A color image encryption method based on new 4-dimensional hyperchaos and DNA random coding calculation

Abstract

The present application is directed to the problem that static DNA encoding and calculation rules are single, encryption process is separated from plaintext, and plaintext is vulnerable to attack, and proposes a color image encryption method based on new 4-dimensional hyperchaos and DNA random encoding calculation. The method first designs a new 4-dimensional hyperchaotic system, iterates the system to generate multiple pseudo-random sequences, generates new pseudo-random sequences and matrices by calculation and modification, decomposes the color image into R, G and B channel components, and then fuses them into a matrix, then encodes and calculates the image and the pseudo-random matrix according to the newly generated pseudo-random sequence, and then performs DNA random decoding, decomposes the matrix into channel components, and fuses to generate the final ciphertext image, wherein the initial value of the chaotic system is calculated by the SHA-512 algorithm. The encryption method proposed by the present application not only has large key space and strong sensitivity to plaintext, but also can effectively resist statistical, brute force and differential attacks.

Description

Technical Field

[0001] This invention belongs to the field of digital image encryption technology, specifically relating to a color image encryption method based on novel 4D hyperchaos and DNA random coding computation. Background Technology

[0002] With the rapid development of electronic communication technology, images have become one of the most important means of communication, serving as a primary carrier of information. In real life, a large amount of private image information is transmitted via the Internet, and the leakage and tampering of military classified images, personal or commercial private images frequently occur. How to securely transmit this image information has become an urgent problem to be solved, and image encryption technology is an effective solution to protect the secure transmission of images.

[0003] Due to the characteristics of images, such as high redundancy, large data capacity, and strong correlation between pixels, traditional encryption methods, such as DES and AES, are no longer sufficient for image encryption requirements. Chaotic systems, however, possess pseudo-randomness and non-periodicity, and can generate unpredictable pseudo-random sequences within a short time. Therefore, chaotic systems have a natural advantage in the field of image encryption. Currently, chaotic encryption technology is widely used in image encryption. [1-5] .

[0004] Due to the ultra-large-scale storage capacity and low energy consumption of DNA molecules, their application in image encryption has unique advantages. In recent years, image encryption methods based on DNA technology have been widely used. [6-8] . Summary of the Invention

[0005] To address the vulnerabilities of existing color image encryption methods, such as independent encryption of each channel component, simplistic DNA encoding calculation rules, and encryption processes detached from plaintext, which make these methods susceptible to plaintext attacks, this paper designs a novel 4D hyperchaos to ensure the pseudo-randomness of the generated sequence. During encryption, the R, G, and B channel components of the color image are concatenated for encryption, closely linking each channel component. DNA random encoding and DNA random computation operations are used to avoid the problem of simplistic DNA encoding and computation rules. DNA-level plaintext-related scrambling is added during encryption, and the initial value of the chaotic system is generated from the plaintext using SHA-512 computation, enhancing the encryption method's sensitivity to both plaintext and the key.

[0006] This invention discloses a color image encryption method based on novel 4D hyperchaos and DNA random coding computation, comprising the following steps:

[0007] The first step is to decompose the color image P of size M×N×3 into three M×N R-channel components, G-channel components, and B-channel components. Then, these three channel components are expanded into one-dimensional vectors R1, G1, and B1 by columns. These three vectors are then expanded into binary vectors R2, G2, and B2 with M×N rows and 8 columns, respectively. Finally, the fusion matrix Q = [R2 G2B2] is generated.

[0008] The second step is to use SHA-512 to calculate a 512-bit hash value for the color plaintext image, and then convert it into a 128-bit decimal representation, generating k = {K1, k2, ..., k}. 128 Then, the initial values ​​y1, y2, y3, and y4 of the new 4D hyperchaotic system are calculated and generated, along with parameters r1 and r2 that control the number of iterations. Given the parameter values ​​and initial values ​​of the chaotic system, the chaotic system is iterated r1+r2+100 times. The transition state of the chaotic system is skipped, and the chaotic system is iterated M×N times to generate four pseudo-random sequences. Then, the sum of the first quarter of the pixels of the R-channel component matrix is ​​calculated as Sp1, the sum of the last quarter of the pixels of the R-channel component matrix is ​​calculated as Sp2, and the sum of all pixels of the R-channel component matrix is ​​calculated as Sup. These sequences are used to calculate and correct the pseudo-random sequence X that selects the DNA random coding rule, as well as the pseudo-random sequence U and pseudo-random matrix W that select the DNA random calculation method.

[0009] The equations for the new 4D hyperchaotic system used in the design are as follows:

[0010]

[0011] Where y1, y2, y3 and y4 are the state variables of the system, and a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44, β and γ are the control parameters of the system. When a11 = -0.5, a12 = -4.6, a13 = 5.1, a14 = 1, a21 = 4.8, a22 = -3.5, a23 = 0.5, a24 = 1, a31 = -5.1, a32 = -0.1, a33 = 3, a34 = 1, a41 = -2, a42 = 2, a43 -3, a44 = -0.05, β = [4,18], γ = [1,16], the system exhibits a hyperchaotic state.

[0012] The third step is to convert the pseudo-random matrix W into a binary generation matrix W1. Each row of the image information matrix Q is assigned a DNA encoding rule according to the value of the corresponding row of sequence X, thereby generating matrix Q1 through random DNA encoding. Similarly, each row of matrix W1 is assigned a DNA encoding rule according to the value of the corresponding row of sequence X, thereby generating matrix W2 through random DNA encoding. The row values ​​of matrices Q1 and W2 are assigned a random DNA calculation method according to the row values ​​of sequence U, thereby generating matrix Q2 through random DNA calculation.

[0013] The fourth step is to calculate the total number of "A", "C", "G", and "T" in matrix Q2, and use them to calculate and correct the pseudo-random sequences V and T for DNA-level plaintext correlation scrambling, as well as the pseudo-random sequence L for selecting DNA random decoding rules. Then, matrix Q4 is generated by performing plaintext correlation scrambling on the columns and rows of matrix Q2 based on the pseudo-random sequences V and T.

[0014] The fifth step involves selecting the DNA decoding rule according to the row values ​​of sequence L for matrix Q4, performing random DNA decoding to generate matrix Q5, converting Q5 to decimal, and decomposing it to generate M×N one-dimensional vectors R3, G3, and B3. After reshaping the three vectors into M×N matrices, they are fused into the final M×N×3 ciphertext image. Attached Figure Description

[0015] Figure 1 This is a flowchart of a color image encryption method based on a novel 4D hyperchaos and DNA random coding computation according to the present invention;

[0016] Figure 2 The novel 4D hyperchaos Lyapunov exponent plot used in this invention;

[0017] Figure 3 This is a diagram illustrating the process of random DNA encoding in color images in this invention.

[0018] Figure 4 The experimental results are for a 256×256 Lena color image in this invention;

[0019] Figure 5 This is a histogram of the plaintext and ciphertext of each channel component of the Lena color image in this invention;

[0020] Figure 6 This is a correlation distribution diagram of adjacent pixels of plaintext and ciphertext in each channel component of the Lena color image in this invention. Detailed Implementation

[0021] To further understand the technical solution of the present invention, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0022] This invention discloses a color image encryption method based on novel 4D hyperchaos and DNA random coding computation, the process of which is as follows: Figure 1 As shown, this invention relates to four main modules. The first module is the generation of a fusion matrix, a pseudo-random sequence, and a pseudo-random matrix; the second module is DNA random encoding, DNA random computation, and DNA-level plaintext-related scrambling operations; and the third module is DNA random decoding and the generation of ciphertext images.

[0023] 1. Generation of fusion matrices, pseudo-random sequences, and pseudo-random matrices

[0024] 1.1 Generation of the fusion matrix

[0025] A color image P of size M×N×3 is decomposed into three M×N R-channel components, G-channel components, and B-channel components. These three channel components are then expanded into one-dimensional vectors R1, G1, and B1. These three vectors are then expanded into binary vectors R2, G2, and B2 with M×N rows and 8 columns, respectively. Finally, a fusion matrix Q = [R2 G2 B2] is generated.

[0026] 1.2 Generation of Pseudorandom Sequences and Pseudorandom Matrices

[0027] This invention designs a novel 4-dimensional hyperchaotic system, whose equations are:

[0028]

[0029] Where y1, y2, y3, and y4 are the system's state variables, a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44, and β and γ are the system's control parameters, with values ​​of a11 = -0.5, a12 = -4.6, a13 = 5.1, a14 = 1, and a21 = 4.8. When a22 = -3.5, a23 = 0.5, a24 = 1, a31 = -5.1, a32 = -0.1, a33 = 3, a34 = 1, a41 = -2, a42 = 2, a43 -3, a44 = -0.05, β = [4, 18], γ = [1, 16], the system exhibits a hyperchaotic state. When β = 10, γ = 8, the Lyapunov exponent of the new 4-dimensional hyperchaotic system is as follows: Figure 2 As shown.

[0030] The plaintext image of the color image is calculated using SHA-512 to generate a 512-bit hash value, which serves as the initial key for this invention. This hash value is then converted into a 128-bit decimal representation, denoted by K, where K = {k1, k2, ..., kk}. 128The initial values ​​of the new 4-dimensional hyperchaotic system and the parameters controlling the number of iterations are obtained according to the following formula:

[0031]

[0032]

[0033] Sup is the sum of the pixel values ​​of the R-channel component matrix of a color plaintext image, calculated using the following formula:

[0034]

[0035] Sp1 is the sum of the first quarter pixel values ​​in the R channel component matrix of a color plaintext image, calculated using the following formula:

[0036]

[0037] Sp2 is the sum of the last quarter of pixel values ​​in the R-channel component matrix of a color plaintext image, calculated using the following formula:

[0038]

[0039] floor(t) returns the largest integer less than or equal to the number t.

[0040] Given the initial values ​​and parameter values ​​of the system, where β = 10 and γ = 8, iterate the chaotic system r1 + r2 + 100 times, skipping the transition state, and continue iterating the chaotic system M × N times to generate four pseudo-random sequences y1(a1, a2, ..., a M×N ), y2(b1,b2,…,b M×N ), y3(c1,c2,…,c M×N ) and y4(d1,d2,…,d M×N By calculating and correcting these four pseudo-random sequences, pseudo-random sequences X and Y and a pseudo-random matrix W are generated:

[0041]

[0042] Y(i)=mod(floor((y2(i)+y4(i)))×10 14 ×Sp2),3)+1 (8)

[0043]

[0044] Then the pseudo-random matrix is ​​W = [W1 W2 W3];

[0045] Where i = 1, 2, ..., M × N, floor(t) represents returning the largest integer less than or equal to t, and mod(n,t) represents taking the remainder of n with respect to t.

[0046] 2. DNA random coding, DNA random computation, and DNA-level plaintext-related scrambling operations

[0047] 2.1 DNA random coding

[0048] DNA is a double-stranded macromolecule with three components: deoxyribose, phosphate, and nitrogenous bases. There are four types of nitrogenous bases: A, C, G, and T. A and T, and G and C, are complementary. Each pixel in a grayscale image can be represented by an 8-bit binary number. Since 0 and 1 are complementary, 00 and 11, and 01 and 10 are also complementary. Therefore, if the four nitrogenous bases A, C, G, and T represent the binary numbers 00, 10, 01, and 11 respectively, then each pixel value can be represented by a DNA sequence of length 4. There are eight encoding rules that satisfy the complementary relationships between DNA bases, as shown in Table 1.

[0049] Table 1. Eight DNA coding rules

[0050]

[0051] The specific formula for random DNA coding is as follows:

[0052] Q1=DNA_Random_Engcoding(Q(i,j),X(i)) (10)

[0053] This means that the fusion matrix Q(i,j) is randomly encoded according to the values ​​of the pseudo-random sequence X(i), i.e., one of the DNA encoding rules in Table 1. For example, if the value of X(i) is 1, the i-th row of Q(i,j) will be encoded using rule 1; if the value of X(i) is 2, the i-th row of Q(i,j) will be encoded using rule 2, and so on, for example, if the value of X(i) is 8, the i-th row of Q(i,j) will be encoded using rule 8. After random DNA encoding, a DNA matrix Q1 is generated, where i = 1, 2, ..., M × N, j = 1, 2, ..., 24. The random DNA encoding process is as follows: Figure 3 As shown.

[0054] 2.2 Randomization of DNA Sequences

[0055] DNA addition and subtraction methods are similar to traditional algebraic calculations. The rules for DNA addition are shown in Table 2, the rules for DNA subtraction are shown in Table 3, and the rules for DNA XOR are shown in Table 4.

[0056] Table 2 DNA Addition Rules

[0057]

[0058] Table 3. DNA Subtraction Rules

[0059]

[0060] Table 4 DNA XOR Rules

[0061]

[0062] The pseudo-random matrix W is converted into binary W1, and then DNA random encoding is performed according to the following formula:

[0063] W2=DNA_Random_Encoding(W1(i,j),X(i)) (11)

[0064] Similarly, based on the value of the pseudo-random sequence X(i), each row of the pseudo-random matrix W1(i,j) is randomly encoded to generate the DNA matrix W2, where i = 1, 2, ..., M × N, j = 1, 2, ..., 24.

[0065] The formula for randomly calculating DNA sequences is as follows:

[0066] Q2=DNA_Random_Operation(Q1(i,j),W2(i,j),Y(i)) (12)

[0067] Based on the value of the pseudo-random Y(i), matrix Q2 is generated by randomly calculating each row of the DNA matrix Q1(i,j) and the pseudo-random DNA matrix W2(i,j). That is, each row is calculated using one of the following rules: DNA addition, DNA subtraction, and DNA XOR. If the value of Y(i) is 1, DNA addition is performed on the i-th row of matrix Q1 and W2. If the value of Y(i) is 2, DNA subtraction is performed on the i-th row of matrix Q1 and W2. If the value of Y(i) is 3, DNA XOR is performed on the i-th row of matrix Q1 and W2. Where i = 1, 2, ..., M × N, j = 1, 2, ..., 12.

[0068] 2.3 DNA-level plaintext-related scrambling

[0069] Calculate the number of 'A's in matrix Q2 as tR1, the number of 'C's in matrix Q2 as tR2, the number of 'G's in matrix Q2 as tR3, and the number of 'T's in matrix Q2 as tR4.

[0070] Based on the values ​​of tR1, tR2, tR3, and tR4, pseudo-random sequences V and T are generated for scrambling, and sequence L is generated for random DNA decoding. The specific formulas are as follows:

[0071]

[0072]

[0073]

[0074] The DNA-level plaintext-related scrambling of matrix Q2 includes the following two processes:

[0075] Column-level scrambling: Q3(:,j)=circshift(Q2(:,j),V(j),1), which means circularly shifting each column of the image information matrix Q2(:,j) by V(j) units, where j=1,2,…,12;

[0076] Row-level scrambling: Q4(i,:) = circshift(Q3(i,:), T(i), 2), which means circularly shifting each row of the image information matrix Q3(i,:) by T(i) units, where i = 1, 2, ..., M × N.

[0077] 3. Random DNA Decoding and Generation of Ciphertext Images

[0078] The rules for DNA decoding are the reverse of the encoding rules in Table 1. The formula for random DNA decoding is as follows:

[0079] Q5=DNA_Random_Decoding(Q4(i,j),L(i)) (16)

[0080] This means that each row of the image DNA matrix Q4(i,j) is DNA decoded according to the value of the pseudo-random sequence L(i) to generate a binary matrix Q5, where i = 1, 2, ..., M × N, j = 1, 2, ..., 12.

[0081] Perform matrix decomposition on Q5 using R3 = Q5(1:M×N,1:8), G3 = Q5(1:M×N,9:16), and B3 = Q5(1:M×N,17:24). Then, convert R3, G3, and B3 into decimal R4, G4, and B4. Finally, reshape the R4, G4, and B4 matrices into M×N matrices and fuse them to generate the final M×N×3 ciphertext image.

[0082] The process of image decryption is the reverse of encryption, and will not be elaborated here.

[0083] To verify the effectiveness of this invention, a simulation experiment is conducted below to further explain and illustrate the invention. The invention is tested on a Windows 10 platform (Intel(R) Core(TM) i5-4590, 3.30GHz, RAM 4.00GB) and Matlab 2017a, and the security of the encryption method of this invention is analyzed. Figure 4 The experimental results are for a 256×256 Lena color image, where... Figure 4(a) in the image is the plaintext image of Lena's color image. Figure 4 (b) in the image is the encrypted image of Lena's color image. Figure 4 (c) in the image is the decrypted image by Lena; Figure 5 This is a histogram of each channel component of the plaintext and ciphertext in the Lena color image. Figure 5 In the image, (a), (c), and (e) are histograms of the R, G, and B channel components of the plaintext of the Lena color image, respectively; and (b), (d), and (f) are histograms of the R, G, and B channel components of the ciphertext of the Lena color image, respectively. Figure 6 This is a correlation distribution map of adjacent pixels in each channel component of the plaintext and ciphertext of the Lena color image. Figure 6 Images (a), (b), and (c) show the correlation distribution between adjacent pixels in the horizontal, vertical, and diagonal directions of the plaintext R channel components of Lena color images. Figure 6 In the diagram, (d), (e), and (f) are the correlation distribution maps between adjacent pixels in the horizontal, vertical, and diagonal directions of the R channel components of the Lena color image ciphertext. Figure 6 (g), (h), and (i) are the correlation distribution maps between adjacent pixels in the horizontal, vertical, and diagonal directions of the plaintext G channel components of the Lena color image. Figure 6 In the diagram, (j), (k), and (l) represent the correlation distribution between adjacent pixels in the horizontal, vertical, and diagonal directions of the G channel components of the Lena color image ciphertext. Figure 6 (m), (n), and (o) represent the correlation distribution between adjacent pixels in the horizontal, vertical, and diagonal directions of the plaintext B-channel components of the Lena color image. Figure 6 In the diagram, (p), (q), and (r) represent the correlation distribution between adjacent pixels in the horizontal, vertical, and diagonal directions of the B-channel components of the Lena color image ciphertext.

[0084] from Figure 4 As can be seen, the ciphertext image after using this encryption method is similar to noise, and no information about the plaintext image can be obtained from the ciphertext image. The decrypted image is the same as the plaintext image, thus achieving the purpose of encrypting and decrypting the image.

[0085] 1. Key Space Analysis

[0086] The security of an encryption method is highly dependent on its key space; generally, the larger the key space, the stronger its resistance to brute-force attacks. The encryption method of this invention uses a 512-bit key generated from the plaintext using SHA-512, as well as the values ​​of Sup, Sp1, Sp2, tR1, tR2, tR3, and tR4 related to the plaintext during the encryption process. Therefore, the key must be greater than 10. 200Therefore, it can be seen that the encryption method of the present invention has a large key space, which can effectively resist brute-force attacks.

[0087] 2. Histogram Analysis

[0088] A histogram represents the frequency distribution of image pixels, describing the statistical correlation of the image. Generally, the more uniformly the histogram of image pixel gray levels follows a distribution, the more effectively it resists attacks from statistical analysis. [9] The grayscale histograms of each channel component of the plaintext and ciphertext in Lena's color image are as follows: Figure 5 As shown in the figure, it can be seen that the pixel values ​​of each channel component of the encrypted image are evenly distributed, indicating that the image encryption method of the present invention has a good ability to resist statistical analysis. Attackers cannot analyze the gray value distribution of the original image from the encrypted image.

[0089] 3. Pixel Correlation Analysis

[0090] In plaintext images, adjacent pixels exhibit strong correlations, containing partial information from the plaintext. This information can be easily exploited by malicious actors. To resist statistical analysis, it is essential to reduce the correlation between pixels. The formula for calculating pixel correlation is as follows:

[0091]

[0092] Where N is the number of pairs of arbitrarily chosen adjacent pixels, and their grayscale values ​​are (u i ,v i ), i=1,2,…,N, vector u={u i}, vector v = {v i}

[0093] In each channel component of the color Lena plaintext and ciphertext images, 2000 pairs of adjacent pixels were randomly selected, and their correlation coefficients in the horizontal, vertical, and diagonal directions were calculated. The results are shown in Table 5. The correlation diagrams of adjacent pixels in the horizontal, vertical, and diagonal directions for each channel component of the plaintext and ciphertext images are shown below. Figure 6 As shown in Table 5 and Figure 6 We can see that the correlation coefficient between adjacent pixels in the plaintext image is close to 1, while the correlation coefficient between adjacent pixels in the ciphertext image is basically 0. This indicates that the method of the present invention breaks the correlation between adjacent pixels, and malicious actors cannot effectively attack it through statistical analysis.

[0094] Table 5 Comparison of Correlation Between Adjacent Pixels

[0095]

[0096] 4. Information Entropy Analysis

[0097] Information entropy reflects the uncertainty of an image. Generally, the better the encryption effect of the algorithm, the closer the information entropy of the image is to 8, and the greater the information content and randomness of the image. [9] The formula for calculating information entropy is as follows:

[0098]

[0099] Where L is the gray level of the image, and p(i) represents the probability of gray value i appearing.

[0100] Table 6 Information Entropy Values

[0101]

[0102] The information entropy values ​​are shown in Table 6. As can be seen from Table 6, the information entropy values ​​of each channel component of the ciphertext image are very close to its theoretical value of 8, indicating that the possibility of information leakage of the ciphertext is very small, which further proves that the method of the present invention can effectively resist statistical analysis attacks.

[0103] 5. Plaintext Sensitivity Analysis

[0104] Plaintext sensitivity analysis aims to analyze the difference between two ciphertext images obtained by encrypting an image using the same key when the plaintext undergoes a slight change. If the two ciphertext images are significantly different, it indicates that the encryption method is highly sensitive to plaintext; if the difference is small, it is said to be less sensitive. It can be measured by pixel change rate (NPCR) and normalized average change rate (UACI), and their calculation formulas are as follows:

[0105]

[0106] Where M and N represent the number of rows and columns of the image, respectively; c1(i,j) represents the pixel value at position (i,j) in the original ciphertext image; and c2(i,j) represents the pixel value at position (i,j) in the slightly modified ciphertext image. If c1(i,j) = c2(i,j), then D(i,j) = 0; otherwise, D(i,j) = 1.

[0107] To verify the sensitivity of the encryption method of this invention to plaintext, the pixel value at a certain position in the color Lena image was changed by 1, and the Lena color image was then encrypted using the same key to obtain the ciphertext image. The two ciphertext images were decomposed to obtain the ciphertext images of each channel component. The NPCR and UACI values ​​were used to measure the difference between the original channel component ciphertext images and the ciphertext images. The results are shown in Table 3.

[0108] Table 7 shows the NPCR and UACI values ​​of the encrypted images of the channel components before and after plaintext changes.

[0109]

[0110] As can be seen from the results in Table 7, the NPCR and UACI values ​​calculated using this invention are very close to their theoretical values, indicating that a small change in the plaintext results in a huge change in the ciphertext image. This further demonstrates that the encryption method of this invention has strong sensitivity to plaintext and can resist differential attacks.

[0111] This invention combines a novel 4D hyperchaotic system, DNA random coding, and computational techniques to encrypt color images, achieving the goal of image encryption. During the encryption process, the various channel components of the color image are closely correlated. Information from the plaintext image participates in the calculation and correction of the pseudo-random sequence, and plaintext-related scrambling operations are performed at the DNA level. The initial value of the chaotic system is generated from the plaintext calculated using SHA-512. This expands the key space of the encryption method and enhances the sensitivity of the encryption method to both plaintext and key.

[0112] References

[0113] [1]Xu Lu, Li Zhi, Li jian and Hua Wei.A novel bit-level image encryption algorithm based on chaotic maps[J].Opt Lasers Eng,2016,78:17-25.

[0114] [2]Li Bo, Liao Xiaofeng and Jiang Yan.A novel image encryption scheme based on improved random number generator and its implementation[J].NonlinearDyn,2019,95(3):1781-1805.

[0115] [3]Zhang Yong,Chen Aiguo,Tang Yingjun,et al.Plaintext-related image encryption algorithm based on perceptron-like network[J].InformationSciences,2020,526:180-202.

[0116] [4] Ye Guodong, Pan Chen, Huang Xiaoling and Mei Qixiang. An efficient pixel-level chaotic image encryption algorithm[J]. Nonlinear Dyn, 2018, 94(1): 745-756.

[0117] [5] Hua Zhongyun, Zhou Yicong and Huang Hejiao. Cosine-transform-based chaotic system for image encryption[J]. Information Sciences, 2019, 480: 403-419.

[0118] [6] Wang Xingyuan, Wang Yu, Zhu Xiaoqiang, et al. Image encryption scheme based on chaotic and DNA plane operations[J]. Multimedia Tools Appl, 2019, 78(1): 15605-15621.

[0119] [7] Chai Xiuli, Chen Yiran and Broyde Lucie. A novel chaos-based image encryption algorithm using DNA sequence operations[J]. Opt Lasers Eng, 2017, 88: 197-213.

[0120] [8] Zhang Jian and Huo Da. Image encryption algorithm based on quantum chaotic map and DNA coding[J]. Multimedia Tools Appl, 2019, 78(1): 15605-15621.

[0121] [9] Zhang Yong. Chaotic Digital Image Encryption[M]. Beijing: Tsinghua University Press, 2016: 79-104.

Claims

1. A color image encryption method based on novel 4D hyperchaos and DNA random coding computation, characterized in that, Includes the following steps: The first step is to decompose the color image P of size M×N×3 into three M×N R-channel components, G-channel components, and B-channel components. Then, these three channel components are expanded into one-dimensional vectors R1, G1, and B1 by columns. These three vectors are then expanded into binary vectors R2, G2, and B2 with M×N rows and 8 columns, respectively. Finally, the fusion matrix Q = [R2 G2 B2] is generated. The second step is to use SHA-512 to calculate a 512-bit hash value for the color plaintext image, and then convert it into a 128-bit decimal value to generate K = {k1, k2, ..., k 128 Then, the initial values ​​y1, y2, y3, and y4 of the new 4D hyperchaotic system are calculated and generated, along with parameters r1 and r2 that control the number of iterations. Given the parameter values ​​and initial values ​​of the chaotic system, the chaotic system is iterated r1+r2+100 times. The transition state of the chaotic system is skipped, and the chaotic system is iterated M×N times to generate four pseudo-random sequences. Then, the sum of the first quarter of the pixels of the R-channel component matrix is ​​calculated as Sp1, the sum of the last quarter of the pixels of the R-channel component matrix is ​​calculated as Sp2, and the sum of all pixels of the R-channel component matrix is ​​calculated as Sup. These are used to calculate and correct the pseudo-random sequence X that selects the DNA random coding rule, as well as the pseudo-random sequence U and pseudo-random matrix W that select the DNA random calculation method. The equations for the new 4D hyperchaotic system used in the design are as follows: Where y1, y2, y3 and y4 are the state variables of the system, a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44, and β and γ are the control parameters of the system. When a11 = -0.5, a12 = -4.6, a13 = 5.1, a14 = 1, a21 = 4.8, a22 = -3.5, a23 = 0.5, a24 = 1, a31 = -5.1, a32 = -0.1, a33 = 3, a34 = 1, a41 = -2, a42 = 2, a43 -3, a44 = -0.05, β = [4,18], γ = [1,16], the system exhibits a hyperchaotic state. The third step is to convert the pseudo-random matrix W into a binary generation matrix W1. Each row of the image fusion matrix Q is assigned a DNA encoding rule according to the value of the corresponding row of sequence X, thereby performing DNA random encoding to generate matrix Q1. Similarly, each row of matrix W1 is assigned a DNA encoding rule according to the value of the corresponding row of sequence X, thereby performing DNA random encoding to generate matrix W2. The row values ​​of matrices Q1 and W2 are assigned a DNA random calculation method according to the row values ​​of sequence U, thereby performing DNA random calculation to generate matrix Q2. The fourth step is to calculate the total number of "A", "C", "G" and "T" in matrix Q2, and use them to calculate and correct the pseudo-random sequences V and T for DNA-level plaintext correlation scrambling, as well as the pseudo-random sequence L for selecting DNA random decoding rules. Then, matrix Q4 is generated by performing plaintext correlation scrambling on the columns and rows of matrix Q2 based on the pseudo-random sequences V and T. The fifth step involves selecting the DNA decoding rule according to the row values ​​of sequence L for matrix Q4, performing random DNA decoding to generate matrix Q5, converting Q5 to decimal, and decomposing it to generate M×N one-dimensional vectors R3, G3, and B3. After reshaping the three vectors into M×N matrices, they are fused into the final M×N×3 ciphertext image.

Images