Hyperchaos image encryption method based on magic cube three-dimensional space parallel rotation scrambling

Abstract

The invention provides a hyperchaotic image encryption method based on magic cube three-dimensional space parallel rotation scrambling, and the method comprises the steps: generating a pseudo-random sequence as a preprocessing parameter, an Arnold transformation parameter and a magic cube scrambling parameter through a seven-dimensional hyperchaotic system, and carrying out the preprocessing of an R channel, a G channel and a B channel of a plaintext image through the pseudo-random sequence, the Arnold transformation parameter and the magic cube scrambling parameter, then, Arnold transformation is controlled by a pseudorandom sequence to scramble the preprocessed image so as to improve the defect that data aggregation easily occurs during subsequent scrambling of the three-dimensional magic cube, then, an obtained two-dimensional chaos matrix is converted into a three-dimensional matrix, a rotating shaft, the number of rotating layers and the rotating angle are dynamically selected by the pseudorandom sequence, and the three-dimensional chaos matrix is obtained. And parallel rotation scrambling of the magic cube three-dimensional space is carried out. According to the method, the image pixel values are mapped to all the small cubes contained in the whole Rubik's cube for three-dimensional space scrambling, and the characteristics of the three-dimensional structure of the Rubik's cube are better utilized, so that the scrambling complexity is improved, the safety of the ciphertext image is improved, the key space is larger, and the scrambling effect is better.

Description

Technical Field

[0001] The present invention relates to the technical field of image encryption, and in particular to a hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space. Background Art

[0002] With the development of network technology and artificial intelligence technology, the information transmission method based on digital images has brought great convenience to people due to its intuitive, vivid, and large amount of information. However, these digital images involving secret information face threats such as illegal theft and tampering during transmission, so it is necessary to encrypt these digital image information to ensure the security of image information.

[0003] Some scholars have tried to use traditional text information encryption methods to encrypt images, but due to the characteristics of images such as high correlation between adjacent pixels, large data capacity and high redundant information, traditional methods used for text encryption are difficult to effectively ensure efficient and secure encryption of digital images. Therefore, there is an urgent need to develop encryption algorithms suitable for digital images.

[0004] In recent years, some scholars have found that chaos is very suitable for image encryption due to its ergodic, non-periodic and pseudo-random characteristics. At present, chaotic image encryption has become a hot topic in the field of image encryption research (see references 1-11). In order to enhance the encryption effect, chaotic image encryption generally includes two steps: image diffusion and image scrambling: image diffusion uses a chaotic pseudo-random sequence to change the pixel value, while image scrambling uses some scrambling methods to scramble the image pixel positions.

[0005] In the image scrambling process, the existing image scrambling methods mainly include: Arnold transformation (see reference 12), Zigzag transformation (see reference 13-14), DNA coding (see reference 15-17), Rubik's cube scrambling (see reference 18-19) and other scrambling methods. Among these scrambling methods, the Rubik's cube scrambling method can correspond the pixels of the image to the Rubik's cube and scramble the pixels by rotating the Rubik's cube. It is a simple and efficient scrambling method. Therefore, the image encryption technology that combines the Rubik's cube and chaos has gradually become a research hotspot.

[0006] In recent years, due to the efficiency and convenience of Rubik's Cube scrambling, the image encryption algorithm based on Rubik's Cube scrambling has attracted the attention of some scholars and achieved some good research results (see references 18-28). Some chaotic image encryption methods based on Rubik's Cube scrambling usually use the displacement characteristics of the Rubik's Cube to perform two-dimensional scrambling of the plane. For example: Yang Libo used the rotation and cyclic shift characteristics of the Rubik's Cube to propose an image encryption algorithm based on the combination of Rubik's Cube transformation and DNA coding (see reference 18); Ma Cong introduced the idea of ​​cyclic shift of the Rubik's Cube to scramble the pixels of the image, thereby realizing image encryption (see reference 19); R. Vidhya and M. Brindha used the Rubik's Cube cyclic shift method to scramble the pixels, and combined with the chaotic system, proposed an image encryption method (see reference 20); Zhao et al. decomposed the six faces of the Rubik's Cube and arranged them in a specific order on the two-dimensional plane, and then randomly mapped each pixel value of the image to the Rubik's Cube, and controlled the rotation of the Rubik's Cube through a random sequence to achieve image scrambling and encryption (see reference 21). There are also some chaotic image encryption methods based on Rubik's Cube scrambling. When scrambling, the image pixels are mapped to the Rubik's Cube surface and the scrambling is performed by rotating the Rubik's Cube. For example: Chen et al. proposed an image encryption method based on DNA coding, Rubik's Cube and chaos. The six color matrices of two color images are regarded as the six faces of the Rubik's Cube. The pixels in each matrix are scrambled by rotating the Rubik's Cube (see reference 22); Zhao et al. spliced ​​the scrambled pixel matrix and five chaotic matrices into a hexahedral structure and dynamically scrambled the Rubik's Cube through a pseudo-random sequence (see reference 23); Wang Bin et al. used the R, G, and B components of the two images as the six faces of the Rubik's Cube, and controlled the scrambling of the Rubik's Cube through a pseudo-random sequence generated by a chaotic system, thereby achieving encryption (see reference 24). ); Zhang Tian proposed mapping the image pixel information to the surface of several third-order Rubik's cubes, completing the spatial scrambling of the image pixels by controlling the rotation of the Rubik's cube, and combining it with quantum walk for encryption (see reference 25); Zheng et al. combined the R, G, and B layers of two images into a cube that can be unfolded in different orders, and exchanged the rows, columns, or surface pixels of each image by rotating the cube, thereby achieving image scrambling (see reference 26); Sun Guangmin et al. rearranged the pixels and password data into a hexahedral structure, confused the data on the surface and bit in the form of a cross axis, and achieved encryption (see reference 27).

[0007] In the existing literature, there are few results on mapping image pixels to the entire Rubik's cube for scrambling. Gao et al. proposed an image encryption algorithm based on three-dimensional cube and hyperchaotic mapping. After splitting multiple images by columns, multiple planes of fixed size are superimposed to obtain a regular cube, and then each tangent plane is rotated counterclockwise around a fixed Z axis at different angles for scrambling (see reference 28).

[0008] In summary, although the existing chaotic image encryption research has achieved some good results, with the passage of time and the advancement of technology, there are still the following shortcomings:

[0009] 1) Most of the existing Rubik's Cube scrambling methods use the Rubik's Cube circular shift characteristics or simply map image pixels to the surfaces of the six faces of the Rubik's Cube for scrambling. They do not fully consider the three-dimensional properties of the Rubik's Cube and do not map image pixels to all the small cubes contained in the entire Rubik's Cube for scrambling, which affects the scrambling effect. Although some literatures map image pixels to the entire Rubik's Cube for scrambling, they simply rotate it around a fixed axis at different angles for scrambling, and the scrambling performance is low.

[0010] 2) Some results did not utilize or did not fully utilize the pseudo-random sequence generated by the chaotic system to participate in the Rubik's Cube scrambling, and did not dynamically control variables such as the Rubik's Cube rotation axis, number of rotation layers and rotation angle, resulting in poor scrambling effects.

[0011] References are as follows:

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[19] Ma Cong. Research on image encryption algorithm based on magic cube theory[D]. Lanzhou, Gansu: Northwest University for Nationalities, 2018.

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[20] R. Vidhya, M. Brindha. A chaos based image encryption algorithm using Rubik's cube and prime fractorization process [J]. Journal of King Saud University-Computer and Information Sciences, 34 (2022) 2000-2016.

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[21] J. Zhao, T. Zhang, J. Jiang, et al. Color image encryption scheme based on alternate quantum walk and controlled Rubik's cube [J]. Scientific Reports, 12 (2022) 14253.

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[23] Y.Zhao,R.Meng,Y.Zhang,et al.Image encryption algorithm based on a new chaotic system with Rubik's cube transform and Brownian motion model[J].Optik-International Journal for Light and Electron Optics,273(2023)170342.

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[24] Wang Bin, Li Haixiao, Chen Rongrong. A dual color image encryption system based on an improved lifting scheme[J]. Computer Science, 51(6)(2024)230500007.

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[25] Zhang Tian. Research on image encryption based on quantum walk and magic cube transformation[D]. Qingdao, Shandong: Qingdao University of Technology, 2023.

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[26] H.Zheng,G.Li,W.Xu,et al.A compressive sensing encryption scheme for dual color images based on discrete memristor map and Rubik's cubescramble[J].Optik-International Journal for Light and Electron Optics,286(2023)170991.

[0038]

[27] Sun Guangmin, Wang Hao. Image encryption and decryption technology based on Rubik's Cube cipher[J]. Journal of Beijing University of Technology, 47(8)(2021)833-841.

[0039]

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[0040]

[29] Yang Lingbing. Research on complex dynamics of controlled high-dimensional hyperchaotic systems[D]. Guangzhou: South China University of Technology, 2020.

[0041]

[30] Zhang Bo. Research on digital image scrambling method based on Matlab[J]. Computers and Digital Engineering, 2010, 38(7):139-142. Summary of the invention

[0042] The invention proposes a hyper-chaotic image encryption method based on parallel rotation scrambling of a Rubik's Cube three-dimensional space, and performs three-dimensional space scrambling after mapping image pixel values ​​to all small cubes contained in the entire Rubik's Cube. The complexity of the scrambling is relatively high, and the characteristics of the three-dimensional cubic structure of the Rubik's Cube are better utilized. The invention solves the problems that the Rubik's Cube scrambling method in the prior art does not fully utilize the pseudo-random sequence generated by the chaotic system to participate in the Rubik's Cube scrambling, and does not dynamically control variables such as the Rubik's Cube rotation axis, the number of rotation layers and the rotation angle, resulting in poor scrambling effect.

[0043] The technical solution of the present invention is achieved in this way:

[0044] The first aspect of the present invention provides a hyperchaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space, comprising the following steps:

[0045] The key K1 is selected to iterate the Logistic chaotic system for multiple times to generate a chaotic sequence, which is then converted into a chaotic matrix A6 after integer processing;

[0046] The key K2 is selected to iterate the seven-dimensional hyperchaotic system to generate a hyperchaotic sequence, and then the hyperchaotic sequence is converted into an integer sequence;

[0047] Divide the plaintext image P into R P , G P , B P Three channels, select key K3 to preprocess the pixel values ​​of the three channel images to obtain pixel matrix A1;

[0048] Performing Arnold transformation on the pixel matrix A1 to obtain a transformed matrix A2, and transforming the matrix A2 into a three-dimensional pixel matrix A3;

[0049] Performing a three-dimensional Rubik's cube scrambling on the matrix A3 using an integer sequence to obtain a scrambled three-dimensional pixel matrix A4;

[0050] The matrix A4 is transformed into a two-dimensional pixel matrix A5, and the matrix A5 is XOR-ed with the chaotic matrix A6 to obtain the ciphertext image.

[0051] Specifically, during the encryption process, the key K1=(μ,x0,i1,i q ) as the parameters, initial values, number of iterations and number of removed groups of the Logistic chaotic mapping;

[0052] Among them, μ=3.998, x0=0.720,

[0053] ceil(·) represents the upward rounding function, l = max(M,N), and the size of the plaintext image is M×N;

[0054] The key K1 is used to iterate the Logistic chaotic system multiple times to generate a chaotic sequence of size i1. The first 1000 values ​​are removed to obtain the chaotic sequence x. The chaotic sequence x is converted into a pixel integer value of [0,255] using the following formula:

[0055] X = floor (x × 10 16 )mod 256;

[0056] Among them, floor(·) represents the floor function, and mod represents the remainder function;

[0057] Convert the rounded chaotic sequence X into The two-dimensional chaotic matrix A6.

[0058] Specifically, during the encryption process:

[0059] Select key K2 = (a, b, c, d, e, y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), y7(0), i2, i q ,i') as the parameters, initial values, number of iterations, number of removed groups and Arnold transformation as well as preprocessing parameters of the seven-dimensional hyperchaotic system;

[0060] Among them, the values ​​of a, b, c, d, and e are 10, 100, 2.7, 2, and 3 respectively;

[0061] The values ​​of y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), and y7(0) are all 1;

[0062]

[0063] The seven-dimensional hyperchaotic system is iterated using the key K2 to generate a hyperchaotic sequence of size i2. After removing the first 1000 values, 7 pseudo-random sequences are obtained: y1(i), y2(i), y3(i), y4(i), y5(i), y6(i), y7(i);

[0064] The 7 pseudo-random sequences are integerized using the following formula to obtain 7 integer sequences:

[0065]

[0066] in, T represents the two-dimensional Arnold transform period corresponding to images of different sizes.

[0067] Specifically, during the encryption process, a plaintext image P of size M×N is read in and the plaintext image P is divided into R P , G P , BP Three channels, perform the following encryption operations on the images of the three channels in turn to obtain the encrypted images of each channel;

[0068] Let l = max(M, N), and pad the three channel images of the plaintext image P with zeros to obtain three channel images of size l×l;

[0069] Substitute the parameter i' in the key K2 into the sequence Y1(i), Y2(i), Y3(i) to obtain Y1(i'), Y2(i'), Y3(i');

[0070] Select the Y1(i'), Y2(i'), and Y3(i') values ​​in the key K3 as the preprocessing parameters of the pixel values ​​of the three channel images, and preprocess each channel image to obtain the pixel values ​​of the images of the three channels R2, G2, and B2, respectively:

[0071]

[0072] Among them, the key K3 = {3, 5, 7, 9, 11, 13, 15, ..., 251, 253, 255}.

[0073] Specifically, during the encryption process, taking the R2 channel as an example, it is converted into a pixel matrix A1, i' is substituted into the sequence Y4(i) to obtain Y4(i'), and Y4(i') is used as the number of Arnold transformations to perform Arnold transformation on the matrix A1 to obtain the transformed matrix A2;

[0074] Read matrix A2 as array a in row order and fill in the array after a 0, get array b, read array b in sequence as indivual The two-dimensional matrices of size are stacked from top to bottom to form The size of the three-dimensional pixel matrix is ​​A3.

[0075] Specifically, during the encryption process, the method of performing three-dimensional Rubik's cube scrambling on the matrix A3 is:

[0076] Use the integer sequence Y5(i) to control the rotation axis of the matrix A3:

[0077] When Y5(i)=0, the rotation axis is the X axis; when Y5(i)=1, the rotation axis is the Y axis; when Y5(i)=2, the rotation axis is the Z axis;

[0078] The integer sequence Y6(i) is used to control the rotation layer of the matrix A3 to be the Y6(i)th layer;

[0079] Use the integer sequence Y7(i) to control the rotation angle of the selected layer:

[0080] When Y7(i)=0, rotate 90°; when Y7(i)=1, rotate 180°; when Y7(i)=2, rotate 270°;

[0081] The rotation direction is clockwise, starting from i=1 to Finally, the scrambled three-dimensional pixel matrix A4 is obtained.

[0082] Specifically, during the encryption process, the scrambled three-dimensional pixel matrix A4 is read in reverse order as array c, and the array c is supplemented with 0s to obtain array d, read array d in reverse order as a two-dimensional pixel matrix A5, and perform XOR operation on matrix A5 and chaotic matrix A6 to obtain the encrypted image of a certain channel, and then merge the encrypted images of the three channels into the final ciphertext image.

[0083] Specifically, during the decryption process, the ciphertext image is decrypted using the same chaotic matrix and chaotic sequence as in the encryption step to obtain the original plaintext image. The decryption process of the ciphertext image is the inverse process of the encryption process of the plaintext image.

[0084] A second aspect of the present invention provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and wherein the processor implements the steps of the image encryption method when executing the computer program.

[0085] A third aspect of the present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and wherein the computer program implements the steps of the image encryption method when executed by a processor.

[0086] Compared with the prior art, the beneficial effects of the present invention are:

[0087] (1) The present invention generates mutually independent chaotic pseudo-random sequences as preprocessing parameters, Arnold transformation parameters, Rubik's cube scrambling parameters, etc. through a seven-dimensional hyperchaotic system, and applies them to perform different preprocessing on the three channels of R, G, and B of the plaintext image, and then uses the chaotic pseudo-random sequence to control the Arnold transformation to scramble the preprocessed image, and maps the image pixel values ​​to all small cubes contained in the entire Rubik's cube for three-dimensional space scrambling, which better utilizes the characteristics of the three-dimensional structure of the Rubik's cube, thereby increasing the complexity of scrambling and improving the security of the ciphertext image;

[0088] (2) The present invention utilizes a chaotic pseudo-random sequence to dynamically control the rotation axis, number of rotation layers, and rotation angle, resulting in better randomness, better encryption effect, larger key space, and better scrambling effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0090] Figure 1 A schematic diagram of a process for encrypting a plaintext image in an embodiment of the present invention;

[0091] Figure 2 A schematic diagram of the process of decrypting a ciphertext image in an embodiment of the present invention;

[0092] Figure 3 A comparison diagram of a plaintext image, a ciphertext image, and a decrypted image in an embodiment of the present invention; Figure 3 In the figure, (a) is the plaintext image, (b) is the ciphertext image, and (c) is the decrypted image;

[0093] Figure 4 A comparison chart of key sensitivity test results in an embodiment of the present invention; Figure 4 In the figure, (a) is the image decrypted by the correct key, and (b) is the image decrypted by the wrong key;

[0094] Figure 5 is a histogram of a plaintext image and a ciphertext image in an embodiment of the present invention; Figure 5 In the figure, (a) is the histogram of the three channels R, G, and B of the plaintext image, and (b) is the histogram of the three channels R, G, and B of the ciphertext image;

[0095] Figure 6 A comparison diagram of the correlation between adjacent pixels of a plaintext image and a ciphertext image in an embodiment of the present invention; Figure 6In the figure, (a) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the R channel of the plaintext image; (b) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the R channel of the ciphertext image; (c) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the R channel of the plaintext image; (d) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the R channel of the ciphertext image; (e) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the R channel of the plaintext image; (f) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the R channel of the ciphertext image; (g) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the G channel of the plaintext image; (h) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the G channel of the ciphertext image; (i) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the G channel of the plaintext image ; (j) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the G channel of the ciphertext image; (k) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the G channel of the plaintext image; (l) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the G channel of the ciphertext image; (m) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the B channel of the plaintext image; (n) is a schematic diagram of the correlation of adjacent pixels in the horizontal direction of the B channel of the ciphertext image; (o) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the B channel of the plaintext image; (p) is a schematic diagram of the correlation of adjacent pixels in the vertical direction of the B channel of the ciphertext image; (q) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the B channel of the plaintext image; (r) is a schematic diagram of the correlation of adjacent pixels in the diagonal direction of the B channel of the ciphertext image;

[0096] Figure 7 is a decrypted image after being subjected to a shear attack in an embodiment of the present invention; Figure 7 In the figure, (a) is the decrypted image after 1 / 16 cropping, (b) is the decrypted image after 1 / 8 cropping, and (c) is the decrypted image after 1 / 4 cropping;

[0097] Figure 8 is a decrypted image after being attacked by noise in an embodiment of the present invention; Figure 7 In the figure, (a) is the decrypted image with noise (0.001), (b) is the decrypted image with noise (0.005), and (c) is the decrypted image with noise (0.01). DETAILED DESCRIPTION

[0098] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0099] Reference Figure 1 The first aspect of the present invention provides a hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space, comprising the following steps:

[0100] The key K1 is selected to iterate the Logistic chaotic system for multiple times to generate a chaotic sequence, which is then converted into a chaotic matrix A6 after integer processing;

[0101] The key K2 is selected to iterate the seven-dimensional hyperchaotic system to generate a hyperchaotic sequence, and then the hyperchaotic sequence is converted into an integer sequence;

[0102] Divide the plaintext image P into R P , G P , B P Three channels, select key K3 to preprocess the pixel values ​​of the three channel images to obtain pixel matrix A1;

[0103] Performing Arnold transformation on the pixel matrix A1 to obtain a transformed matrix A2, and transforming the matrix A2 into a three-dimensional pixel matrix A3;

[0104] Performing a three-dimensional Rubik's cube scrambling on the matrix A3 using an integer sequence to obtain a scrambled three-dimensional pixel matrix A4;

[0105] The matrix A4 is transformed into a two-dimensional pixel matrix A5, and the matrix A5 is XOR-ed with the chaotic matrix A6 to obtain the ciphertext image.

[0106] Specifically, during the encryption process, the key K1=(μ,x0,i1,i q ) as the parameters, initial values, number of iterations and number of removed groups of the Logistic chaotic mapping;

[0107] Among them, μ=3.998, x0=0.720,

[0108] ceil(·) represents the upward rounding function, l = max(M,N), and the size of the plaintext image is M×N;

[0109] The key K1 is used to iterate the Logistic chaotic system multiple times to generate a chaotic sequence of size i1. The first 1000 values ​​are removed to prevent transient effects, and the chaotic sequence x is obtained. The chaotic sequence x is converted to a pixel integer value of [0,255] using the following formula:

[0110] X = floor (x × 10 16 )mod 256;

[0111] Among them, floor(·) represents the floor function, and mod represents the remainder function;

[0112] Convert the rounded chaotic sequence X into The two-dimensional chaotic matrix A6.

[0113] Specifically, during the encryption process:

[0114] Select key K2 = (a, b, c, d, e, y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), y7(0), i2, i q ,i') as the parameters, initial values, number of iterations, number of removed groups and Arnold transformation as well as preprocessing parameters of the seven-dimensional hyperchaotic system;

[0115] Among them, the values ​​of a, b, c, d, and e are 10, 100, 2.7, 2, and 3 respectively;

[0116] The values ​​of y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), and y7(0) are all 1;

[0117]

[0118] The seven-dimensional hyperchaotic system is iterated using the key K2 to generate a hyperchaotic sequence of size i2. The first 1000 values ​​are removed to prevent transient effects, and 7 pseudo-random sequences are obtained:

[0119] y1(i),y2(i),y3(i),y4(i),y5(i),y6(i),y7(i);

[0120] The 7 pseudo-random sequences are integerized using the following formula to obtain 7 integer sequences:

[0121]

[0122] in, T represents the two-dimensional Arnold transformation period corresponding to images of different sizes (see Table 1 below).

[0123] Furthermore, the present invention uses Logistic mapping to generate a chaotic pseudo-random sequence, which is expressed as follows:

[0124] x n+1 =μx n (1-x n );

[0125] Among them, x n is the state variable of the system, μ is the control parameter of the system, when μ∈[0,4], x n ∈(0,1), the Logistic map will appear chaotic state; the Logistic chaotic map can generate a two-dimensional chaotic pseudo-random sequence matrix for diffusion.

[0126] A seven-dimensional hyperchaotic system is used to generate a hyperchaotic pseudo-random sequence, and its expression is as follows:

[0127]

[0128] Among them, y1, y2, y3, y4, y5, y6, y7 are the state variables of the system, and a, b, c, d, e are the control parameters of the system;

[0129] When the control parameters (a, b, c, d, e) = (10, 100, 2.7, 2, 3) and the initial values ​​of the state variables (y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), y7(0)) = (1, 1, 1, 1, 1, 1, 1), the system exhibits a hyperchaotic state (see reference 29); the seven-dimensional hyperchaotic system can be used to generate preprocessing parameters, Arnold transformation times and three-dimensional Rubik's cube scrambling parameters in encryption algorithms.

[0130] Specifically, during the encryption process, a color plaintext image P of size M×N is read in and the plaintext image P is divided into R P , G P , B P Three channels, perform the following encryption operations on the images of the three channels in turn to obtain the encrypted images of each channel;

[0131] R P Taking the channel image as an example, let l = max(M,N), for R P The channel image is padded with zeros to obtain an R1 channel image of size l×l, K4=(M,N);

[0132] Substitute the parameter i' in the key K2 into the sequence Y1(i), Y2(i), Y3(i) to obtain Y1(i'), Y2(i'), Y3(i');

[0133] Select the Y1(i'), Y2(i'), and Y3(i') values ​​in the key K3 as the preprocessing parameters of the pixel values ​​of the three channel images, and preprocess each channel image to obtain the pixel values ​​of the images of the three channels R2, G2, and B2, respectively:

[0134]

[0135] Among them, the key K3 = {3, 5, 7, 9, 11, 13, 15, ..., 251, 253, 255}.

[0136] Specifically, during the encryption process, the image of the R2 channel is converted into a pixel matrix A1, the value of i' is substituted into the sequence Y4(i) to obtain Y4(i'), and Y4(i') is used as the number of Arnold transformations to perform Arnold transformation on the matrix A1 to obtain the transformed matrix A2;

[0137] Read matrix A2 as array a in row order and fill in the array after a 0, get array b, read array b in sequence as indivual The two-dimensional matrices of size are stacked from top to bottom to form The size of the three-dimensional pixel matrix is ​​A3.

[0138] Arnold transformation (see reference 30) is a transformation proposed by VJ Arnold in the study of ergodic theory. In Arnold transformation, for an N×N image, if the pixel coordinates

[0139] x,y∈{0,1,2,3,…,N-1}, the discretized Arnold transformation can be:

[0140]

[0141] Among them, x, y are the coordinates of the pixel in the original image, x', y' are the coordinates of the pixel in the new image, and mod is the modulus function.

[0142] The inverse Arnold transform is:

[0143]

[0144] The Arnold transform is periodic. When it iterates to a certain step, the original image will be obtained again. Through the program (refer to the program given in reference 30), the two-dimensional Arnold transform period of the image under different orders N can be calculated as shown in Table 1 below:

[0145] Table 1 Two-dimensional Arnold transform period corresponding to images of different orders

[0146]

[0147] It can be observed that the period of the two-dimensional Arnold transform is related to the image size, but not proportional.

[0148] Lemma: If (a×b)mod256=c, a,b,c∈[0,255], a,b,c∈Z, and (a,256)=1, if a and c are known, then b has a unique solution.

[0149] Proof: If (a×b)mod256=c, a,b,c∈[0,255],a,b,c∈Z, and (a,256)=1, then there exists a -1 Make a·a -1 ≡1mod256. Therefore, the original formula is equivalent to a -1 ·a·b≡a -1cmod256, that is, b≡a -1 cmod256, because a -1 unique, so b is unique.

[0150] In encryption and decryption algorithms, this theorem can be used in image preprocessing and inverse processing to ensure the uniqueness of the decomposition and synthesis of the three channels of R, G, and B.

[0151] From the Euler function, we know that there are 128 integers in [0,255] that are coprime with 256, which are {1,3,5,7,9,11,13,15,…,251,253,255}. However, if the first element 1 is brought into the aforementioned preprocessing formula to preprocess the channel image, the pixel value after preprocessing may not change, which will lead to poor encryption effect of the final image. Therefore, the present invention removes the first element 1 in the original set and obtains the key set required for the encryption algorithm of the present invention:

[0152] K3 = {3, 5, 7, 9, 11, 13, 15, …, 251, 253, 255}, which contains 127 elements in total.

[0153] Specifically, during the encryption process, the method of performing three-dimensional Rubik's cube scrambling on the matrix A3 is:

[0154] Use the integer sequence Y5(i) to control the rotation axis of the matrix A3:

[0155] When Y5(i)=0, the rotation axis is the X axis; when Y5(i)=1, the rotation axis is the Y axis; when Y5(i)=2, the rotation axis is the Z axis;

[0156] The integer sequence Y6(i) is used to control the rotation layer of the matrix A3 to be the Y6(i)th layer;

[0157] Use the integer sequence Y7(i) to control the rotation angle of the selected layer:

[0158] When Y7(i)=0, rotate 90°; when Y7(i)=1, rotate 180°; when Y7(i)=2, rotate 270°;

[0159] The rotation direction is clockwise, starting from i=1 to Finally, the scrambled three-dimensional pixel matrix A4 is obtained.

[0160] Specifically, during the encryption process, the scrambled three-dimensional pixel matrix A4 is read in reverse order as array c, and the array c is supplemented with 0s to obtain array d, read array d in reverse order as a two-dimensional pixel matrix A5, and perform XOR operation on matrix A5 and chaotic matrix A6 to obtain the encrypted image of a certain channel, and then merge the encrypted images of the three channels into the final ciphertext image.

[0161] Specifically, during the decryption process, the ciphertext image is decrypted using the same chaotic matrix and chaotic sequence as in the encryption step to obtain the original plaintext image. The decryption process of the ciphertext image is the inverse process of the encryption process of the plaintext image.

[0162] like Figure 2 As shown, the decryption process of the ciphertext image is as follows:

[0163] The key K1 is used to iterate the Logistic chaotic system multiple times to generate a chaotic sequence of size i1. The first 1000 values ​​are removed to prevent transient effects, and the chaotic sequence x is obtained. The chaotic sequence x is converted to a pixel integer value of [0,255] using the following formula:

[0164] X = floor (x × 10 16 )mod 256;

[0165] Among them, floor(·) represents the floor function, and mod represents the remainder function;

[0166] Convert the rounded chaotic sequence X into The two-dimensional chaotic matrix A7.

[0167] The seven-dimensional hyperchaotic system is iterated using the key K2 to generate a hyperchaotic sequence of size i2. The first 1000 values ​​are removed to prevent transient effects, and 7 pseudo-random sequences are obtained:

[0168] y1(i),y2(i),y3(i),y4(i),y5(i),y6(i),y7(i);

[0169] The 7 pseudo-random sequences are integerized to obtain 7 integer sequences:

[0170] Y1(i),Y2(i),Y3(i),Y4(i),Y5(i),Y6(i),Y7(i);

[0171] Substitute the parameter i' in the key K2 into the sequence Y1(i), Y2(i), Y3(i) to obtain Y1(i'), Y2(i'), Y3(i');

[0172] Divide the ciphertext image into R C , G C , B C For three channels, perform the following decryption steps on each channel in turn to obtain the initial decrypted image of each channel;

[0173] R C Channel as an example, convert it into pixel matrix A C , the matrix A C Performing an XOR operation with the chaotic matrix A7 to obtain a two-dimensional pixel matrix A8;

[0174] Read the matrix A8 into array e in row order;

[0175] Remove the front of array e 0, and then read it in reverse order as array f, and read array f in order as indivual The two-dimensional matrices of size are stacked from top to bottom to form The size of the three-dimensional pixel matrix A9.

[0176] The matrix A9 is scrambled in reverse order. The specific method is as follows:

[0177] Use the integer sequence Y5(i) to control the rotation axis of the matrix A9:

[0178] When Y5(i)=0, the rotation axis is the X axis; when Y5(i)=1, the rotation axis is the Y axis; when Y5(i)=2, the rotation axis is the Z axis;

[0179] The integer sequence Y6(i) is used to control the rotation layer of the matrix A9 to be the Y6(i)th layer;

[0180] Use the integer sequence Y7(i) to control the rotation angle of the selected layer:

[0181] When Y7(i)=0, rotate 90°; when Y7(i)=1, rotate 180°; when Y7(i)=2, rotate 270°;

[0182] The direction of rotation is counterclockwise, from Start rotating to i=1, and finally get the scrambled three-dimensional pixel matrix A 10 .

[0183] The scrambled three-dimensional pixel matrix A 10 Read in reverse order as array g, and remove the end of array g 0 to get the array h, and read the array h as a two-dimensional pixel matrix A of l×l 11 .

[0184] Let Y4(i') be the number of inverse Arnold transformations, and 11 Perform inverse Arnold transform to get the transformed matrix A 12 , the pixel matrix R 12 Convert to channel image;

[0185] Select the values ​​Y1(i'), Y2(i'), and Y3(i') in the key K3 as the three channels R 12 , G 12 , B 12 The inverse processing parameters of the pixel values ​​are used to inversely process each channel to obtain three channels R P' , G P' , B P' The pixel values ​​of the image are:

[0186]

[0187] The initial decrypted images of the three channels are merged and converted into a color image P', whose size is l×l. According to K4=(M,N), the last l is removed 2 -M×N pixels with a pixel value of 0, and obtain the final decrypted image P with a size of M×N.

[0188] A second aspect of the present invention provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and wherein the processor implements the steps of the image encryption method when executing the computer program.

[0189] A third aspect of the present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and wherein the computer program implements the steps of the image encryption method when executed by a processor.

[0190] This embodiment uses MATLAB R2022a to simulate and verify the image encryption and decryption method of the present invention. The specific operating environment is as follows: 13th Gen Intel (R) Core (TM) i7-13700H @ 2.40GHz, 32GB memory, 64-bit operating system, and X64-based processor. In order to intuitively evaluate the encryption effect of the algorithm proposed in the present invention, the present invention selects the Lena graph as the experimental object to encrypt and decrypt it.

[0191] from Figure 3 It can be seen that the encrypted image presents the characteristics of random noise, and the decrypted image is completely consistent with the original image. The image encryption and decryption algorithm proposed in the present invention can effectively realize image encryption and decryption.

[0192] Obviously, from Figure 3 In (b), no information related to the plaintext can be seen. Next, various image encryption performance indicators are used to study the performance of this method.

[0193] 1) Key sensitivity analysis

[0194] Key sensitivity is an important indicator to measure the security of encryption algorithms. In order to test the sensitivity of the algorithm of the present invention to key changes, the ciphertext image is decrypted using the correct key and the wrong key with a slight change to the correct key.

[0195] The error key is:

[0196]

[0197] K2, K3, and K4 remain unchanged;

[0198] The decryption result is as follows Figure 4 As shown, it can be seen that even if the difference between the wrong key and the correct key is very small, the plaintext image cannot be decrypted. Therefore, the algorithm proposed in the present invention has good key sensitivity.

[0199] 2) Key space analysis

[0200] In order to effectively resist brute force attacks, the key space of the encryption algorithm must be at least greater than 2 100 The key used by the algorithm of the present invention is:

[0201]

[0202] K2=(a,b,c,d,e,y1(0),y2(0),y3(0),y4(0),y5(0),y6(0),y7(0),i2,i q ,i')

[0203] Among them, the values ​​of a, b, c, d, and e are 10, 100, 2.7, 2, and 3 respectively;

[0204] The values ​​of y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), and y7(0) are all 1;

[0205]

[0206] K3={3,5,7,9,11,13,15,…,251,253,255};

[0207] K4=(M,N);

[0208] On computers with 64-bit operating systems, floating point numbers can have a precision of up to 10 -16 Therefore, the sensitivity of the Logistic chaotic map and the seven-dimensional hyperchaotic system to parameters and initial values ​​is 10 -16 , where the seven-dimensional hyperchaotic system parameter values ​​are fixed, and the integer processing of the pseudo-random sequence is also accurate to 16 decimal places. It can be estimated that the key space size of the algorithm of the present invention is at least (1016 ) 3 ×(10 16 ) 13 ×127 3 ≈2 871 , much larger than 2 100 , which can effectively resist brute force attacks. The key space comparison of different algorithms is shown in Table 2:

[0209] Table 2 Comparison of key spaces of different algorithms

[0210]

[0211] Table 2 compares the key space sizes of the algorithm of the present invention and several other related algorithms. It can be seen that the key space of the algorithm proposed by the present invention is larger and has a better image encryption effect.

[0212] 3) Histogram analysis

[0213] from Figure 5 It can be observed that the histogram of the ciphertext image tends to be evenly distributed, so the encryption algorithm of the present invention can resist statistical analysis attacks.

[0214] 4) Correlation analysis of adjacent pixels

[0215] like Figure 6 As shown, in order to evaluate the scrambling effect of the algorithm of the present invention, the correlation coefficients of adjacent pixels of the plaintext image and the ciphertext image in the horizontal, vertical and diagonal directions are calculated respectively, and the correlation coefficients of the algorithm of the present invention are compared with those of other algorithms. The results are shown in Table 3:

[0216] Table 3 Comparison of correlation coefficients of adjacent pixels

[0217]

[0218] from Figure 6 It can be seen that the correlation coefficient of adjacent pixels of the ciphertext image encrypted by the algorithm of the present invention is much lower than that of the plaintext image, and lower than the correlation coefficients of other documents, and has better performance in image encryption.

[0219] 5) Information entropy analysis

[0220] Table 4 is a comparison of the information entropy of the ciphertext image obtained by the encryption algorithm of the present invention and the Lena color plaintext image and the encryption algorithms in other related image encryption literature. The information entropy comparison results are shown in Table 4 below:

[0221] Table 4 Information entropy comparison table

[0222]

[0223] It can be seen from Table 4 that the information entropy of the algorithm of the present invention is closer to the ideal value of 8, so the encryption algorithm of the present invention has better performance.

[0224] 6) Robustness analysis

[0225] In practical applications, image encryption algorithms should be able to resist cropping attacks and noise attacks. In order to evaluate the robustness of the algorithm, the ciphertext image area was cropped to 1 / 16, 1 / 8, and 1 / 4, respectively, and then decrypted; Gaussian noise with variances of 0.001, 0.005, and 0.01 was added to the ciphertext image, and then decrypted. The results are as follows: Figure 7 and Figure 8 As shown in the figure, it can be seen that after being attacked by shearing or noise, the decrypted image is affected to varying degrees. When the data shearing of the encrypted image is relatively small, part of the original image information can be restored, and after the encrypted image is contaminated by low-intensity noise, part of the original image information can also be restored. This shows that the algorithm of the present invention has a strong anti-attack capability and can maintain basic recoverability in a harsh channel environment.

[0226] 7) Time test comparison

[0227] In order to verify the influence of different scrambling times of the Rubik's Cube in the algorithm on the final encryption effect, according to the actual size of the Lena color image used by the algorithm, the encryption effect of different scrambling times of the Rubik's Cube is analyzed using image encryption performance indicators such as encryption and decryption time, adjacent pixel correlation coefficient, and information entropy. After substituting the Lena color image parameters, the actual value is i=262144, and then the same Lena color image is encrypted with the number of Rubik's cube scrambling i / 10, i / 100, i / 1000, i / 10000 (the actual values ​​are 26215, 2622, 263, 27 respectively), and the performance indicators are compared. The results are shown in Table 5 below:

[0228] Table 5 Comparison of encryption and decryption algorithm time and encryption effect with different Rubik's Cube scrambling times

[0229]

[0230] As can be seen from Table 5, when the encryption algorithms with different scrambling times are used to encrypt the image, the correlation coefficient and information entropy of the adjacent pixels of the encrypted image are slightly different, but the encryption and decryption time increases significantly with the increase of the scrambling times, and the difference is large. Therefore, when the difference in encryption performance is negligible, the encryption algorithm with fewer scrambling times is selected, which will reduce the encryption time and increase the encryption efficiency.

[0231] In order to eliminate the interference of other encryption steps in this encryption method, the influence of different Rubik's Cube scrambling times on the image encryption effect is further studied. The same Lena color image is scrambled with different Rubik's Cube scrambling times. The scrambling effects of different Rubik's Cube scrambling times are compared and analyzed using image encryption performance indicators such as scrambling time and adjacent pixel correlation coefficient. The comparison results are shown in Table 6 below:

[0232] Table 6 Comparison of scrambling time and scrambling effect of different Rubik's Cube scrambling times

[0233]

[0234] From Table 6, we can see that when the number of scrambling times is i and i / 10, the correlation coefficient of adjacent pixels in the scrambled image is low and the difference is not large, but the scrambling time of the former is much longer than that of the latter. Therefore, when the difference in encryption performance is negligible, the encryption algorithm with fewer scrambling times is selected, which will reduce the encryption time and increase the encryption efficiency.

[0235] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space, characterized in that: The following steps are involved: The key K1 is selected to iterate the Logistic chaotic system for multiple times to generate a chaotic sequence, which is then converted into a chaotic matrix A6 after integer processing; The key K2 is selected to iterate the seven-dimensional hyperchaotic system to generate a hyperchaotic sequence, and then the hyperchaotic sequence is converted into an integer sequence; Divide the plaintext image P into R P , G P , B P Three channels, select key K3 to preprocess the pixel values ​​of the three channel images to obtain pixel matrix A1; Performing Arnold transformation on the pixel matrix A1 to obtain a transformed matrix A2, and transforming the matrix A2 into a three-dimensional pixel matrix A3; Performing a three-dimensional Rubik's cube scrambling on the matrix A3 using an integer sequence to obtain a scrambled three-dimensional pixel matrix A4; The matrix A4 is transformed into a two-dimensional pixel matrix A5, and the matrix A5 is XOR-ed with the chaotic matrix A6 to obtain the ciphertext image.

2. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 1, characterized in that: Select the key K1=(μ,x0,i1,i q ) as the parameters, initial values, number of iterations and number of removed groups of the Logistic chaotic mapping; Among them, μ=3.998, x0=0.720, i q =1000; ceil(·) represents the upward rounding function, l = max(M,N), and the size of the plaintext image is M×N; The key K1 is used to iterate the Logistic chaotic system multiple times to generate a chaotic sequence of size i1. The first 1000 values ​​are removed to obtain the chaotic sequence x. The chaotic sequence x is converted into a pixel integer value of [0,255] using the following formula: X=floor(x×10 16 )mod 256; Among them, floor(·) represents the floor function, and mod represents the remainder function; Convert the rounded chaotic sequence X into The two-dimensional chaotic matrix A6.

3. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 1, characterized in that: Select key K2 = (a, b, c, d, e, y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), y7(0), i2, i q ,i') as the parameters, initial values, number of iterations, number of removed groups, Arnold transformation and preprocessing parameters of the seven-dimensional hyperchaotic system; Among them, the values ​​of a, b, c, d, and e are 10, 100, 2.7, 2, and 3 respectively; The values ​​of y1(0), y2(0), y3(0), y4(0), y5(0), y6(0), and y7(0) are all 1; The seven-dimensional hyperchaotic system is iterated using the key K2 to generate a hyperchaotic sequence of size i2. After removing the first 1000 values, 7 pseudo-random sequences are obtained: y1(i), y2(i), y3(i), y4(i), y5(i), y6(i), y7(i); The 7 pseudo-random sequences are integerized using the following formula to obtain 7 integer sequences: in, T represents the two-dimensional Arnold transform period corresponding to images of different sizes.

4. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 3, characterized in that: Read in a plaintext image P of size M×N and divide the plaintext image P into R P , G P , B P Three channels, perform the following encryption operations on the images of the three channels in turn to obtain the encrypted images of each channel; Let l = max(M, N), and pad the three channel images of the plaintext image P with zeros to obtain three channel images of size l×l; Substitute the parameter i' in the key K2 into the sequence Y1(i), Y2(i), Y3(i) to obtain Y1(i'), Y2(i'), Y3(i'); Select the Y1(i'), Y2(i'), and Y3(i') values ​​in the key K3 as the preprocessing parameters of the pixel values ​​of the three channel images, and preprocess each channel image to obtain the pixel values ​​of the images of the three channels R2, G2, and B2, respectively: Among them, the key K3 = {3, 5, 7, 9, 11, 13, 15, ..., 251, 253, 255}.

5. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 4, characterized in that: Convert the image of a certain channel into pixel matrix A1, substitute i' into sequence Y4(i) to obtain Y4(i'), use Y4(i') as the number of Arnold transformation to perform Arnold transformation on matrix A1, and obtain the transformed matrix A2; Read matrix A2 as array a in row order and fill in the array after a 0, get array b, read array b in sequence as indivual The two-dimensional matrices of size are stacked from top to bottom to form The size of the three-dimensional pixel matrix is ​​A3.

6. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 5, characterized in that: The method of performing three-dimensional Rubik's cube scrambling on matrix A3 is: Use the integer sequence Y5(i) to control the rotation axis of the matrix A3: When Y5(i)=0, the rotation axis is the X axis; when Y5(i)=1, the rotation axis is the Y axis; when Y5(i)=2, the rotation axis is the Z axis; The integer sequence Y6(i) is used to control the rotation layer of the matrix A3 to be the Y6(i)th layer; Use the integer sequence Y7(i) to control the rotation angle of the selected layer: When Y7(i)=0, rotate 90°; when Y7(i)=1, rotate 180°; when Y7(i)=2, rotate 270°; The rotation direction is clockwise, starting from i=1 to Finally, the scrambled three-dimensional pixel matrix A4 is obtained.

7. A hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 6, characterized in that: Read the scrambled three-dimensional pixel matrix A4 in reverse order as array c, and add 0s to obtain array d, read array d in reverse order as a two-dimensional pixel matrix A5, and perform XOR operation on matrix A5 and chaotic matrix A6 to obtain the encrypted image of a certain channel, and then merge the encrypted images of the three channels into the final ciphertext image.

8. The hyper-chaotic image encryption method based on parallel rotation scrambling of a magic cube three-dimensional space as claimed in claim 1, characterized in that: The ciphertext image is decrypted using the same chaotic matrix and chaotic sequence as in the encryption step to obtain the original plaintext image. The decryption process of the ciphertext image is the inverse process of the encryption process of the plaintext image.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the steps of the image encryption method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the image encryption method according to any one of claims 1 to 8 are implemented.

Images