An industrial internet of things image encryption method and device based on a multi-cavity memristor discrete cellular neural network

Abstract

The application belongs to the field of image encryption, and discloses an industrial internet of things image encryption method and equipment based on a multi-cavity memristor discrete cellular neural network. The method is based on a memristor and a discrete cellular neural network, and a multi-cavity memristor discrete cellular neural network with super chaotic characteristics and multi-cavity attractors is constructed. Random sequences generated by the multi-cavity memristor discrete cellular neural network are further used for DNA pixel position crossover scrambling and row-column-diagonal pixel diffusion. The application effectively breaks the correlation between adjacent pixels and completely changes the global pixel value of the image. Through testing of various industrial internet of things images, the results show that the scheme has high robustness and effectiveness, and can resist differential attacks and higher exhaustive and quantum attacks. The application has good security and attack resistance, and can be applied to industrial internet of things images in different industrial environments.

Description

Technical Field

[0001] This application relates to the field of image encryption, and in particular to an industrial Internet of Things image encryption method and device based on a multi-cavity memristor discrete cell neural network. Background Technology

[0002] With the rapid development of the Industrial Internet of Things (IIoT), the technology for transmitting and storing electronic data is becoming increasingly sophisticated. However, industrial image data still faces many security challenges during transmission, especially when these images carry critical business information or sensitive data, making it particularly important to ensure their confidentiality and integrity.

[0003] Chaotic systems, due to their ergodicity, pseudo-randomness, and high sensitivity to initial conditions, have been widely applied in image encryption. Research shows that the more complex the topological structure of a chaotic attractor, the richer the system's dynamic behavior, and the more random and unpredictable the generated sequences, thus significantly enhancing the security of encryption algorithms. In recent years, various chaotic image encryption methods based on different chaotic systems have been proposed. For example, Chinese patent CN2023103547885 discloses an image encryption method based on a sinusoidal transform chaotic system, achieving secure image transmission; Chinese patent CN2025100843496 discloses an encryption method for positional plane images using a grid-based multi-vortex conservative chaotic system, achieving good encryption results. Meanwhile, chaotic neural network systems combined with memristors have become a research hotspot. Memristors, with their nonlinearity, non-volatility, and synaptic plasticity characteristics, show broad application prospects in chaotic dynamics and artificial intelligence. Memristor cellular neural networks, constructed by embedding them into cellular neural networks (CNNs), not only generate more complex chaotic attractors but also advance the research on the topological complexity of chaotic systems. In particular, memristor discrete cellular neural networks exhibit highly complex dynamic behaviors in low-dimensional structures, demonstrating significant advantages in areas such as image encryption and secure communication. Therefore, designing an IIoT image encryption method based on memristor discrete cellular neural networks not only expands the theoretical boundaries of chaotic systems but also provides a practical new path for achieving high-security, low-resource-consumption information protection. Summary of the Invention

[0004] The purpose of this application is to provide an industrial IoT image encryption method and device based on a multi-cavity memristor discrete cell neural network, which can improve the security and anti-attack capability of the industrial IoT.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] In one aspect, this application provides an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network, comprising: separating the R, G, and B channels of the original color industrial IoT image, and performing subsequent progressive encryption and combination of the R, G, and B channels; inputting the initial value and system parameters of the multi-cavity memristor discrete cell neural network into the multi-cavity memristor discrete cell neural network to generate four sets of target chaotic sequences; performing three selection and combination processes on the four sets of target chaotic sequences to generate three sets of intermediate chaotic sequences and combining them into a final chaotic sequence; performing splitting, amplification, rounding down to the nearest integer, and modulo 256 operations on the final chaotic sequence to obtain six sets of encrypted chaotic sequences; taking the first set of encrypted chaotic sequences and the second set of encrypted chaotic sequences to determine the scrambling index row number and column number of DNA row crossover and column crossover, and the DNA crossover splitting point, respectively; sequentially taking each row or column in the single-channel image as the current row or column, and combining the pixel data of the current row or column before the DNA crossover splitting point with the pixels of the row or column where the scrambling index row number or column number is located after the DNA crossover splitting point. The data is cross-exchanged and all rows and columns are iterated sequentially to obtain a scrambled matrix. The third and fourth sets of encrypted chaotic sequences are used for row diffusion. The fourth set of encrypted chaotic sequences and a preset constant are used to perform row diffusion on the first row of the scrambled matrix. The current row pixel data is then used with the third set of encrypted chaotic sequences and the previous row pixel data to perform row diffusion, resulting in a row diffusion matrix. The fifth and sixth sets of encrypted chaotic sequences are used for column diffusion. The new constant obtained from the operation of the fifth set of encrypted chaotic sequences and the row diffusion matrix is ​​used to perform column diffusion on the first column of the row diffusion matrix. The current column pixel data is then used with the sixth set of encrypted chaotic sequences and the previous column pixel data to perform column diffusion, resulting in a column diffusion matrix. A diagonal diffusion encryption operation is performed on the column diffusion matrix. First, the pixels in the first row and first column of the column diffusion matrix are diffused. Then, pre-diffusion operations are performed on the first row and first column of the processed column diffusion matrix. Finally, a diagonal diffusion operation is performed on the pre-diffusion matrix to obtain the ciphertext matrix. The R, G, and B channel ciphertext matrices are combined to obtain the ciphertext image.

[0007] Preferably, the plaintext images of the square matrix and non-square matrix are used to obtain ciphertext images through an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network.

[0008] Preferably, four sets of initial values ​​and system parameters are input into a multi-cavity memristor discrete-cell neural network to generate four sets of target chaotic sequences. Based on these four sets of target chaotic sequences, through three selection and combination processes and operations of splitting, expanding, rounding down, and modulo 256, six sets of encrypted chaotic sequences are obtained, including:

[0009] Four sets of initial values ​​and system parameters are input into a multi-cavity memristor discrete cell neural network to generate four sets of target chaotic sequences; the length of each of the four sets of target chaotic sequences is equal to the sum of the row length and column length of the plaintext image.

[0010] The four sets of target chaotic sequences are selected and combined three times. The sum of the three sets of target chaotic sequences is divided by 3 to generate three sets of intermediate chaotic sequences. The length of each of the three sets of intermediate chaotic sequences is equal to the sum of the row length and column length of the plaintext image.

[0011] The three intermediate chaotic sequences are combined to obtain a final chaotic sequence; the length of the final chaotic sequence is equal to three times the sum of the row length and column length of the plaintext image.

[0012] The final chaotic sequence is split, amplified, rounded down to the nearest integer, and modulo 256 to generate six sets of encrypted chaotic sequences. The lengths of the first, third, and fifth sets of encrypted chaotic sequences are equal to the column length of the plaintext image, and the lengths of the second, fourth, and sixth sets of encrypted chaotic sequences are equal to the row length of the plaintext image.

[0013] Preferably, the scrambling process based on DNA chromosome crossover includes:

[0014] Take the first set of encrypted chaotic sequences, determine the scrambling index row number and DNA crossover split point of the DNA row crossover, cross-exchange the pixel data before the DNA crossover split point of the current row with the pixel data after the DNA crossover split point of the row where the scrambling index row number is located, and cycle through all rows in turn to obtain the row scrambling matrix;

[0015] Take the second set of encrypted chaotic sequences, determine the scrambling index column number and DNA crossover split point of the DNA column, cross-exchange the pixel data of the current column before the DNA crossover split point with the pixel data of the column where the scrambling index column number is located after the DNA crossover split point, and cycle through all columns in turn to obtain the scrambling matrix.

[0016] Preferably, the diffusion process according to row-column-diagonal diffusion includes:

[0017] Perform row diffusion operation on the third and fourth sets of encrypted chaotic sequences; perform diffusion operation on the first row of pixels of the scrambled matrix using the fourth set of encrypted chaotic sequence and a constant; perform row diffusion operation on the current row of pixel data, the third set of encrypted chaotic sequence, and the previous row of pixel data to obtain the row diffusion matrix.

[0018] Perform column diffusion operation on the fifth and sixth groups of encrypted chaotic sequences; perform diffusion operation on the first column of the row diffusion matrix using the new constant obtained from the operation of the fifth group of encrypted chaotic sequences and the row diffusion matrix; perform column diffusion operation on the current column pixel data, the sixth group of encrypted chaotic sequences, and the previous column pixel data to obtain the column diffusion matrix.

[0019] Diagonal diffusion encryption is performed on the column diffusion matrix. First, diffusion operations are performed on the pixel data of the first row and first column, the pixel data of the last column of the first row, and the last pixel data of the first column. Then, pre-diffusion operations are performed on the first row and first column of the processed column diffusion matrix. Finally, diagonal diffusion operations are performed on the pre-diffusion matrix to obtain the ciphertext matrix.

[0020] Preferably, during the diffusion process, the last row of the row diffusion matrix is ​​summed and the remainder is taken to generate the column diffusion constant. The column diffusion constant is then associated with the row diffusion matrix to generate a constant for column diffusion.

[0021] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the industrial Internet of Things image encryption method based on a multi-cavity memristor discrete cell neural network.

[0022] Compared with existing technologies, this application discloses the following technical effects: This application provides an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network. The cells of the discrete cell neural network model are exposed to external electromagnetic radiation, and a magnetically controlled memristor is used to describe the electromagnetic induced current to construct a multi-cavity memristor discrete cell neural network. This chaotic system has high initial value sensitivity, and the generated chaotic sequence has complex pseudo-randomness. Using the characteristics of this chaotic system for image encryption can better resist common cryptographic attacks, such as brute-force attacks, quantum attacks, statistical attacks, and differential attacks. During the encryption process, the chaotic sequence generated by the multi-cavity memristor discrete cell neural network realizes DNA cross-scrambling and row-column-diagonal diffusion, which can improve the security and anti-hacking ability of the encryption process. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A flowchart of the industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network provided in this application;

[0025] Figure 2The phase diagrams of the multi-cavity memristor discrete cell neural network provided in this application with the initial value (1,1,1,1) as P changes; wherein, (a) is the phase diagram when parameter P=0, (b) is the phase diagram when parameter P=1, (c) is the phase diagram when parameter P=2, (d) is the phase diagram when parameter P=3, (e) is the phase diagram when parameter P=4, and (f) is the phase diagram when parameter P=5.

[0026] Figure 3 The phase diagrams of the multi-cavity memristor discrete cell neural network provided in this application with Q value change under the initial value (1,1,1,1); wherein, (a) is the phase diagram when parameter Q=0, (b) is the phase diagram when parameter Q=1, (c) is the phase diagram when parameter Q=2, (d) is the phase diagram when parameter Q=3, (e) is the phase diagram when parameter Q=4, and (f) is the phase diagram when parameter Q=5;

[0027] Figure 4 This application provides encrypted and decrypted images and histograms of four color industrial IoT images: "Metal Welding," "Equipment," "Industrial Metal," and "Warehouse." Specifically, (a) is the plaintext image of the "Metal Welding" image, (b) is the encrypted image of the "Metal Welding" image, (c) is the decrypted image of the "Metal Welding" image, (d) is the histogram of the plaintext image of the "Metal Welding" image, (e) is the histogram of the encrypted image of the "Metal Welding" image, (f) is the plaintext image of the "Equipment" image, (g) is the encrypted image of the "Equipment" image, (h) is the decrypted image of the "Equipment" image, and (i) is the plaintext image of the "Equipment" image. Histogram of the text image, (j) is the histogram of the ciphertext image of the "equipment" image, (k) is the plaintext image of the "industrial metal" image, (l) is the ciphertext image of the "industrial metal" image, (m) is the decrypted image of the "industrial metal" image, (n) is the histogram of the plaintext image of the "industrial metal" image, (o) is the histogram of the ciphertext image of the "industrial metal" image, (p) is the plaintext image of the "warehouse" image, (q) is the ciphertext image of the "warehouse" image, (r) is the decrypted image of the "warehouse" image, (s) is the histogram of the plaintext image of the "warehouse" image, (t) is the histogram of the ciphertext image of the "warehouse" image;

[0028] Figure 5The images provided in this application show the correlation test results of the "metal welding" image. Among them, (a) shows the correlation test results of the "metal welding" image in the horizontal direction of the R, G, and B channels; (b) shows the correlation test results of the "metal welding" image in the vertical direction of the R, G, and B channels; (c) shows the correlation test results of the "metal welding" image in the diagonal direction of the R, G, and B channels; (d) shows the correlation test results of the encrypted image of the "metal welding" image in the horizontal direction of the R, G, and B channels; (e) shows the correlation test results of the encrypted image of the "metal welding" image in the vertical direction of the R, G, and B channels; and (f) shows the correlation test results of the encrypted image of the "metal welding" image in the diagonal direction of the R, G, and B channels.

[0029] Figure 6 This is a key sensitivity test result diagram of the "metal welding" image provided in this application; where (a) is the system key x0+10. -15 The phase diagram at time (b) is the system key y0+10. -15 The decrypted image at time (c) is the system key z0+10 -15 The decrypted image at that time, (d) is the system key. The decrypted image at that time, (e) is the system parameter A 11 +10 -15 The decrypted image at that time, (f) is the system parameter A 13 +10 -15 The decrypted image at that time, (g) is the system parameter B 31 +10 -15 The decrypted image at time (h) is the system parameter k+10. -16 Decrypted image at that time;

[0030] Figure 7 The images provided in this application are shear resistance test results of the "metal welding" image; wherein, (a) is the image after cropping the encrypted image of the "metal welding" image by 1 / 64, (b) is the decrypted image after cropping the encrypted image of the "metal welding" image by 1 / 64, (c) is the image after cropping the encrypted image of the "metal welding" image by 1 / 32, (d) is the decrypted image after cropping the encrypted image of the "metal welding" image by 1 / 32, (e) is the image after cropping the encrypted image of the "metal welding" image by 1 / 16, (f) is the decrypted image after cropping the encrypted image of the "metal welding" image by 1 / 16, (g) is the image after cropping the encrypted image of the "metal welding" image by 1 / 4, and (h) is the decrypted image after cropping the encrypted image of the "metal welding" image by 1 / 4.

[0031] Figure 8The following are noise immunity test results of the "metal welding" image provided in this application: (a) is the image after adding 0.1% salt and pepper noise to the encrypted image of the "metal welding" image; (b) is the decrypted image after cropping the encrypted image of the "metal welding" image and adding 0.1% salt and pepper noise; (c) is the image after adding 1% salt and pepper noise to the encrypted image of the "metal welding" image; (d) is the decrypted image after adding 1% salt and pepper noise to the encrypted image of the "metal welding" image; (e) is the image after adding 2% salt and pepper noise to the encrypted image of the "metal welding" image; (f) is the decrypted image after adding 2% salt and pepper noise to the encrypted image of the "metal welding" image; (g) is the image after adding 5% salt and pepper noise to the encrypted image of the "metal welding" image; and (h) is the decrypted image after adding 5% salt and pepper noise to the encrypted image of the "metal welding" image.

[0032] Figure 9 The image shows the results of a plaintext attack test on the image encryption method for industrial IoT based on a multi-cavity memristor discrete cell neural network; where (a) is the original black image, (b) is the encrypted black image, (c) is the decrypted black image, (d) is the original white image, (e) is the encrypted white image, and (f) is the decrypted white image.

[0033] Figure 10 This is a hardware architecture diagram of a cryptographic system for an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network. Detailed Implementation

[0034] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0035] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1:

[0037] In one exemplary embodiment, this application provides an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network. In this embodiment, as shown... Figure 1 As shown, the method includes steps 1 to 8.

[0038] Step 1: Separate the R, G, and B channels of the original color industrial IoT image.

[0039] Step 2: Decompose the initial values ​​and parameters of the multi-cavity memristor discrete cell neural network system.

[0040] The inputs are respectively fed into a multi-cavity memristor discrete cell neural network to generate four sets of target chaotic sequences.

[0041] Step 3: Generate three intermediate chaotic sequences based on the four target chaotic sequences, combine them into a final chaotic sequence, and then generate six encrypted chaotic sequences based on this.

[0042] Step 4: Take the first set of encrypted chaotic sequences and the second set of encrypted chaotic sequences and perform DNA row crossover and column crossover to obtain the scrambling matrix.

[0043] Step 5: Take the third and fourth groups of encrypted chaotic sequences and perform row diffusion operation to obtain the row diffusion matrix.

[0044] Step 6: Take the fifth and sixth groups of encrypted chaotic sequences and perform column diffusion operation to obtain the column diffusion matrix.

[0045] Step 7: Perform diagonal diffusion encryption on the column diffusion matrix. First, perform diffusion operation on the pixels in the first row and first column. Then, perform pre-diffusion operation on the first row and first column of the processed column diffusion matrix. Finally, perform diagonal diffusion operation on the pre-diffusion matrix to obtain the ciphertext matrix.

[0046] Step 8: Combine the ciphertext matrices of the R, G, and B channels to obtain the ciphertext image.

[0047] This application constructs a novel cellular neural network chaotic system, namely a multi-cavity memristor discrete cellular neural network, and applies it to image encryption in the Industrial Internet of Things (IIoT). The following sections provide a detailed explanation of both the construction of the multi-cavity memristor discrete cellular neural network chaotic system and the implementation of the IIoT image encryption method.

[0048] Inspired by the impulse-driven mechanisms and synaptic plasticity in biological neural systems, brain-like neural networks have paved the way for brain-like research, making brain-like computing a key paradigm in neuromorphic engineering. These neural networks excel at simulating highly sensitive dynamic behaviors, closely resembling the behavior of the human brain. Even minute adjustments to synaptic weight can induce significant structural and functional changes in these systems. Many artificial neural network models have emerged, such as Hopfield neural networks, backpropagation neural networks, Hindmarsh-Rose neural networks, and cellular neural networks. Artificial neural networks have sparked an emerging research field, primarily focused on image and video processing and segmentation, robot vision, and defect detection applications. Among these models, cellular neural networks utilize neuromorphic properties such as local connectivity and topographic cell arrangement to achieve real-time data processing and low-cost computation in interconnected devices. Therefore, constructing improved cellular neural networks with energy-efficient computing and complex chaotic attractors can further promote the development of secure data transmission in the Industrial Internet of Things (IIoT). This application uses a magnetically controlled memristor to simulate the action potential of neurons through electromagnetic induction, constructing a multi-cavity memristor discrete cellular neural network chaotic system. The Lyapunov exponent, phase diagram, bifurcation diagram, and initial lifting coexistence attractor of the chaotic system were analyzed by numerical simulation using MATLAB.

[0049] Memristors are often used to simulate variable synaptic weights and characterize the effect of electromagnetic induction on neuronal action potentials. This application proposes a novel memristor based on a magnetically controlled memristor, the model of which is as follows:

[0050]

[0051] Where k is the memristor parameter, i n For discrete input current, W n This refers to the memristor function. It also includes the nonlinear multi-stage step function and state function. Represented as:

[0052]

[0053] In the formula, P and Q are two integer control parameters greater than zero. sgn(·) is the signum function, which can be adjusted by setting the control parameters P or Q.

[0054] The cellular neural network is a classic neural network model, and its mathematical model is as follows:

[0055]

[0056] In this cellular neural network, the cell unit in the i-th row and j-th column is denoted as C(i,j), and this cell unit is synaptactically linked to other neighboring cell units. N(i,j) is the set of neighboring cells of this cell unit, and R and U represent the radii of the cell's neighborhood. C(k,l)∈N R (i,j) represents the area surrounding the central unit C. (i,j) The R-neighborhood cells. x, v, and y represent the state, output, and input, respectively, while I represents the cell bias shared by the cells. Feedback matrix a M×N Represents C(i,j) and its interacting neighborhood N R The output signal v emitted by the adjacent unit R within (i,j) is... kl The dynamic coupling between them. Control matrix b M×N Describes the control neighborhood N U The input signal u of the adjacent unit within (i,j) kl The interaction between them. Setting I = 0 to zero, this configuration describes a 3×3 discrete-time DCNN model:

[0057]

[0058] The discrete cell neural network model of this application has the following characteristics: tanh, hsigm, and ssign are the heterogeneous activation functions of the multi-cavity memristor discrete cell neural network. The activation function of this system is defined as follows:

[0059]

[0060] This application exposes the cells of a discrete-cell neural network model to external electromagnetic radiation and uses a magnetically controlled memristor to describe the electromagnetically induced current, thus constructing the mathematical model of a multi-cavity memristor discrete-cell neural network as follows:

[0061]

[0062] In the formula, n is a natural number, x, y, and z are the state variables of each cell, and ε is the coupling strength between membrane potential and magnetic flux. This refers to the internal state variables of the memristor. A 11 A 13 and B 31 These are the system parameters for the discrete cell neural network model. Here, is the conductance, k represents the memristor parameter, and G(·) represents the nonlinear multi-stage step function state function of the memristor.

[0063] The discrete-cell neural network model of this application is characterized as follows: the cells of the discrete-cell neural network model are exposed to external electromagnetic radiation; the system uses a magnetically controlled memristor to describe the electromagnetically induced current; and the feedback matrix a... M×N and control matrix bM×N for

[0064]

[0065] To further verify the dynamic changes and complexity of chaotic systems, initial conditions are fixed. And parameters of multi-cavity memristor discrete cell neural network system (A 11 A 13 B 31 Given the parameters (k, ε) = (3.36, 1.3, 1.7, 0.2, 0.001), plot the phase diagram of the system for different parameters P and Q. When P = 0, 1, 2, 3, 4, 5..., the multi-cavity memristor discrete cell neural network generates 1, 3, 5, 7, 9, and 11 multi-cavity chaotic attractors, respectively. Figure 2 As shown. When Q = 0, 1, 2, 3, 4, 5..., this multi-cavity memristor discrete cellular neural network generates 2, 4, 6, 8, 10, and 12 multi-cavity chaotic attractors, respectively, as shown. Figure 3 As shown.

[0066] The 0-1 test is a commonly used algorithm for evaluating the existence of chaotic patterns in discrete sequences. Industrial Internet of Things (IIoT) encryption places high demands on the randomness of chaotic sequences. This application performs a 0-1 test on the multi-cavity memristor discrete cell neural network (MCM-DCNN). Table 1 provides the 0-1 test results for the MCM-DCNN under different parameters. The test results show that the sequence trajectories generated by the MCM-DCNN are irregular and exhibit chaotic characteristics.

[0067] Table 10-1 Test Results

[0068] <![CDATA[Parameter (A 11 , A 13 , B 31 , k)]]> Sequence X Sequence Y Sequence Z Sequence Ψ Average (3.36,1.3,1.7,0.2) 0.971 0.973 0.974 0.806 0.931 (3.36,1.3,1.7,0.12) 0.906 0.879 0.898 0.749 0.858 (4.6,-0.3,2.1,0.2) 0.970 0.969 0.970 0.882 0.948 (4.6,-0.3,2.1,0.12) 0.903 0.909 0.904 0.697 0.853

[0069] The NIST test is designed to evaluate binary sequences generated by cryptographic random or pseudo-random number generators. This application applies the NIST test to the multi-cavity memristor discrete-cell neural network. Table 2 shows the NIST results for this multi-cavity memristor discrete-cell neural network. All four sequences generated by this multi-cavity memristor discrete-cell neural network successfully passed all 15 tests, confirming the randomness of the chaotic sequences.

[0070] Table 2 NIST Test Results

[0071]

[0072]

[0073] The multi-cavity memristor discrete-cell neural network chaotic system proposed in this application helps researchers study the influence of cellular units on neural networks through electromagnetic induction. Furthermore, dynamic and stochastic analyses were performed on this proposed multi-cavity memristor discrete-cell neural network chaotic system. Bifurcation diagrams, Lyapunov exponents, spectral entropy, permutation entropy, attractor phase diagrams, and coexistence attractors demonstrate that this multi-cavity memristor discrete-cell neural network chaotic system possesses complex hyperchaotic dynamic characteristics and a multi-cavity attractor structure, making it highly suitable for encrypting privacy data in the Industrial Internet of Things (IIoT). NIST and 0-1 tests highlight the unpredictability of this multi-cavity memristor discrete-cell neural network chaotic system, which can generate complex analog signals and has wide applications in communication, sensing, random number generation, and neuroscience research.

[0074] This application proposes a novel color image encryption method for the Industrial Internet of Things (IIoT). The plaintext image (size P = M × N × 3) is separated into R, G, and B channels, and the data from each channel is processed separately. Initial values ​​and parameters of a multi-cavity memristor discrete-cell neural network (MCN) system are input into a MCN chaotic system. Four sets of target chaotic sequences generated by the MCN system are preprocessed to obtain six sets of encrypted chaotic sequences, which are used for scrambling and diffusion operations. The first and second sets of encrypted chaotic sequences are subjected to row and column crossover to obtain a scrambling matrix. The third and fourth sets of encrypted chaotic sequences are subjected to row diffusion to obtain a row diffusion matrix. The fifth and sixth sets of encrypted chaotic sequences are subjected to column diffusion to obtain a column diffusion matrix. A diagonal diffusion encryption operation is performed on the column diffusion matrix to obtain a ciphertext matrix. The R, G, and B channel ciphertext matrices are combined to obtain the encrypted image. The specific steps of this image encryption method are as follows.

[0075] Step 1: Separate the R, G, and B channels of the original color industrial IoT image.

[0076] Step 2: Set the given initial input values ​​x0, y0, z0, ... And parameters A of the multi-cavity memristor discrete cell neural network system 11 A 13 B 31 The inputs k are fed into a multi-cavity memristor discrete cell neural network, and the chaotic system is subjected to n0+M×N iterations. In order to increase the unpredictability of the chaotic sequence, the first n0 values ​​are discarded, resulting in four sets of target chaotic sequences X, Y, Z, and Ψ.

[0077] Step 3: Based on the four target chaotic sequences, generate three intermediate chaotic sequences (X+Y+Z) / 3, (X+Y+Ψ) / 3, and (X+Z+W) / 3, and combine them into a final chaotic sequence W = [(X+Y+Z) / 3, (X+Y+Ψ) / 3, (X+Z+W) / 3]. Based on this, generate six encrypted chaotic sequences.

[0078] The generation method is as follows.

[0079]

[0080] in, `x` represents the function to round down to the nearest integer, and `mod(x,y)` represents the remainder function after dividing x and y. `K1` and `K2` are used for pixel scrambling based on DNA crossover, while `K3`, `K4`, `K5`, and `K6` are used for row and column diffusion.

[0081] Step 4: Perform DNA row and column crossover on the first and second sets of encrypted chaotic sequences to obtain a scrambling matrix. Based on the chaotic sequence K1, perform dynamic index calculation, generating scrambling row numbers rsi = 1 + i + mod(K1(i), Mi) and split points rsp = 2 + mod(i + K1(i), N-2) row by row. Cross-exchange the pixel data before the split point in the current row with the pixels after rsp in the rsi-th row. The exchange process is as follows:

[0082]

[0083] Dynamic indexing is performed based on the chaotic sequence K2. Row-by-row, scrambled column numbers csi = 1 + j + mod(K2(j), Nj) and split points csp = 2 + mod(j + K2(j), M-2) are generated. The pixels of the first csp portion of the current column are then cross-swapped with the pixels of the last csp portion of the csi-th column. The swapping process is as follows:

[0084]

[0085] Step 5: Perform row diffusion operation on the third and fourth sets of encrypted chaotic sequences to obtain the row diffusion matrix. Based on the chaotic sequences K3 and K4, perform row diffusion encryption operation on the image data (c0 = 25). Specifically, first, perform a pre-diffusion operation on the pixel rows before row diffusion of the scrambled matrix: The subsequent diffusion process involves the combined action of the initial image and the encrypted chaotic sequence, calculated using a modulo-XOR operation. The row diffusion matrix can be obtained using the following formula:

[0086]

[0087] Step Six: Perform column diffusion operations on the fifth and sixth groups of encrypted chaotic sequences to obtain the column diffusion matrix. Then, operate on the last row of the row diffusion matrix: s0 = (∑P(m,:)) mod 256 to obtain the diffusion random factor. Based on the diffusion random factor and the chaotic sequences K5 and K6, perform row diffusion encryption on the image data. Specifically, first, pre-difflate the pixel columns before column diffusion of the row diffusion matrix: The subsequent diffusion process involves the combined action of the initial image and the encrypted chaotic sequence, calculated using a modulo-XOR operation. The column diffusion matrix can be obtained using the following formula:

[0088]

[0089] Step 7: Perform diagonal diffusion encryption on the column diffusion matrix. First, perform a summation and modulo diffusion operation on the pixels of the first row and first column: C(1,1)=(P(1,1)+P(1,N)+P(M,1))mod256. Then, perform a pre-diffusion operation on the first row of the processed column diffusion matrix: C(1,j)=(P(1,j)+C(1,j-1)+P(M,j))mod256, j=2,...N. Next, perform a summation and modulo pre-diffusion operation on the first column: C(i,1)=(P(i,1)+C(i-1,1)+P(i,N))mod256, i=2,...M. Finally, perform a diagonal diffusion operation on the matrix to obtain the ciphertext matrix. The diagonal diffusion matrix can be obtained by the following formula:

[0090] C(i,j)=(P(i,j)+C(i-1,j)+C(i,j-1))mod256, i=2,3...,M; j=2,3...,N

[0091] Step 8: Combine the ciphertext matrices of the R, G, and B channels to obtain the ciphertext image.

[0092] The decryption algorithm is the reverse process of the encryption algorithm, and will not be described in detail in this application.

[0093] The encryption and decryption algorithms described above together constitute the encryption system. To ensure the security and reliability of the designed industrial IoT color image encryption system, a security analysis of the cryptographic system was conducted. The simulation platform was MATLAB 2022a, and the computer configuration was 512GB SSD, 16GB RAM, Intel(R) Core(TM) i7-1165G7 CPU, Xe Graphics GPU, and Windows 11 Professional.

[0094] In this embodiment, the initial values ​​of the multi-cavity memristor discrete-cell neural network are set to... The parameters of the multi-cavity memristor discrete cell neural network system are set as follows: (A) 11 A13 B 31 ,k)=(3.36,1.3,1.7,0.2), the test images in this application are "metal welding" (from MIAD Dataset), "equipment" (from pixabay), "industrial metal" (from Dataset of Industrial Metal Objects), and "warehouse" (same source as "equipment"). To more comprehensively verify the security of the encryption system, feasibility analysis, histogram testing, post-encryption image correlation testing, information entropy analysis, encryption efficiency analysis, key sensitivity and key space analysis, robustness analysis, chosen-plaintext attack analysis, and differential attack resistance analysis are performed on the encryption system.

[0095] 1. Feasibility Analysis. To verify the feasibility of the algorithm, the encryption and decryption results of this application are as follows: Figure 4 As shown, the encrypted image effectively hides the original information, and the decrypted image matches the original image perfectly. This strongly demonstrates the feasibility of the algorithm.

[0096] 2. Histogram Test. Histograms can visually display the statistical information of an image, representing key information about the image. Figure 4 The histograms of images 1-4 before and after encryption are shown. The results show a significant difference between the histograms before and after encryption. The encrypted image's histogram is more uniformly distributed, effectively encrypting key image information and providing strong protection against statistical attacks by hackers.

[0097] 3. Correlation Test of Encrypted Images. Adjacent pixels in the original image exhibit a high correlation coefficient. A secure industrial IoT encryption system can effectively reduce the correlation between image pixels to protect user privacy. The correlation coefficients between plaintext and ciphertext images are shown in Table 3. Figure 5 This demonstrates the difference in pixel distribution before and after encryption. The pixels in the original image show a clear linear arrangement, while after encryption, the pixel distribution becomes extremely uniform, showing that the encryption scheme effectively reduces the correlation between adjacent pixels.

[0098] Table 3. Correlation coefficients and entropy analysis of image encryption.

[0099]

[0100]

[0101] 4. Information Entropy Analysis. Information entropy can intuitively reflect the visual information and randomness of an image. Therefore, the higher the information entropy, the greater the uncertainty, and the better the protection of user privacy. The information entropy calculation results for industrial IoT images are shown in Table 3. The results show that the encrypted information entropy is significantly improved, effectively masking plaintext information.

[0102] 5. Encryption Efficiency Analysis. An encryption system with excessively low encryption efficiency not only indicates poor encryption performance but also suggests that the system consumes too many resources. This application tested the encryption efficiency using images of different sizes, and the results are shown in Table 4.

[0103] Table 4 Encryption time consumption for different image sizes

[0104]

[0105] 6. Key Sensitivity and Key Space Analysis. The initial values ​​and system parameters of the input multi-cavity memristor discrete cellular neural network are the keys of the encryption system in this application. For the plaintext image "image 1", the first 7 external keys are modified by adding small changes (10) to each key. -15 ) and the last external key adds a tiny change (10) -16 The decryption result is as follows: Figure 6 As shown. Therefore, the total key space size is the product of the key spaces of the above keys: Ks = (10 15 ) 7 ×10 16 =10 121 ≈2 402 Much greater than 2 100 and 2 256 It can effectively resist brute-force attacks and quantum attacks.

[0106] 7. Robustness Analysis. During the transmission of private data, it is often susceptible to cropping and noise attacks by hackers, i.e., cropping the ciphertext to varying degrees and adding different levels of noise. This application conducts anti-cropping tests on the default image, and the experimental results are as follows: Figure 7 As shown in the figure. Tests were conducted by cropping the encrypted image by 1 / 64, 1 / 32, 1 / 16, and 1 / 4 of the default image, respectively. The results show that the decryption effect becomes increasingly blurred with the increase in the degree of cropping. Subsequently, this application added salt-and-pepper noise with variances of 0.1%, 1%, 2%, and 5% to the encrypted image, and the decryption effects are shown in the figure. Figure 8 As shown in the figure, the results indicate that adding salt-and-pepper noise reduces the clarity of the decryption as the noise level increases. This demonstrates that noise interference worsens the decryption process, but the critical plaintext information is still preserved.

[0107] 8. Selected-plaintext attack analysis. This application provides both pure white and pure black image information to observe the decryption quality of the ciphertext image and test the encryption scheme's ability to resist selected / known-plaintext attacks. Figure 9 The original white and black images, the encrypted image, and their corresponding decrypted images are displayed. It can be seen that the hidden repeating pattern cannot be identified to recover the key.

[0108] 9. Analysis of Resistance to Differential Attacks. Encryption algorithms typically use Normalized Pixel Contrast Ratio (NPCR) and Unified Average Changing Intensity (UACI) to evaluate their resistance to differential attacks. By adding or subtracting 1 from the pixel value of any random pixel in the image, the degree of change caused by subtle variations in the encrypted image is assessed. Specific data are shown in Table 5. The theoretical value of NPCR is 99.6094%, and the theoretical value of UACI is 33.4635%. The data in the table show that the NPCR and UACI values ​​of the industrial IoT image encryption system proposed in this application are higher than the ideal values, with NPCR even reaching 99.80%, indicating that the system is competitive in resisting differential attacks.

[0109] Table 5. Results of NPCR and UACI plaintext sensitivity tests

[0110]

[0111]

[0112] In summary, the multi-cavity memristor discrete-cell neural network chaotic system proposed in this application exhibits complex dynamic behavior. This application simulates the electromagnetic induction effect of neurons by introducing a piecewise nonlinear state function flux memristor. Theoretical analysis and numerical simulations show that MCM-DCNN possesses abundant hyperchaotic multi-cavity attractors, the number of which can be precisely modulated by parameters in the memory state equation. For the proposed multi-cavity memristor discrete-cell neural network chaotic system, randomness tests were conducted on the sequences of the chaotic system. The 0-1 test and NIST test successfully evaluated the chaotic characteristics of the generated sequences. Based on the proposed novel chaotic system, this application proposes an industrial IoT image encryption method and a corresponding cryptographic system. This industrial IoT color image encryption system can effectively hide and restore plaintext information, and exhibits excellent encryption performance in terms of histogram features, correlation, and information entropy. Through key sensitivity analysis and key space analysis of this cryptographic system, it is found to have high key sensitivity, with a key space size of approximately 2. 402 Much greater than 2 100 and 2 256This system effectively resists brute-force and quantum attacks. The correlation test result is close to 0, indicating that the encrypted image pixels are randomly distributed, and the original information has been thoroughly obfuscated. Differential attack resistance test data shows that the NPCR and UACI values ​​of the proposed industrial IoT image encryption system are higher than ideal, with the NPCR even reaching 99.80%, demonstrating the system's competitiveness in resisting differential attacks. Robustness analysis of the cryptographic system verifies that it maintains data security and decryption capabilities even in the face of various attacks, data loss, transmission errors, or noise interference.

[0113] Memristor discrete cellular neural networks exhibit ideal dynamic characteristics in low-dimensional spaces while maintaining a computationally simple mathematical framework, making them particularly suitable for industrial IoT applications. To evaluate their practicality in industrial IoT deployments, this application underwent hardware verification on a Raspberry Pi 4 Model B platform equipped with a BCM2711B0 SoC processor (ARM Cortex-A72 architecture). The specific steps of the implementation process are then described below:

[0114] Step 1: First, load the plaintext image into memory, and then encrypt it using an encryption module to generate a ciphertext image.

[0115] Step 2: Subsequently, the encrypted data will be transmitted through a public communication channel and processed by the decryption module to achieve reconstruction.

[0116] Step 3: Throughout the process, the multi-cavity memristor discrete-cell neural network chaotic sequence generator continuously generates the encryption sequences required for encryption and decryption operations. The decrypted output image is displayed in real time through the integrated VGA display interface.

[0117] The cryptographic system hardware architecture of this application is as follows: Figure 10 As shown, it consists of four core components: a chaotic sequence generator based on a multi-cavity memristor discrete cell neural network, an image encryption module, a decryption module, and a VGA display controller.

[0118] In one exemplary embodiment, this application also provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0119] In one exemplary embodiment, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0120] In one exemplary embodiment, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0121] It should be noted that all actions involving the acquisition of signals, information, or data in this application are carried out in compliance with the relevant data protection laws and policies of the country where the application is located, and with the authorization granted by the owner of the relevant device.

Claims

1. An industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network, characterized in that, Includes the following steps: The original color industrial IoT image is separated into R, G, and B channels, and then the R, G, and B channels are progressively encrypted and combined. The initial values ​​and system parameters of the multi-cavity memristor discrete cell neural network are input into the multi-cavity memristor discrete cell neural network to generate four sets of target chaotic sequences. The four sets of target chaotic sequences are selected and combined three times to generate three sets of intermediate chaotic sequences and combine them into a final chaotic sequence. The final chaotic sequence is split, amplified, rounded down to the nearest integer, and modulo 256 to obtain six sets of encrypted chaotic sequences; Take the first set of encrypted chaotic sequences and the second set of encrypted chaotic sequences, and determine the scrambling index row number and column number of DNA row crossover and column crossover, as well as the DNA crossover split point, respectively; take each row or column in the single-channel image as the current row or column, and cross-exchange the pixel data of the current row or column before the DNA crossover split point with the pixel data of the row or column where the scrambling index row number or column number is located after the DNA crossover split point, and cycle through all rows and columns in turn to obtain the scrambling matrix; Perform row diffusion operation on the third and fourth sets of encrypted chaotic sequences; perform row diffusion operation on the first row of the scrambled matrix using the fourth set of encrypted chaotic sequence and a preset constant; perform row diffusion operation on the current row pixel data, the third set of encrypted chaotic sequence, and the previous row pixel data to obtain the row diffusion matrix. Perform column diffusion operation on the fifth and sixth groups of encrypted chaotic sequences; perform column diffusion operation on the first column of the row diffusion matrix using the new constant obtained from the operation of the fifth group of encrypted chaotic sequences and the row diffusion matrix; perform column diffusion operation on the current column pixel data, the sixth group of encrypted chaotic sequences, and the previous column pixel data to obtain the column diffusion matrix. Perform diagonal diffusion encryption on the column diffusion matrix; first, perform diffusion operation on the pixels in the first row and first column of the column diffusion matrix; Then, pre-diffusion operations are performed on the first row and first column of the processed diffusion matrix respectively; finally, a diagonal diffusion operation is performed on the pre-diffusion matrix to obtain the ciphertext matrix. The ciphertext matrices of the R, G, and B channels are combined to obtain the ciphertext image.

2. The industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network according to claim 1, characterized in that, Plaintext images of both square and non-square matrices are encrypted using an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network.

3. The industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network according to claim 1, characterized in that, Four sets of initial values ​​and system parameters are input into a multi-cavity memristor discrete-cell neural network to generate four sets of target chaotic sequences. Based on these four sets of target chaotic sequences, through three selection and combination processes and operations of splitting, expanding, rounding down, and modulo 256, six sets of encrypted chaotic sequences are obtained, including: Four sets of initial values ​​and system parameters are input into a multi-cavity memristor discrete cell neural network to generate four sets of target chaotic sequences; the length of each of the four sets of target chaotic sequences is equal to the sum of the row length and column length of the plaintext image. The four sets of target chaotic sequences are selected and combined three times. The sum of the three sets of target chaotic sequences is divided by 3 to generate three sets of intermediate chaotic sequences. The length of each of the three sets of intermediate chaotic sequences is equal to the sum of the row length and column length of the plaintext image. The three intermediate chaotic sequences are combined to obtain a final chaotic sequence; the length of the final chaotic sequence is equal to three times the sum of the row length and column length of the plaintext image. The final chaotic sequence is split, amplified, rounded down to the nearest integer, and modulo 256 to generate six sets of encrypted chaotic sequences. The lengths of the first, third, and fifth sets of encrypted chaotic sequences are equal to the column length of the plaintext image, and the lengths of the second, fourth, and sixth sets of encrypted chaotic sequences are equal to the row length of the plaintext image.

4. The industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network according to claim 1, characterized in that, The scrambling process based on DNA chromosome crossover includes: Take the first set of encrypted chaotic sequences, determine the scrambling index row number and DNA crossover split point of the DNA row crossover, cross-exchange the pixel data before the DNA crossover split point of the current row with the pixel data after the DNA crossover split point of the row where the scrambling index row number is located, and cycle through all rows in turn to obtain the row scrambling matrix; Take the second set of encrypted chaotic sequences, determine the scrambling index column number and DNA crossover split point of the DNA column, cross-exchange the pixel data of the current column before the DNA crossover split point with the pixel data of the column where the scrambling index column number is located after the DNA crossover split point, and cycle through all columns in turn to obtain the scrambling matrix.

5. The industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network according to claim 1, characterized in that, The diffusion process according to row-column-diagonal diffusion includes: Perform row diffusion operation on the third and fourth sets of encrypted chaotic sequences; perform diffusion operation on the first row of pixels of the scrambled matrix using the fourth set of encrypted chaotic sequence and a constant; perform row diffusion operation on the current row of pixel data, the third set of encrypted chaotic sequence, and the previous row of pixel data to obtain the row diffusion matrix. Perform column diffusion operation on the fifth and sixth groups of encrypted chaotic sequences; perform diffusion operation on the first column of the row diffusion matrix using the new constant obtained from the operation of the fifth group of encrypted chaotic sequences and the row diffusion matrix; perform column diffusion operation on the current column pixel data, the sixth group of encrypted chaotic sequences, and the previous column pixel data to obtain the column diffusion matrix. Diagonal diffusion encryption is performed on the column diffusion matrix. First, diffusion operations are performed on the pixel data of the first row and first column, the pixel data of the last column of the first row, and the last pixel data of the first column. Then, pre-diffusion operations are performed on the first row and first column of the processed column diffusion matrix. Finally, diagonal diffusion operations are performed on the pre-diffusion matrix to obtain the ciphertext matrix.

6. The industrial IoT image encryption method based on a multi-cavity memristor discrete cellular neural network according to claim 1, characterized in that, During the diffusion process, the last row of the row diffusion matrix is ​​summed and the remainder is taken to generate the column diffusion constant. The column diffusion constant is then associated with the row diffusion matrix to generate a constant used for column diffusion.

7. The industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network according to claim 1, characterized in that, The multi-cavity memristor discrete cell neural network has 3 cells, and the cell bias of the cell unit is 0. The feedback matrix a and control matrix b of the multi-cavity memristor discrete cell neural network are defined as follows: The cells of the multi-cavity memristor discrete cell neural network model are exposed to external electromagnetic radiation, and a magnetically controlled memristor is used to describe the electromagnetically induced current; the mathematical model of the multi-cavity memristor discrete cell neural network model is: Where n is a natural number, x, y, and z are the state variables of each cell, and ε is the coupling strength between membrane potential and magnetic flux. A is the internal state variable of the memristor. 11 A 13 and B 31 The system parameters for the multi-cavity memristor discrete cell neural network model; Here, is the conductance, k represents the coupling gain, and G(·) represents the memristor state function; tanh, hsigm, and ssign are the heterogeneous activation functions of a multi-cavity memristor discrete-cell neural network, defined as follows:

8. A computer device comprising: a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, The processor executes an industrial IoT image encryption method based on a multi-cavity memristor discrete cell neural network, as described in any one of claims 1-7.

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