Image encryption method and system based on hyperchaotic driving and reversible cellular automaton

Abstract

The invention relates to the technical field of image information security, and discloses an image encryption method and system based on hyperchaotic driving and a reversible cellular automaton. The method comprises the following steps: generating a driving parameter and an initial value of the time delay three-dimensional memristor hyperchaotic system according to a plaintext image and an external key; using the driving parameters and the initial values to obtain multiple groups of chaotic sequences; performing pixel-level scrambling on a plaintext to be encrypted to obtain a three-dimensional matrix; performing bit-level scrambling on the three-dimensional matrix by using a chaos sequence to obtain a scrambled three-dimensional matrix; based on the chaos sequence, constructing a dynamic rule pool and an intermediate configuration matrix for reversible second-order cellular automaton evolution; taking the scrambled three-dimensional matrix as an initial cellular state of the reversible second-order cellular automaton, and executing second-order evolution of the reversible second-order cellular automaton in combination with the intermediate configuration matrix and the dynamic rule pool to generate a ciphertext matrix; and reconstructing the ciphertext matrix into a ciphertext image. According to the invention, the randomness, attack resistance and reliability of image encryption can be improved.

Description

Technical Field

[0001] This application relates to the field of image information security technology, and in particular to an image encryption method and system based on hyperchaotic driving and reversible cellular automata. Background Technology

[0002] With the rapid development of digitalization and the Internet of Things (IoT) technologies, images, as a core carrier of information transmission, are widely used in fields such as medical imaging, satellite remote sensing, and IoT terminal data acquisition. When these images are transmitted through public channels, they face multiple security threats, including eavesdropping, tampering, segmentation and destruction, and noise interference. Once sensitive information is leaked or illegally altered, it can lead to serious privacy breaches and security risks. Therefore, ensuring the security and confidentiality of image information transmission has become a key research topic in the field of information security.

[0003] Image encryption technology is a core means of protecting image information security. By scrambling and spreading the original image, its spatial correlation and statistical properties are disrupted, preventing attackers from directly obtaining useful information. Chaotic systems, due to their sensitivity to initial conditions, pseudo-randomness, and ergodicity, have become an important technical support for image encryption. Traditional image encryption algorithms are mostly based on low-dimensional chaotic systems or classical three-dimensional chaotic systems, but these systems have obvious drawbacks: the dynamic behavior of low-dimensional chaotic systems is relatively simple, the key stream is easily predictable, and their resistance to attacks is insufficient; although classical three-dimensional chaotic systems possess a certain degree of pseudo-randomness, their dimensionality is limited, making them vulnerable to chaotic synchronization attacks.

[0004] Meanwhile, cellular automata (CA), as a discrete dynamic system, are also widely used in image encryption. Traditional CAs often employ fixed evolution rules (such as Rule 30 / 87), which suffer from problems such as limited key space, irreversible evolution, and insufficient adaptability, thus limiting the randomness and attack resistance of encryption algorithms. In addition, the loss of precision in floating-point operations, which is common in existing encryption algorithms, also affects the accuracy of encryption and decryption, reducing the reliability of the algorithm.

[0005] In summary, existing color image encryption algorithms suffer from drawbacks such as limited dimensionality of chaotic systems, rigid rules of cellular automata, loss of precision in floating-point operations, and insufficient resistance to attacks, making it difficult to meet the image transmission requirements of high-security scenarios. Therefore, there is an urgent need to design a color image encryption scheme that combines high randomness, strong resistance to attacks, and high reliability. Summary of the Invention

[0006] The purpose of this invention is to address at least one deficiency in the existing technology and provide an image encryption method based on hyperchaotic driving and reversible cellular automata. This invention improves the randomness, anti-attack and reliability of image encryption by coordinating hyperchaotic systems and dynamic reversible cellular automata.

[0007] To achieve the above objectives, in a first aspect, the present invention provides an image encryption method based on hyperchaotic driving and reversible cellular automata, the method comprising the following steps:

[0008] Based on the plaintext image to be encrypted and the external key, generate the driving parameters and initial values ​​of the time-delayed three-dimensional memristor hyperchaotic system. The time-delayed three-dimensional memristor hyperchaotic system is iterated using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences. The plaintext to be encrypted is scrambled at the pixel level to obtain a three-dimensional matrix; The chaotic sequence is used to perform bit-level scrambling on the three-dimensional matrix to obtain the scrambled three-dimensional matrix. Based on the chaotic sequence, a dynamic rule pool and intermediate configuration matrix are constructed for the evolution of the reversible second-order cellular automaton. The scrambled three-dimensional matrix is ​​used as the initial cell state of the reversible second-order cellular automaton. Combined with the intermediate configuration matrix and the dynamic rule pool, the second-order evolution of the reversible second-order cellular automaton is performed to generate the ciphertext matrix. The ciphertext matrix is ​​reconstructed into a ciphertext image.

[0009] Furthermore, the time-delayed three-dimensional memristor hyperchaotic system is constructed by introducing memristor nonlinear elements and a time-delay feedback mechanism into the classical Lorenz system, and its mathematical model is expressed as follows:

[0010] in, x, y, z All are state variables of a time-delayed three-dimensional memristor hyperchaotic system. W ( z () represents the memristor model, and its expression is: W ( z )= , This is a time delay feedback term, reflecting the system's latency. The state of being at any moment The influence of moment state; The parameters of the hyperchaotic system are... For memristor parameters, This is the time delay parameter.

[0011] Furthermore, the step of generating the driving parameters and initial values ​​of the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key specifically includes: Obtain the 256-bit external key and the plaintext image to be encrypted; Perform a SHA-256 hash operation on the plaintext image to be encrypted to obtain a 256-bit first hash value; The plaintext image to be encrypted is decomposed into three channel matrices: R, G, and B. SHA-256 hash operation is performed on the three channel matrices respectively, and the three hash values ​​are XORed to generate image feature hash values. The first hash value and the image feature hash value are XORed to obtain the final mixed hash value; The hybrid hash value is divided into a parameter segment and an initial value segment, and the parameters of the time-delay three-dimensional memristor hyperchaotic system are extracted from the parameter segment and the initial value segment, respectively. and initial value ( ).

[0012] Furthermore, the time-delay three-dimensional memristor hyperchaotic system is iterated using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences, including: substituting the driving parameters and the initial values ​​into the time-delay three-dimensional memristor hyperchaotic system, iteratively calculating new initial values ​​until the iteration threshold is reached, and then outputting multiple sets of chaotic sequences.

[0013] Further, the step of pixel-level scrambling of the plaintext to be encrypted to obtain a three-dimensional matrix includes: The plaintext image to be encrypted is decomposed into three channel matrices: R, G, and B. The size of both the plaintext image to be encrypted and the three channel matrices is M. N; Reorganize the three channel matrices into M. A 3N two-dimensional matrix V; Calculate the average value of each row of pixels in the two-dimensional matrix V, and use the average value as the number of cyclic displacements for that row; Perform a row cyclic displacement operation on each row of the two-dimensional matrix V using the obtained cyclic displacement count to obtain the first matrix after displacement; The first matrix after the displacement is decomposed into three M... An N matrix is ​​concatenated along its rows and reassembled into a 3M matrix. A two-dimensional matrix of N; Regarding 3M Perform a column cyclic shift operation on each row of a two-dimensional matrix N to obtain a second matrix after shifting; The second matrix after the displacement is decomposed into three M... The matrix of N , , The three M The matrix of N , , Reorganized into M N A three-dimensional matrix A of size 3.

[0014] Further, the average value of each row of pixels in the two-dimensional matrix V is calculated, and the average value is used as the number of cyclic displacements for that row. The formula for calculating the number of cyclic displacements is as follows:

[0015] in, shift_rowi For the second dimensional matrix V, the first dimensional matrix V is... i The number of cycle shifts in the row. floor This is a rounding function; a positive result indicates a right shift, and a negative result indicates a left shift.

[0016] Furthermore, in the step of performing bit-level scrambling on the three-dimensional matrix using the chaotic sequence, the bit-level scrambling includes: Obtain the first chaotic sequence X generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; Based on the first chaotic sequence X, each pixel in the three-dimensional matrix A Calculate the corresponding bit cyclic shift number. The calculation formula is as follows:

[0017] in, express The number of bits to cyclically shift at a given pixel bit position; a positive number shifts the pixel to the right, and a negative number shifts it to the left. Based on the calculated shift number For the pixel The binary bits are subjected to the corresponding cyclic shift operation; After performing the bit shift operation on all pixels in the three-dimensional matrix A in sequence, the resulting three-dimensional matrix B is obtained after bit-level scrambling.

[0018] Furthermore, the dynamic rule pool includes at least one of the following four types of integer mapping evolution rules: Logistic mapping, Tent mapping, Chebyshev mapping, and Logistic-Tent combined mapping.

[0019] Further, the step of performing the second-order evolution of the reversible second-order cellular automaton to generate the ciphertext matrix includes: The scrambled three-dimensional matrix is ​​used as the initial cell state of the invertible second-order cellular automaton. Obtain the second chaotic sequence Y and the third chaotic sequence Z generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; Based on the third chaotic sequence Z, calculate the rule index of each cell in the dynamic rule pool. The index calculation formula is as follows:

[0020] in,( i , j , h () represents the position of a cell in a three-dimensional matrix; Based on the rule index, each cell selects a corresponding evolution rule from the dynamic rule pool; The second chaotic sequence Y is reconstructed into an intermediate configuration matrix with the same dimension as the initial cell state. For each cell, the second-order evolution of the reversible second-order cellular automaton is executed based on its current state, the state of the corresponding cell and its neighborhood in the intermediate configuration matrix, and the evolution rule selected for the cell, to update its state. After all cells have completed the second-order evolution in sequence, the ciphertext matrix is ​​output.

[0021] Secondly, the present invention also provides an image encryption system based on hyperchaotic driving and reversible cellular automata, the system being based on the method described in the first aspect, comprising: Initialization module: used to generate driving parameters and initial values ​​for the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key; Iterative loop module: Iterates the time-delay three-dimensional memristor hyperchaotic system using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences; First scrambling module: performs pixel-level scrambling on the plaintext to be encrypted to obtain a three-dimensional matrix; Second scrambling module: Uses the chaotic sequence to perform bit-level scrambling on the three-dimensional matrix to obtain the scrambled three-dimensional matrix; Construction module: Based on the chaotic sequence, construct a dynamic rule pool and intermediate configuration matrix for the evolution of the reversible second-order cellular automaton; Evolution Module: The scrambled three-dimensional matrix is ​​used as the initial cell state of the reversible second-order cellular automaton. Combined with the intermediate configuration matrix and the dynamic rule pool, the second-order evolution of the reversible second-order cellular automaton is performed to generate the ciphertext matrix. Encryption module: Reconstructs the ciphertext matrix into a ciphertext image.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention introduces memristor nonlinearity and time-delay feedback when constructing a time-delayed three-dimensional memristor hyperchaotic system, making the system more complex and unpredictable. The generated chaotic sequence has stronger randomness, improving the key stream's resistance to analysis and prediction. It also employs a two-level scrambling mechanism combining pixel-level and bit-level scrambling, dynamically perturbing at the pixel spatial location and binary bit level respectively, effectively resisting statistical analysis and differential attacks. At the same time, it uses a reversible second-order cellular automaton for diffusion encryption, overcoming the weakness of traditional cellular automata's single rule and enhancing the nonlinear complexity and attack robustness of the encryption process. Attached Figure Description

[0023] Figure 1 This is a flowchart of an image encryption method based on hyperchaotic driving and reversible cellular automata according to Embodiment 1 of the present invention; Figure 2 This is a block diagram of an image encryption system based on hyperchaotic driving and reversible cellular automata according to Embodiment 3 of the present invention; Figure 3 The image to be encrypted is shown in Embodiment 2 of the present invention, wherein, (a) Peppers original image, (b) Boboon original image, (c) Goldhill original image; Figure 4 This is the ciphertext image of the encrypted image in Embodiment 2 of the present invention, wherein, (a) Peppers ciphertext image, (b) Boboon ciphertext image, (c) Goldhill ciphertext image; Figure 5 This is a key sensitivity comparison decryption image from Embodiment 2 of the present invention, wherein, (a) Normal key decryption result, (b) Parameters Decryption result, (c) parameters Decryption result, (d), initial value Decryption result; Figure 6 Here is a comparison chart of the correlation between adjacent pixels in Embodiment 2 of the present invention: (a), (b), and (c) are views of the correlation between adjacent pixels in the horizontal RGB three channels of the Peppers original image; (d), (e), and (f) are views of the correlation between adjacent pixels in the vertical RGB three channels of the Peppers original image; (g), (h), and (i) are views of the correlation between adjacent pixels in the diagonal RGB three channels of the Peppers original image; (j), (k), and (l) are views of the correlation between adjacent pixels in the horizontal RGB three channels of the Pepper ciphertext image; (m), (n), and (o) represent the correlation view of adjacent pixels in the vertical RGB three channels of the Peppers encrypted image; (p), (q), and (r) are views of the correlation between adjacent pixels in the RGB three channels along the diagonal of the Peppers encrypted image; Figure 7 The following is a Boboon noise test diagram from Embodiment 2 of the present invention: (a) is the decrypted image obtained by applying Gaussian noise of intensity 0.15 to the ciphertext image; (c) is the decrypted image obtained by applying Gaussian noise of intensity 0.2 to the ciphertext image; (b) is the decrypted image obtained by applying salt-and-pepper noise of intensity 0.15 to the ciphertext image; (d) is the decrypted image obtained by applying salt-and-pepper noise of intensity 0.2 to the ciphertext image; Figure 8 The following is a Peppers cutting test diagram from Embodiment 2 of the present invention: (a) is a 50% cut ciphertext image; (b) is the decrypted image corresponding to (a); (c) is a 25% cut ciphertext image; (d) is the decrypted image corresponding to (c); (e) is a 20% cut ciphertext image; (f) is the decrypted image corresponding to (e); (g) is an 8% cut ciphertext image; (h) is the decrypted image corresponding to (g). Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0025] Example 1 Please see Figure 1 A preferred embodiment of the present invention provides an image encryption method based on hyperchaotic driving and reversible cellular automata, the method comprising the following steps: S1: Generate the driving parameters and initial values ​​of the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key; S2: Iterate the time-delay three-dimensional memristor hyperchaotic system using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences; S3: Scramble the plaintext to be encrypted at the pixel level to obtain a three-dimensional matrix; S4: Use the chaotic sequence to perform bit-level scrambling on the three-dimensional matrix to obtain the scrambled three-dimensional matrix; S5: Based on the chaotic sequence, construct a dynamic rule pool and intermediate configuration matrix for the evolution of the reversible second-order cellular automaton; S6: Using the scrambled three-dimensional matrix as the initial cell state of the reversible second-order cellular automaton, and combining the intermediate configuration matrix and the dynamic rule pool, perform the second-order evolution of the reversible second-order cellular automaton to generate the ciphertext matrix. S7: Reconstruct the ciphertext matrix into a ciphertext image.

[0026] This embodiment introduces memristor nonlinearity and time-delay feedback when constructing a time-delayed three-dimensional memristor hyperchaotic system, making the system more complex and unpredictable. The generated chaotic sequence has stronger randomness, improving the key stream's resistance to analysis and prediction. It also adopts a two-level scrambling mechanism combining pixel-level and bit-level, dynamically perturbing at the pixel spatial location and binary bit level respectively, effectively resisting statistical analysis and differential attacks. At the same time, it uses a reversible second-order cellular automaton for diffusion encryption, overcoming the weakness of traditional cellular automata's single rule and enhancing the nonlinear complexity and attack robustness of the encryption process.

[0027] In an optional embodiment, in step S1, to address the shortcomings of the classical Lorenz system, this invention introduces the nonlinear characteristics of the memristor and a time-delay feedback mechanism to construct a time-delay three-dimensional memristor hyperchaotic system, the mathematical model of which is shown in the following equation:

[0028] in, x, y, z All are state variables of a time-delayed three-dimensional memristor hyperchaotic system. W ( z () represents the memristor model, and its expression is: W ( z )= , This is a time delay feedback term, reflecting the system's latency. The state of being at any moment The influence of moment state; The parameters of the hyperchaotic system are... For memristor parameters, This is the time delay parameter.

[0029] To determine whether a time-delayed three-dimensional memristor hyperchaotic system (for simplicity, all references to this system below, unless otherwise specified, refer to this system) can generate hyperchaotic signals suitable for encryption, a suitable combination of parameters needs to be selected. Analysis shows that when the time delay parameter... When = 1, the system can maintain a double positive Lyapunov exponent over a relatively wide parameter range, i.e., it enters a hyperchaotic state. Based on this, a typical set of parameter combinations is selected as follows: =25, =100, =10, =2, =1, =1. Calculations show that under these parameters, the Lyapunov exponents of the system are LE1 = 2.514270, LE2 = 0.305163, and LE3 = 1. 38.834926. Due to the presence of two positive Lyapunov exponents, the system is in a hyperchaotic state. This means that the key stream sequence generated by this system iteratively has higher complexity and unpredictability compared to the sequence generated by the classic Lorenz system, thus providing stronger security for image encryption.

[0030] In this embodiment, in order for the system to iteratively calculate the chaotic sequence used for encryption, it is necessary to first generate the system's driving parameters and initial values, specifically including: S101: Obtain a 256-bit external key and a plaintext image to be encrypted, wherein the plaintext image to be encrypted is a color image with a size of M. N; S102: Perform a SHA-256 hash operation on the plaintext image to be encrypted to obtain a 256-bit first hash value H; S103: Decompose the plaintext image to be encrypted into three channel matrices: R, G, and B. Perform SHA-256 hash operation on each of the three channel matrices, and XOR the three hash values ​​to generate the image feature hash value. ; S104: Combine the first hash value H with the image feature hash value Perform an XOR operation to obtain the final mixed hash value. ; S105: Transfer the mixed hash value The system is divided into a parameter segment (paramSegment) and an initial value segment (initSegment). Parameters of the time-delay three-dimensional memristor hyperchaotic system are extracted from the parameter segment and the initial value segment, respectively. and initial value ( Specifically, the mixed hash values The first 160 bits are divided into a parameter segment, and the last 96 bits are divided into an initial value segment. The first 80 bits are extracted from the parameter segment, normalized, and then used as the parameters of the L3D-TDMHS system. Extract the last 81-160 bits from the parameter segment as the system parameters. Extract the first 40 bits from the initial value segment and use them as the system initial value. Extract bits 41-80 from the initial value segment and use them as the system initial value. Extract bits 81-96 from the initial value segment and use them as the system initial value. ; indicates the following:

[0031] This embodiment introduces the nonlinear characteristics and time delay feedback mechanism of memristors into the traditional Lorenz system, which has higher randomness than two-dimensional memristor chaotic mapping and better efficiency than higher-dimensional chaotic systems, effectively balancing the efficiency and security of image encryption.

[0032] In an optional embodiment, step S2 includes: setting the driving parameters and the initial value ( Substitute the values ​​into the time-delayed three-dimensional memristor hyperchaotic system, iteratively calculate new initial values ​​until an iteration threshold (e.g., 1000 iterations) is reached, ensuring the system enters a stable attractor and eliminates transient effects. Finally, output 3. M In this embodiment, a total of three chaotic sequences are generated: the first chaotic sequence X, the second chaotic sequence Y, and the third chaotic sequence Z.

[0033] This embodiment generates random sequences using a time-delayed three-dimensional memristor hyperchaotic system, which has strong randomness and helps to improve the security and reliability of image encryption.

[0034] In an optional embodiment, step S3 includes: S301: Decompose the plaintext image to be encrypted into three channel matrices: R, G, and B, wherein the size of the plaintext image to be encrypted and the three channel matrices is M. N; S302: Reorganize the three channel matrices into M A 3N two-dimensional matrix V; S303: Calculate the average pixel value of each row in the two-dimensional matrix V, and use the average value as the number of cyclic displacements for that row; in this embodiment, the formula for calculating the number of cyclic displacements is as follows:

[0035] in, shift_rowi For the second dimensional matrix V, the first dimensional matrix V is... i The number of cycle shifts in the row. floor This is a rounding function; a positive result indicates a right shift, and a negative result indicates a left shift.

[0036] S304: Perform a row cyclic displacement operation on each row of the two-dimensional matrix V using the obtained cyclic displacement count to obtain the first matrix after displacement; S305: Decompose the first matrix after displacement into three M... An N matrix is ​​concatenated along its rows and reassembled into a 3M matrix. A two-dimensional matrix of N; S306: Regarding this 3M Perform a column cyclic shift operation on each row of a two-dimensional matrix N to obtain a second matrix after shifting; S307: Decompose the second matrix after displacement into three M... The matrix of N , , The three M The matrix of N , , Reorganized into M N A three-dimensional matrix A of size 3.

[0037] In this embodiment, by dynamically perturbing the pixel space, statistical analysis and differential attacks are effectively resisted, thereby improving the security and reliability of image encryption.

[0038] In an optional embodiment, step S4 includes: S401: Obtain the first chaotic sequence X generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; S402: Based on the first chaotic sequence X, for each pixel in the three-dimensional matrix A Calculate the corresponding bit cyclic shift number. The calculation formula is as follows:

[0039] in, express The number of bits to cyclically shift at a given pixel bit position; a positive number shifts the pixel to the right, and a negative number shifts it to the left. S403: Based on the calculated shift value For the pixel The binary bits are subjected to the corresponding cyclic shift operation; S404: After performing the bit shift operation on all pixels in the three-dimensional matrix A in sequence, the three-dimensional matrix B after bit-level scrambling is output.

[0040] In this embodiment, bit space scrambling effectively resists statistical analysis and differential attacks, thereby improving the security and reliability of image encryption.

[0041] In an optional embodiment, in step S5, the reversible second-order cellular automaton (RSCA) originates from the cellular automaton (CA), which is a dynamic system discrete in space and time. It comprises an array of cells. Each such cell can acquire a value from a finite number of possibilities and is synchronously updated in discrete time steps according to interaction rules. Since many cryptographic algorithms are based on RNGs, cellular automata are very suitable; traditional, simple cellular automata are generally used as RNGs, offering several advantages. The reversible second-order cellular automaton of this embodiment differs from well-known second-order cellular automata by employing a dynamic rule pool, a higher-order evolution mechanism, and integer arithmetic design, achieving significant improvements in security, randomness, and adaptability.

[0042] In this embodiment, the dynamic rule pool includes four types of integer mapping evolution rules: Logistic mapping, Tent mapping, Chebyshev mapping, and Logistic-Tent combined mapping. Specifically, Rule 1 (Integer Logistic Mapping):

[0043] in, express t The cell of time, L ( r , ) represents the Logistic mapping:

[0044] r The parameters for the Logistic mapping are represented as follows: , r The generation of requires the participation of a third chaotic sequence Z generated by the chaotic system; This represents the pixel value after the previous RSCA evolution. for t+ Configure the sum of the neighboring cells at time 1.

[0045] Rule 2 (Integer Tent Mapping):

[0046]

[0047] The above is the mapping between the encryption formula and Tent, and the formula for generating parameters. Unlike the parameter generation formula in Rule 1, the remaining parameters are the same as in Rule 1.

[0048] Rule 3 (Integer Chebyshev Mapping):

[0049]

[0050] Rule 4 (Logistic-Tent combined mapping):

[0051]

[0052] Among them and These are the Logistic mapping and Tent mapping in Rule 1 and Rule 2, respectively, and the formulas for obtaining the parameters are consistent with the solution formulas for Rule 1 and Rule 2.

[0053] In an optional embodiment, step 6 specifically includes: S601: Use the scrambled three-dimensional matrix B as the initial cell state of the invertible second-order cellular automaton; S602: Obtain the second chaotic sequence Y and the third chaotic sequence Z generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; S603: Based on the third chaotic sequence Z, calculate the rule index of each cell in the dynamic rule pool. The index calculation formula is:

[0054] in,( i , j , h () represents the position of a cell in a three-dimensional matrix; S604: Based on the rule index, select the corresponding evolution rule from the dynamic rule pool for each cell; S605: Reconstruct the second chaotic sequence Y into an intermediate configuration matrix with the same dimension as the initial cell state; set t+ At time 1, the neighborhood involved in the evolution has 7 cells (including itself). Assume the position of the pixel to be processed in matrix B is... Then the neighborhood of the configuration cell, besides In the matrix In addition to the cell at position, there are six other cells: , , , , , (This CA is finitely cyclic) This structure enhances the spatial correlation and information diffusion efficiency between cells, while avoiding the "information loss" problem in the evolution of boundary cells.

[0055] S606: For each cell, based on its current state, the state of the corresponding cell and its neighborhood in the intermediate configuration matrix, and the evolution rule selected for the cell, execute the second-order evolution of the reversible second-order cellular automaton to update its state. S607: After completing the second-order evolution of all cells in sequence, output the ciphertext matrix.

[0056] In this embodiment, RSCA adopts the "current state" -Intermediate configuration -Evolutionary Results The second-order evolutionary architecture of "[Cell Name]" relies not only on the cell itself and its 7-neighborhood states (including its own finite cyclic neighborhood structure), but also introduces an intermediate configuration matrix driven by the L3D-TDMHS chaotic sequence, forming a "dual-state coupling" mechanism. Compared to the traditional CA's "single-order state transition" (which only relies on...), this approach... (Time state), this characteristic significantly increases the nonlinear complexity and unpredictability of the evolution trajectory.

[0057] In an optional embodiment, in step S7, the ciphertext image can be obtained by reconstructing the ciphertext matrix obtained in S6, thereby completing the encryption.

[0058] Example 2 Please see Figure 3-8 This embodiment is based on the encryption method proposed in Embodiment 1. Through a series of simulation experiments and quantitative analysis, the encryption effect, key sensitivity and anti-attack capability of the algorithm are comprehensively verified.

[0059] 1. Experimental Setup and Encryption Effect Demonstration: The experiment selected three color images with different texture features from the standard test image library as plaintext: (a) Peppers (512×512), (b) Baboon (512×512), (c) Goldhill (720×576), as shown below. Figure 3 As shown. On an Intel Core i7-9700K CPU @ 3.60GHz, 16GB RAM, Windows 10 operating system, and MATLAB R2021a platform, the method of Example 1 was applied to encrypt three images. The encrypted ciphertext images are shown below. Figure 4 As shown, visual comparison reveals that the encrypted images all exhibit uniformly random noise textures, completely masking any visual features of the original images, thus preliminarily verifying the effectiveness of the encryption algorithm.

[0060] 2. Key Sensitivity Test: A secure encryption algorithm should be highly sensitive to its key. To verify this characteristic, a Baboon image is used as an example for testing: First, the correct original key is used to decrypt the image, resulting in a clear original image. Figure 5 -a); then, the control parameters ρ and initial value x0 of the L3D-TDMHS system are modified very slightly (e.g., by an order of magnitude of 10^-15), and the same ciphertext is decrypted using these slightly different incorrect keys. The decryption result is as follows: Figure 5 As shown in -b, c, and d, even extremely minor changes to the key fail to decrypt any image with a visible structure; the decryption result remains random noise. This demonstrates that the algorithm possesses extremely high key sensitivity and can effectively resist key analysis-based attacks.

[0061] 3. Security Quantification Analysis: To objectively evaluate the security of the algorithm, several statistical and differential tests were conducted: Key space: The algorithm's key space is approximately 2^256, which can effectively resist brute-force attacks.

[0062] Statistical characteristics: After encrypting multiple test images, the average information entropy was calculated to be 7.9993, very close to the ideal value of 8, indicating that the ciphertext information is distributed extremely uniformly. The correlation coefficients of adjacent pixels in the horizontal, vertical, and diagonal directions decreased to 0.0012, -0.0008, and 0.0006 respectively, approaching 0. Figure 6 The comparison of the correlation between Peppers images before and after encryption is shown, proving that the algorithm completely destroys the statistical characteristics of the original image and can resist statistical attacks.

[0063] Differential attack: The average NPCR (number of pixels change rate) and UACI (normalized average change intensity) values ​​reached 99.60% and 33.47% respectively, which are far higher than the expected values ​​of an ideal random sequence (NPCR≈99.6094%, UACI≈33.4635%), indicating that the algorithm has a strong diffusion effect on small changes in plaintext and can effectively resist differential attacks.

[0064] Noise and cropping attack resistance test: To simulate interference during transmission, salt-and-pepper noise with an intensity of 5% was applied to the encrypted image. Figure 7 -b) and decryption are performed; the decrypted image still clearly retains the original main content. Furthermore, the ciphertext image is decrypted after being cropped by 25%. Figure 8 (-d) Most of the image information can still be effectively recovered. These test results show that the algorithm still has a certain degree of robustness even when some data is lost or contaminated by noise.

[0065] In summary, this embodiment demonstrates through comprehensive experimental verification that the encryption method provided by the present invention can not only effectively encrypt images, but also exhibits excellent performance in terms of key sensitivity, statistical characteristics, differential characteristics, and resistance to robust attacks, thus meeting the application requirements for high-security image encryption.

[0066] Example 3 Please see Figure 2 An image encryption system based on hyperchaotic driving and reversible cellular automata, comprising: Initialization module: used to generate driving parameters and initial values ​​for the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key; Iterative loop module: Iterates the time-delay three-dimensional memristor hyperchaotic system using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences; First scrambling module: performs pixel-level scrambling on the plaintext to be encrypted to obtain a three-dimensional matrix; Second scrambling module: Uses the chaotic sequence to perform bit-level scrambling on the three-dimensional matrix to obtain the scrambled three-dimensional matrix; Construction module: Based on the chaotic sequence, construct a dynamic rule pool and intermediate configuration matrix for the evolution of the reversible second-order cellular automaton; Evolution Module: The scrambled three-dimensional matrix is ​​used as the initial cell state of the reversible second-order cellular automaton. Combined with the intermediate configuration matrix and the dynamic rule pool, the second-order evolution of the reversible second-order cellular automaton is performed to generate the ciphertext matrix. Encryption module: Reconstructs the ciphertext matrix into a ciphertext image.

[0067] The system proposed in this embodiment is based on the method of embodiment 1. Therefore, the options proposed in embodiment 1 are also applicable to this embodiment. To avoid repetition, they will not be described again here.

[0068] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. An image encryption method based on hyperchaotic driving and reversible cellular automata, characterized in that, The method includes the following steps: Based on the plaintext image to be encrypted and the external key, generate the driving parameters and initial values ​​of the time-delayed three-dimensional memristor hyperchaotic system. The time-delayed three-dimensional memristor hyperchaotic system is iterated using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences. The plaintext to be encrypted is scrambled at the pixel level to obtain a three-dimensional matrix; The chaotic sequence is used to perform bit-level scrambling on the three-dimensional matrix to obtain the scrambled three-dimensional matrix. Based on the chaotic sequence, a dynamic rule pool and intermediate configuration matrix are constructed for the evolution of the reversible second-order cellular automaton. The scrambled three-dimensional matrix is ​​used as the initial cell state of the reversible second-order cellular automaton. Combined with the intermediate configuration matrix and the dynamic rule pool, the second-order evolution of the reversible second-order cellular automaton is performed to generate the ciphertext matrix. The ciphertext matrix is ​​reconstructed into a ciphertext image.

2. The method according to claim 1, characterized in that, The time-delayed three-dimensional memristor hyperchaotic system is constructed by introducing memristor nonlinear elements and a time-delay feedback mechanism into the classical Lorenz system. Its mathematical model is expressed as follows: in, x, y, z All are state variables of a time-delayed three-dimensional memristor hyperchaotic system. W ( z () represents the memristor model, and its expression is: W ( z )= , This is a time delay feedback term, reflecting the system's latency. The state of being at any moment The influence of moment state; The parameters of the hyperchaotic system are... For memristor parameters, This is the time delay parameter.

3. The method according to claim 2, characterized in that, The step of generating the driving parameters and initial values ​​of the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key specifically includes: Obtain a 256-bit external key and the plaintext image to be encrypted; Perform a SHA-256 hash operation on the plaintext image to be encrypted to obtain a 256-bit first hash value; The plaintext image to be encrypted is decomposed into three channel matrices: R, G, and B. SHA-256 hash operation is performed on the three channel matrices respectively, and the three hash values ​​are XORed to generate image feature hash values. The first hash value and the image feature hash value are XORed to obtain the final mixed hash value; The hybrid hash value is divided into a parameter segment and an initial value segment, and the parameters of the time-delay three-dimensional memristor hyperchaotic system are extracted from the parameter segment and the initial value segment, respectively. and initial value ( ).

4. The method according to claim 1, characterized in that, The time-delay three-dimensional memristor hyperchaotic system is iterated using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences, including: substituting the driving parameters and the initial values ​​into the time-delay three-dimensional memristor hyperchaotic system, iteratively calculating new initial values ​​until the iteration threshold is reached, and then outputting multiple sets of chaotic sequences.

5. The method according to claim 1, characterized in that, The step of scrambling the plaintext to be encrypted at the pixel level to obtain a three-dimensional matrix includes: The plaintext image to be encrypted is decomposed into three channel matrices: R, G, and B. The size of both the plaintext image to be encrypted and the three channel matrices is M. N; Reorganize the three channel matrices into M. A 3N two-dimensional matrix V; Calculate the average value of each row of pixels in the two-dimensional matrix V, and use the average value as the number of cyclic displacements for that row; Perform a row cyclic displacement operation on each row of the two-dimensional matrix V using the obtained cyclic displacement count to obtain the first matrix after displacement; The first matrix after the displacement is decomposed into three M... An N matrix is ​​concatenated along its rows and reassembled into a 3M matrix. A two-dimensional matrix of N; Regarding 3M Perform a column cyclic shift operation on each row of a two-dimensional matrix N to obtain a second matrix after shifting; The second matrix after the displacement is decomposed into three M... The matrix of N , , The three M The matrix of N , , Reorganized into M N A three-dimensional matrix A of size 3.

6. The method according to claim 5, characterized in that, The average pixel value of each row in the two-dimensional matrix V is calculated, and the average value is used as the number of cyclic displacements for that row. The formula for calculating the number of cyclic displacements is as follows: in, shift_rowi For the second element in a two-dimensional matrix V, the first element is... i The number of cycle shifts in the row. floor This is a rounding function; a positive result indicates a right shift, and a negative result indicates a left shift.

7. The method according to claim 6, characterized in that, In the bit-level scrambling of the three-dimensional matrix using the chaotic sequence, the bit-level scrambling includes: Obtain the first chaotic sequence X generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; Based on the first chaotic sequence X, each pixel in the three-dimensional matrix A Calculate the corresponding bit cyclic shift number. The calculation formula is as follows: in, express The number of bits to cyclically shift at a given pixel bit position; a positive number shifts the pixel to the right, and a negative number shifts it to the left. Based on the calculated shift number For the pixel The binary bits are subjected to the corresponding cyclic shift operation; After performing the bit shift operation on all pixels in the three-dimensional matrix A in sequence, the resulting three-dimensional matrix B is obtained after bit-level scrambling.

8. The method according to any one of claims 1 to 7, characterized in that, The dynamic rule pool includes at least one of the following four types of integer mapping evolution rules: Logistic mapping, Tent mapping, Chebyshev mapping, and Logistic-Tent combined mapping.

9. The method according to claim 8, characterized in that, The step of performing the second-order evolution of the reversible second-order cellular automaton to generate the ciphertext matrix includes: The scrambled three-dimensional matrix is ​​used as the initial cell state of the invertible second-order cellular automaton. Obtain the second chaotic sequence Y and the third chaotic sequence Z generated iteratively by the time-delayed three-dimensional memristor hyperchaotic system; Based on the third chaotic sequence Z, calculate the rule index of each cell in the dynamic rule pool. The index calculation formula is as follows: in,( i , j , h () represents the position of a cell in a three-dimensional matrix; Based on the rule index, each cell selects a corresponding evolution rule from the dynamic rule pool; The second chaotic sequence Y is reconstructed into an intermediate configuration matrix with the same dimension as the initial cell state. For each cell, the second-order evolution of the reversible second-order cellular automaton is executed based on its current state, the state of the corresponding cell and its neighborhood in the intermediate configuration matrix, and the evolution rule selected for the cell, to update its state. After all cells have completed the second-order evolution in sequence, the ciphertext matrix is ​​output.

10. An image encryption system based on hyperchaotic driving and reversible cellular automata, characterized in that, The system, based on the method according to any one of claims 1-9, includes: Initialization module: used to generate driving parameters and initial values ​​for the time-delayed three-dimensional memristor hyperchaotic system based on the plaintext image to be encrypted and the external key; Iterative loop module: used to iterate the time-delay three-dimensional memristor hyperchaotic system using the driving parameters and the initial values ​​to obtain multiple sets of chaotic sequences; First scrambling module: used to scramble the plaintext to be encrypted at the pixel level to obtain a three-dimensional matrix; The second scrambling module is used to perform bit-level scrambling on the three-dimensional matrix using the chaotic sequence to obtain the scrambled three-dimensional matrix. Construction module: used to construct a dynamic rule pool and intermediate configuration matrix for the evolution of a reversible second-order cellular automaton based on the chaotic sequence; Evolution module: Used to take the scrambled three-dimensional matrix as the initial cell state of the reversible second-order cellular automaton, and combine it with the intermediate configuration matrix and the dynamic rule pool to perform the second-order evolution of the reversible second-order cellular automaton to generate the ciphertext matrix; Encryption module: used to reconstruct the ciphertext matrix into a ciphertext image.

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