserving the privacy and confidentiality of images.

Claims (1)

1. a digital image encryption method based on five-dimensional non-equilibrium point hyperchaos, it is characterized in that, described method step is as follows: Step 1, by selecting appropriate parameters and initial values for the five-dimensional non-equilibrium point hyperchaotic system, the chaotic password generation module generates five random matrices through a specific method to prepare for the subsequent diffusion and scrambling of D; Step 1 is specifically implemented according to the following steps: Step 1.1, take [x ₀ ,y ₀ ,z ₀ ,u ₀ ,v ₀ ] as the initial value of the five-dimensional non-equilibrium hyper-chaotic system, and take [0.1,0.1,-5,2.5,2], where the five-dimensional The non-equilibrium point hyperchaotic system (1) is as follows: In system (1), b and c are the control parameters of the system, x, y, z, u, v are the state variables of the system, and the given plaintext gray image P has a size of M×N, and the Runge-Kutta algorithm is used to Iterate MN+r times, where r=r ₁ +r ₂ +r ₃ +r ₄ , remove the previous r values, and get a variable sequence {x _i },{y _i },{z _i },{ w _i },{v _i }, i=1,2,...MN; Step 1.2, calculate the last digit of the sequence {x _i },{y _i },{z _i },{w _i },{v _i }, as follows: The function of formula (2) is to limit the size of x _MN , y _MN , z _MN , w _MN , and v _MN to [-10,10]; Step 1.3, will As the initial value of system (1), iterate MN+r times, at this time, r=r ₅ +r ₂ +r ₃ +r ₄ , remove the previous r values, and obtain a variable sequence with length MN/> Step 1.4, perform the following operations on the state sequence in the above steps to obtain five random matrices X, Y, Z, W, V, X, V for the forward diffusion module, Y, V for the reverse diffusion module, Z, W is used to scramble the module; u=1,2,...M, v=1,2,...N. X, V are used for forward diffusion module, Y, V are used for reverse diffusion module, Z, W are used for scrambling module; Step 2, carry out forward diffusion processing on the original plaintext image P, and convert the plaintext P into a matrix R; step 2 is implemented according to the following steps: Step 2.1, convert P(1,j) into R(1,j), j=2,3,...N; R(1,1)＝mod(P(1,1)+X(1,1)+V(1,1)+r ₁ +r ₃ +r ₅ ,256) (4) R(1,j)=mod(P(1,j)+X(1,j)+R(1,j-1)+V(1,j),256)(5) Step 2.2, converting P(i,1) into R(i,1), i=2,3,...M; R(i,1)=mod(P(i,1)+X(i,1)+V(i,1)+R(i-1,1),256) (6) Step 2.3, converting P(i,j) into R(i,j), i=2,3,...M, j=2,3,...N; R(i,j)=mod(P(i,j)+X(i-1,j)+V(i,j)+R(i,j-1)+R(i-1,j), 256) (7) Step 3, scrambling the matrix R, and replacing the pixel points in step 2; Step 3 is specifically implemented according to the following steps: Step 3.1, calculate the sum of all elements (excluding R(i,j)) in the row where R(i,j) is located, denoted as rs _i , namely rs _i = sum(R(i,1:N))-R(i,j) (8) Step 3.2, calculate the sum of all elements (excluding R(i,j)) in the column where R(i,j) is located, denoted as cs _j , namely cs _j = sum(R(1:M,j))-R(i,j) (9) Step 3.3, Calculation Parameters value; Step 3.4, according to step 3.1 to step 3.3, first scramble the element R(M,1:N-1), then scramble the element R(1:M-1,N), and then from top to bottom from left to right Shuffle the element R(1:M-1,1:N-1), and finally shuffle the element R(M,N); Step 4, denote the image obtained after scrambling as D, perform reverse diffusion processing, convert matrix D to matrix C, and generate a ciphertext image; Step 4 is specifically implemented according to the following steps: Step 4.1, converting D(M,j) into C(M,j), j=N-1, N-2,...1; C(M,N)=mod(D(M,N)+Y(M,N)+V(M,N)+r ₂ +r ₄ +r ₅ ,256) (12) C(M,j)=mod(D(M,j)+Y(M,j)+V(M,j)+C(M,j+1),256) (13) Step 4.2, converting D(i, N) into C(i, N), i=M-1, M-2,...1; C(i,N)=mod(D(i,N)+Y(i,N)+V(i,N)+C(i+1,N),256) (14) Step 4.3, D(i, j) is transformed into C(i, j), j=N-1, N-2...1, i=M-1, M-2,...1; C(i,j)=mod(D(i,j)+Y(i,j)+V(i,j)+C(i+1,j)+C(i,j+1),256) (15) Through the reverse diffusion process from step 4.1 to step 4.3, the ciphertext matrix C is obtained, that is, the encrypted image is obtained.