Hybrid chaotic image encryption method based on tetrahedron rubik's cube spatial permutation

Abstract

The application provides a hybrid chaotic image encryption method based on tetrahedron Rubik's cube three-dimensional space permutation, chaotic pseudo-random sequences are generated through a 4D hyperchaotic system and a 3D-HSCM chaotic system, and the chaotic pseudo-random sequences are subjected to integerization processing to obtain chaotic pseudo-random integer sequences; then, a proved lemma is applied to pre-process R, G and B three channels of a plaintext image respectively, a first diffusion is realized, a processed two-dimensional image pixel matrix is converted into a tetrahedron, a chaotic pseudo-random integer sequence is used to dynamically select a rotation axis, a rotation layer number and a rotation angle, and tetrahedron Rubik's cube three-dimensional space permutation is carried out; then, the permuted tetrahedron is converted into a two-dimensional matrix, and an exclusive OR operation is performed between the two-dimensional matrix and a chaotic matrix formed by the chaotic integer sequence, a second diffusion is realized; finally, encrypted images of the R, G and B three channels are combined to obtain a ciphertext image, so that encryption is realized. The application can improve the encryption effect of a color image.

Description

Technical Field

[0001] This invention relates to the field of chaotic image encryption technology, and more specifically to a hybrid chaotic image encryption method based on tetrahedral Rubik's Cube three-dimensional spatial scrambling. Background Technology

[0002] With the increasing urgency of information transmission and storage security requirements, image encryption technology, as one of the main means of information security, has become a research hotspot in the field of image encryption. Traditional image encryption methods face challenges in their resistance to statistical analysis due to improvements in computing power and the evolution of attack algorithms. In recent years, chaotic systems have gradually attracted attention due to their ergodicity, non-periodicity, and pseudo-randomness. Rubik's Cube scrambling technology has advantages such as multi-dimensional transformation, and combining the two can further enhance the security of encryption algorithms.

[0003] Reference [1] proposes a new method for generating multidimensional chaotic signals using LSTNet and applies it to the designed two-stage pixel / bit level scrambling and dynamic diffusion (TSSDD) color image encryption algorithm. Through various analyses, the high chaos, randomness and resistance to common attacks of the method are verified. Reference [2] designs a new seventh-order hybrid memristor chaotic circuit, establishes its mathematical model and analyzes the equilibrium point, dissipation and other characteristics. Based on the chaotic key generated by the circuit, a new image encryption algorithm is designed. Through security analysis methods such as grayscale histogram, correlation and robustness, it is shown that the encryption algorithm has higher security and anti-decoding ability. Moreover, the circuit model is closer to the actual memristor chaotic circuit, which is of great significance to the commercial realization of memristor circuit. Reference [3] proposes a grayscale and color image encryption model based on a composite-order fusion cube. The fusion cube is constructed by a composite method. It utilizes the pseudo-randomness, large key space and structural complexity to achieve encryption in the scrambling and diffusion stages. No additional components are required. The randomness is also improved by layer shuffling. Experiments have verified that it is effective for images of different resolutions and formats and is suitable for medical images to ensure data security in telemedicine. Reference [4] proposes a 3D multi-image encryption scheme based on a cube-poker model. Multiple images are constructed into a 3D cube. The key and operation sequence are generated by interleaving logic mapping. The cube is scrambled by combining cube plane rotation and poker shuffling. Encryption is then completed by XORing the 3D key. This scheme has flexible input, low time cost and strong resistance to attacks and data loss recovery capabilities. Reference [5] proposes a multi-color image encryption algorithm based on three-dimensional cube scrambling, multi-wave chaotic system, genetic information diffusion and dynamic shift diffusion. It integrates color images of different sizes into a three-dimensional cube, and achieves scrambling by controlling the rotation of each plane of the cube through chaotic sequence. It combines the genetic mechanisms such as DNA / RNA replication and mutation with dynamic shift XOR to complete double diffusion, and has a large key space and strong anti-attack capability.

[0004] In existing research, the hexahedral Rubik's Cube, due to its regular six-sided structure and good scrambling effect, is widely used in the scrambling process for image encryption. However, this type of method has two limitations: first, the hexahedral Rubik's Cube has a limited selection of rotation axes, and as research progresses, the scrambling space expansion gradually becomes limited; second, existing methods have not fully explored the scrambling effects of other regular polyhedra, such as the tetrahedral Rubik's Cube, which has four rotation axes, making its spatial transformation path more complex. Summary of the Invention

[0005] To address the shortcomings of existing hexahedral Rubik's Cube scrambling methods in terms of structural innovation and encryption dimension, this invention proposes a hybrid chaotic image encryption method based on tetrahedral Rubik's Cube three-dimensional spatial scrambling, which improves the image encryption effect.

[0006] The technical solution of this invention is implemented as follows: In one aspect, this invention proposes a hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling, comprising the following steps: Read plaintext image P of size Chaotic pseudo-random sequences are generated using 4D hyperchaotic systems and 3D-HSCM chaotic systems. and After integerization, a chaotic pseudo-random integer sequence is obtained. ; The R, G, and B channels of the plaintext image P are preprocessed separately, using integer chaotic sequences. The first diffusion is achieved by processing the two-dimensional image pixel matrix. Convert to tetrahedron ; Using chaotic pseudo-random integer sequences Dynamically select the rotation axis, number of rotation layers, and rotation angle to scramble the three-dimensional space of a tetrahedron. The disordered tetrahedron Convert to a two-dimensional matrix Then, with chaotic integer sequences The constructed chaotic matrix Perform an XOR operation to achieve a second diffusion; Encrypting images with R, G, and B channels The images are merged to obtain the ciphertext image C, thus achieving encryption.

[0007] In another aspect, this invention proposes a method for decrypting a hybrid chaotic image based on the scrambling of a tetrahedral cube's three-dimensional space, which obtains the decrypted image from the encrypted image obtained by the above-mentioned image encryption method through inverse operation.

[0008] In another aspect, the present invention provides an electronic device including a memory and a processor, wherein the memory stores a computer program executable on the processor, and the processor executes the computer program to implement the steps of the image encryption method and / or the image decryption method.

[0009] In another aspect, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the image encryption method and / or the image decryption method.

[0010] The beneficial effects of this invention are as follows: 1. The pixel values ​​of the R, G, and B channels of the color image are multiplied by different parameters and then preprocessed by performing the same modulo operation. Combined with XOR diffusion, two depth diffusion operations are performed. 2. After mapping the image pixel values ​​to all the small cubes contained in the entire tetrahedral Rubik's Cube, scrambling is performed in three-dimensional space. The scrambling complexity is high, which makes better use of the characteristics of the three-dimensional cube structure of the Rubik's Cube; tetrahedral three-dimensional space scrambling is used to break the limitations of hexahedral Rubik's Cube scrambling. 3. By using chaotic pseudo-random sequences to dynamically control the rotation axis, number of rotation layers, and rotation angle of the Rubik's Cube, the randomness is better and the encryption effect is better. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the encryption process of the present invention.

[0013] Figure 2 This is a structural diagram of a regular tetrahedron.

[0014] Figure 3 This is a flowchart of the decryption process of the present invention.

[0015] Figure 4 The images are plaintext, ciphertext, and decrypted images, as shown in the embodiments of the method of the present invention. in Figure 4 (a) is a plaintext image. Figure 4 (b) is a ciphertext image. Figure 4 (c) is the decrypted image.

[0016] Figure 5 This is the result of the key sensitivity test. in Figure 5 (a) is the image decrypted with the correct key. Figure 5 (b) Image decrypted with the wrong key.

[0017] Figure 6 shows the histograms of the plaintext and ciphertext images. Figure 6(a) shows the histograms of the R, G, and B channels of the Lena plaintext image, and Figure 6(b) shows the histograms of the R, G, and B channels of the Lena ciphertext image.

[0018] Figure 7 To compare the correlation between adjacent pixels in Lena's plaintext and ciphertext images, in Figure 7 (a) shows the horizontal direction of the R channel in the original image. Figure 7 (b) represents the horizontal direction of the R channel in the dense map. Figure 7 (c) represents the vertical direction of the R channel in the original image. Figure 7 (d) represents the vertical direction of the R channel in the dense diagram. Figure 7 (e) represents the diagonal direction of the R channel in the original image. Figure 7 (f) represents the diagonal direction of the R channel in the dense map. Figure 7 (g) represents the horizontal direction of channel G in the original image. Figure 7 (h) represents the horizontal direction of the G channel in the dense map. Figure 7 (i) represents the vertical direction of channel G in the original image. Figure 7 (j) represents the vertical direction of the G channel in the dense map. Figure 7 (k) represents the diagonal direction of the G channel in the original image. Figure 7 (l) represents the diagonal direction of the G channel in the dense graph. Figure 7 (m) represents the horizontal direction of channel B in the original image. Figure 7 (n) represents the horizontal direction of channel B in the dense map. Figure 7 (o) represents the vertical direction of channel B in the original image. Figure 7 (p) represents the vertical direction of channel B in the dense map. Figure 7 (q) represents the diagonal direction of channel B in the original image. Figure 7 (r) represents the diagonal direction of the B channel in the dense map.

[0019] Figure 8 These are decrypted images after being subjected to cut-and-paste attacks of different proportions. in, Figure 8 (a) is the decrypted image after being cut to 1 / 16. Figure 8 (b) is the decrypted image after being cut to 1 / 8. Figure 8 (c) is the decrypted image after being cut 1 / 4.

[0020] Figure 9 These are the decrypted images after being attacked by noise of varying variance. in, Figure 9(a) is the image decrypted with noise (0.001). Figure 9 (b) Decrypting the image with noise (0.005), Figure 9 (c) is the image decrypted from noise (0.01). Detailed Implementation

[0021] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] This paper proposes to use a 4D hyperchaotic system and a 3D-HSCM to generate chaotic pseudo-random sequences.

[0023] The expression for a 4D hyperchaotic system is as follows:

[0024] in For the system's state variables, For the system control parameters, when the parameter initial value At that time, the 4D hyperchaotic system will exhibit a chaotic state. [6] .

[0025] The expression for a 3D-HSCM chaotic system is as follows:

[0026] in, For the system's state variables, Here are the system control parameters, mod is the remainder function, and sin is the sine function. When the parameters... initial value At that time, the system exhibits a chaotic state. [7] .

[0027] In the following sections, a 4D hyperchaotic system is used to generate chaotic pseudo-random sequences, which are used as preprocessing parameters in the encryption algorithm and to form a two-dimensional chaotic pseudo-random sequence matrix for diffusion. A 3D-HSCM is used to generate chaotic pseudo-random sequences, which are used as tetrahedral cube spatial scrambling control parameters in the encryption algorithm.

[0028] In one aspect of the present invention, such as Figure 1 As shown, a hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling is provided, including the following steps: Step 1: Read the plaintext image P, size P is Chaotic pseudo-random sequences are generated using 4D hyperchaotic systems and 3D-HSCM chaotic systems. and After integerization, a chaotic pseudo-random integer sequence is obtained. .

[0029] Selecting parameters for the expression of a 4D hyperchaotic system initial value Number of iterations Remove group number and preprocessing parameters As a key After multiple iterations, a size of [size missing] is generated. The chaotic pseudo-random sequence is obtained by removing the first 999 values ​​to prevent transient effects. .

[0030] Selecting parameters for the expression of a 3D-HSCM chaotic system initial value Number of iterations and the number of groups removed As a key After multiple iterations, a size of [size missing] is generated. The chaotic pseudo-random sequence is obtained by removing the first 999 values ​​to prevent transient effects. .

[0031] For chaotic pseudo-random sequences Integerization is performed to obtain an integer chaotic sequence. ,

[0032] in, It is the floor function. It is the floor function.

[0033] Integer chaotic sequence Convert to size Chaotic matrix .

[0034] Step 2: Perform preprocessing on the R, G, and B channels of the plaintext image P, using integer chaotic sequences. The first diffusion was achieved.

[0035] Plain text image Divided into Three channels to process pre-processed parameters Substitute the value into the integer chaotic sequence get ,exist Select the first Each value is respectively used as Preprocessing parameters for the pixel values ​​of the three channels are used to preprocess the images of each channel, resulting in the three channels. The pixel values ​​of the image are as follows:

[0036] Channel The images are converted into two-dimensional pixel matrices respectively. .

[0037] Remainder-related knowledge

[0038] Lemma if , , and If it is known and ,but There is a unique solution.

[0039] Prove if , , and Then it exists Make =1 mod 256. Therefore, the original expression is equivalent to... = mod256, that is = mod256, and because Unique, therefore only. Certification completed.

[0040] in, It is the modulo function. In encryption and decryption methods, this theorem can be used to ensure the uniqueness of the decomposition and synthesis of the R, G, and B channels during image preprocessing and inverse processing.

[0041] According to Euler's totient function, there are 128 integers in the range [0, 255] that are relatively prime to 256. However, substituting the first element 1 into the formula might result in the preprocessed pixel values ​​remaining unchanged, leading to poor final image encryption. Therefore, removing the first element 1 from the original set yields the key set required by the encryption algorithm of this invention. It contains a total of 127 elements.

[0042] Step 3, process the pixel matrix of the two-dimensional image. Convert to tetrahedron .

[0043] Two-dimensional pixel matrix Read the array m in row-by-row order and fill it with padding. - We obtain an array n by adding zeros, and then map the pixels in n sequentially onto each unit tetrahedron contained in the tetrahedral cube space, resulting in a pixel-based array. Tetrahedron Its number of pixels is .

[0044] Step 4, using a chaotic pseudo-random integer sequence Dynamically select the rotation axis, number of rotation layers, and rotation angle to scramble the three-dimensional space of a tetrahedron.

[0045] like Figure 2 As shown, tetrahedron The four vertices A, B, C, and D, , Control the tetrahedrons separately Is the axis of rotation a cubic axis of rotation passing through point A, point B, point C, or point D? Control tetrahedron The number of layers rotated is the first. layer; The selected layer can be rotated either to 120° or 240°, with the rotation direction always clockwise. from Start operation to The scrambled tetrahedron is obtained. .

[0046] Step 5, scramble the tetrahedron Convert to a two-dimensional matrix Then, with chaotic integer sequences The constructed chaotic matrix Performing an XOR operation to achieve a second diffusion includes: The disordered tetrahedron The pixels contained therein are read as array j by reversing the process of converting the processed two-dimensional pixel matrix into a tetrahedron in step 3, and then padded to the end. Get an array k by adding zeros, and map the pixels in k sequentially to an array of size k. Two-dimensional pixel matrix Up; General and Perform an XOR operation to obtain the final encrypted images for the R, G, and B channels respectively. .

[0047] Step 6: Encrypt the image using the R, G, and B channels. The images are merged to obtain the ciphertext image C, thus achieving encryption.

[0048] In one aspect of the present invention, such as Figure 3 As shown, a method for decrypting hybrid chaotic images based on tetrahedral Rubik's Cube spatial scrambling is provided. The inverse process of the above encryption process specifically includes the following steps: Step 1: Read in the color ciphertext image C, select the 4D hyperchaotic system according to the key. After iterating and removing the first 999 sets of values, a chaotic pseudo-random sequence is obtained. .

[0049] Selecting a 3D-HSCM chaotic system based on the key Iterating through (2) and removing the first 999 sets of values ​​yields a chaotic pseudo-random sequence. .

[0050] For chaotic pseudo-random sequences Integerization is performed to obtain an integer chaotic sequence. .Will Substitute the value into the sequence get Then, the integer chaotic sequence Convert to size Chaotic matrix .

[0051] Step 2, divide the color encrypted image C into... Three channels, Convert them into pixel matrices respectively ,and XOR generates a two-dimensional pixel matrix .

[0052] Will Read the array j in row-order order, then remove the last row from j. We obtain an array k by adding zeros, and then map the pixels in k sequentially onto each unit tetrahedron contained in the tetrahedral cube space, resulting in a pixel-based array. Tetrahedron Its number of pixels is .

[0053] Step 3, for the tetrahedron Perform a reverse scramble of a tetrahedron in three-dimensional space. The four vertices A, B, C, and D, , Control the tetrahedrons separately Is the axis of rotation a cubic axis of rotation passing through point A, point B, point C, or point D? Control tetrahedron The number of layers rotated is the first. layer; The selected layer is rotated either 120° or 240°, with the rotation direction always counter-clockwise; from Start operation to The scrambled tetrahedron is obtained. .

[0054] Step 4, turn the tetrahedron The contained pixels are read into array m by reversing step 2, and the last few pixels of m are removed. - The result is an array n, containing zeros. n is then read as... Two-dimensional pixel matrix of size Then it is converted into an initial decrypted image with R, G, and B channels. .

[0055] Step 5, in Select the first Each value is respectively used as The inverse processing parameters of the pixel values ​​are used to perform inverse processing on each channel image to obtain three channels. The pixel values ​​of the image are as follows:

[0056] Step 6: Decrypt the images from the three channels. The images are merged to obtain the final decrypted image P.

[0057] Simulation results and performance analysis

[0058] This paper uses MATLAB R2022a to simulate and verify the proposed method. The specific operating environment is as follows: 13th Gen Intel(R) Core(TM) i7-13700H@2.40GHz, 32GB RAM, 64-bit operating system, x64-based processor. To intuitively evaluate the encryption effect of the proposed method, a 512×512×3 Lena standard color image was selected as the experimental object for encryption and decryption. Figure 4 As can be seen, the encrypted image exhibits the characteristics of random noise, and the decrypted image is completely identical to the original image. Therefore, the image encryption and decryption method proposed in this paper can effectively realize image encryption and decryption.

[0059] (1) Key sensitivity analysis

[0060] Key sensitivity is a crucial indicator of the security of an encryption algorithm. To assess the sensitivity of the algorithm presented in this paper to key changes, we tested it using both a correct key and an incorrect key (the incorrect key being a result of a minor alteration to the correct key). , Decrypting the ciphertext image (keeping it unchanged) yields the following result: Figure 5 As shown in the figure, even a slight difference between the incorrect key and the correct key is insufficient to decrypt the correct image. Therefore, the algorithm proposed in this paper has good key sensitivity.

[0061] (2) Key space analysis

[0062] The key space of the encryption algorithm must be at least larger than Only in this way can we effectively resist brute-force attacks. The key used in the algorithm presented in this paper is... , , On a computer with a 64-bit operating system, the floating-point precision can reach... Therefore, the sensitivity of 4D hyperchaotic systems and 3D-HSCM to parameters and initial values ​​is... It can be estimated that the key space size of the algorithm in this paper is at least [size missing]. Much larger This indicates a strong ability to resist violent attacks.

[0063] Table 1. Comparison of Key Spaces for Different Algorithms

[0064] Table 1 compares the key space size of the algorithm in this paper with several other related algorithms. It can be seen that the algorithm proposed in this paper has a larger key space and better image encryption effect.

[0065] (3) Histogram analysis

[0066] As can be observed from Figure 6, the histogram of the plaintext image is undulating and has obvious characteristics, while the histogram of the ciphertext image tends to be uniformly distributed, indicating that the encryption algorithm in this paper can resist statistical analysis attacks.

[0067] (4) Correlation analysis of adjacent pixels

[0068] from Figure 7 It can be seen that the correlation between adjacent pixels in the plaintext image of Lena is very high, while the correlation between adjacent pixels in the ciphertext image is very low.

[0069] To further evaluate the correlation between adjacent pixels in the proposed method, the correlation coefficients of adjacent pixels in the plaintext and ciphertext images of Lena were calculated in the horizontal, vertical, and diagonal directions, respectively. The correlation coefficients of the proposed algorithm were compared with those of other algorithms, and the results are shown in Table 2.

[0070] Table 2 Comparison of Correlation Coefficients of Adjacent Pixels

[0071] As can be seen from Table 2, the correlation coefficient between adjacent pixels of the encrypted image obtained by the method in this paper is much lower than that of the plaintext image, and is generally lower than the correlation coefficient of other literature, showing superior performance in image encryption.

[0072] (5) Information entropy analysis

[0073] Table 3 Comparison of Information Entropy

[0074] Table 3 compares the information entropy of Lena's plaintext and ciphertext images with that of encryption algorithms in other relevant image encryption literature. The image encrypted using the method presented in this paper has an information entropy closer to the ideal value of 8 compared to images encrypted using other methods; therefore, the encryption algorithm presented in this paper exhibits superior performance.

[0075] (6) Robustness analysis

[0076] In practical applications, image encryption methods should be resistant to cropping and noise attacks. To evaluate the robustness of the algorithm, 1 / 16, 1 / 8, and 1 / 4 of the area of ​​the Lena ciphertext image were cropped before decryption. Gaussian noise with variances of 0.001, 0.005, and 0.01 was added to the ciphertext image before decryption, and the results are shown below. Figure 8 and Figure 9 As shown, observations reveal that the decrypted image is affected to varying degrees after being subjected to shearing or noise attacks. When the sheared portion of the image is small or the noise contamination intensity is low, some information from the original image can be recovered. This demonstrates that the algorithm presented in this paper has strong anti-attack capabilities and can maintain basic recoverability in harsh channel environments.

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Claims

1. A hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling, characterized in that, Includes the following steps: Read plaintext image P of size Chaotic pseudo-random sequences are generated using 4D hyperchaotic systems and 3D-HSCM chaotic systems. and After integerization, a chaotic pseudo-random integer sequence is obtained. ; The R, G, and B channels of the plaintext image P are preprocessed separately, using integer chaotic sequences. The first diffusion is achieved by processing the two-dimensional image pixel matrix. Convert to tetrahedron ; Using chaotic pseudo-random integer sequences Dynamically select the rotation axis, number of rotation layers, and rotation angle to scramble the three-dimensional space of a tetrahedron Rubik's Cube; The disordered tetrahedron Convert to a two-dimensional matrix Then, with chaotic integer sequences The constructed chaotic matrix Perform an XOR operation to achieve a second diffusion; Encrypting images with R, G, and B channels The images are merged to obtain the ciphertext image C, thus achieving encryption.

2. The hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling as described in claim 1, characterized in that, Chaotic pseudo-random sequences are generated using 4D hyperchaotic systems and 3D-HSCM chaotic systems. and After integerization, a chaotic pseudo-random integer sequence is obtained. ,include: Selecting parameters for the expression of a 4D hyperchaotic system initial value Number of iterations Remove group number and preprocessing parameters As a key After multiple iterations, a size of [size missing] is generated. The chaotic pseudo-random sequence is obtained by removing the first 999 values ​​to prevent transient effects. ; Selecting parameters for the expression of a 3D-HSCM chaotic system initial value Number of iterations and the number of groups removed As a key After multiple iterations, a size of [size missing] is generated. The chaotic pseudo-random sequence is obtained by removing the first 999 values ​​to prevent transient effects. ; For chaotic pseudo-random sequences Integerization is performed to obtain an integer chaotic sequence. , in, It is the floor function. It is the floor function.

3. The hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling as described in claim 1, characterized in that, For size The plaintext image P undergoes preprocessing of its R, G, and B channels, using integer chaotic sequences. Achieving the first diffusion includes: Plain text image Divided into Three channels to process pre-processed parameters Substitute the value into the integer chaotic sequence get ,exist Select the first Each value is respectively used as Preprocessing parameters for the pixel values ​​of the three channels are used to preprocess the images of each channel, resulting in the three channels. The pixel values ​​of the image are as follows: Channel The images are converted into two-dimensional pixel matrices respectively. .

4. The hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling as described in claim 3, characterized in that, The processed two-dimensional image pixel matrix Convert to tetrahedron ,include: Two-dimensional pixel matrix Read the array m in row-by-row order and fill it with padding. - We obtain an array n by adding zeros, and then map the pixels in n sequentially onto each unit tetrahedron contained in the tetrahedral cube space, resulting in a matrix composed of pixels. Tetrahedron Its number of pixels is .

5. The hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling as described in claim 1, characterized in that, Using chaotic pseudo-random integer sequences Dynamically select the rotation axis, number of rotation layers, and rotation angle to scramble the three-dimensional space of a tetrahedron, including: tetrahedron The four vertices A, B, C, and D, , Control the tetrahedrons separately Is the axis of rotation a cubic axis of rotation passing through point A, point B, point C, or point D? Control tetrahedron The number of layers rotated is the first. layer; The selected layer can be rotated either to 120° or 240°, with the rotation direction always clockwise. from Start operation to The scrambled tetrahedron is obtained. .

6. The hybrid chaotic image encryption method based on tetrahedral Rubik's Cube spatial scrambling as described in claim 1, characterized in that, The disordered tetrahedron Convert to a two-dimensional matrix Then, with chaotic integer sequences The constructed chaotic matrix Performing an XOR operation to achieve a second diffusion includes: The disordered tetrahedron The contained pixels are read as array j by reversing the process of converting the processed two-dimensional pixel matrix into a tetrahedron, and then padded to the end. We obtain an array k by adding zeros, and then map the pixels in k sequentially to an array of size k. Two-dimensional pixel matrix superior; Integer chaotic sequence Convert to size Chaotic matrix , Will and Perform an XOR operation to obtain the final encrypted images for the R, G, and B channels respectively. .

7. A method for decrypting hybrid chaotic images based on tetrahedral Rubik's Cube spatial scrambling, characterized in that, The encrypted image obtained by the image encryption method according to any one of claims 1-6 is decrypted by performing an inverse operation.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the image encryption method as described in any one of claims 1-6 or / and the image decryption method as described in claim 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the image encryption method as described in any one of claims 1-6 or / and the image decryption method as described in claim 7.

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