An image encryption method based on multi-stable memristor and four-dimensional chaotic neural network

Abstract

The present invention relates to the field of image processing, and relates to an image encryption method based on a multi-stable memristor and a four-dimensional chaotic neural network. The present invention simultaneously couples the memristor model with a traditional Hopfield neural network to form a memristor neural network, and utilizes the rich dynamic chaos phenomenon of the memristor neural network to introduce a chaotic sequence into the image encryption and decryption process; then introduces the Arnold Cat Map to scramble the image pixels, and randomly selects two numbers from the chaotic sequence as the control parameters of the Arnold Cat Map, and then uses an XOR operation to perform pixel diffusion encryption. The present invention can quickly and effectively perform image encryption, and can be successfully applied to FPGA hardware chips, and has good development prospects in the future in terms of large-scale Internet of Things multimedia communication confidentiality and other aspects.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and in particular to an image encryption method based on a multi-stable memristor and a four-dimensional chaotic neural network. Background Art

[0002] With the rapid development of computer technology and communication technology, information has become an important resource in today's society, and the information security issues caused by it are becoming increasingly prominent. In order to ensure the security of information, cryptographic technology is applied to information systems to achieve confidentiality, integrity, availability, controllability and non-repudiation of information. In recent years, the network has developed rapidly, but it has also brought some problems. Network security is one of the most serious problems. As an important carrier of information transmission in our daily communication, images are a very critical part of the field of communication information technology. It plays an important role in information communication, medical imaging, digital multimedia systems and other fields. As we all know, image information is different from other text information and language information. The amount of information contained in image pixels is huge, and image pixels influence each other, and the correlation between them in different directions is also very large, which leads to the fact that text encryption technology will no longer be applicable to image encryption technology.

[0003] In order to improve the performance of image encryption algorithms, the research results of neural network systems and chaotic systems have been applied to image encryption technology, which not only improves the security of image encryption systems, but also enables the system to effectively resist various attacks. Since neural networks have good nonlinear characteristics and associative memory functions, after the number of neurons, the type of neural network, and the weights of the connections are determined, any data of the neural network can be saved and used. The data obtained by the neural network has good pseudo-randomness and can be used in image encryption algorithms. It is a good choice. When the neural network and the chaotic system are combined, a larger random matrix will be formed; compared with a single chaotic system, it not only expands the key space, but also produces greater space complexity. Summary of the invention

[0004] The present invention designs a novel memristor model, and couples the memristor model with a traditional Hopfield neural network to form a memristor neural network. The rich dynamic chaos phenomenon of the memristor neural network is used to introduce a chaotic sequence into the image encryption and decryption process. Arnold Cat Map is then introduced to scramble image pixels, and two numbers are randomly selected from the chaotic sequence as control parameters of Arnold Cat Map. Then, an XOR operation is used to perform pixel diffusion encryption, and finally the encrypted image is output.

[0005] The technical solution of the present invention is as follows:

[0006] An image encryption method based on a multi-stable memristor and a four-dimensional chaotic neural network, the steps are as follows:

[0007] Step 1: To realize that the memristor neural network of the encryption system has rich nonlinear dynamic phenomena, a new type of multi-stable memristor is designed according to the definition of universal memristor. Its mathematical expression is:

[0008] i=G(x)v=(cx+dcos(x))v, (1)

[0009] dx / dt=g(x,v)=abcos(x)tanh(x)-v, (2)

[0010] Under sinusoidal external stimulation, the parameters of equations (1) and (2) are set as follows:

[0011] a is set to 10; b is set to 0.3, c is set to 500, and d is set to 0.4. Such a setting can meet the "three major fingerprints" of the memristor to the greatest extent, and has characteristics such as "multi-stable", as shown in Figure 2; at the same time, it has good nonlinear properties and is very suitable for simulating human brain synapses.

[0012] Assuming v = 0, the memristor state equation (2) becomes dx / dt = g(x, 0) = abcos(x)tanh(x). Through the "POP" steady-state point analysis method, it is found that this memristor has infinite discrete steady-state points, which can be expressed as In particular, the equilibrium steady-state point can be expressed as

[0013] This "multi-stable" property is further applied to neural network models to enable them to produce coexisting chaotic attractors.

[0014] Step 2: By coupling the memristor proposed in the previous step with the traditional Hopfield neural network, a memristor neural network is obtained, whose mathematical expression is:

[0015]

[0016] Among them G 1 =500z 1 +0.4cOs(z 1 ), G 2 =5002 2 +0.4cos(z 2 ), G 1 , G 2 represents a multi-stable universal memristor, used to simulate neural synapses, and ρ 1 , 2 is the system coupling coefficient, representing the coupling strength of the memristor to the neural network, x iIt is used to represent the membrane voltage between the outside and inside of neuron i, tanh(x i ) is the activation function of the neuron. The topological structure diagram of the memristor neural network of the present invention is shown in the attached Figure 3 .

[0017] At the same time, by setting the right side of equation (3) to 0, it can be found that the memristor neural network has an infinite number of discrete steady-state points, see equation (4).

[0018]

[0019] where i = 1, 2, 3, 4. k∈(0, 1, 2, 3, ...)

[0020] By modifying the phase space state, the memristor neural network has infinite equilibrium points along the z1 axis, which shows that the unique multistable memristor synapses are crucial for the formation of infinite equilibrium.

[0021] At a given initial value, by adjusting the memristor coupling coefficient ρ of the neural network 1 , 2 , and given different initial states, the memristor neural network can produce rich dynamic phenomena, such as limit cycle motion, multi-period motion, chaos, hyperchaos, etc. (see Figures 4 and 5).

[0022] Finally, according to formula (4), we select a set of real numbers As the initial state of the memristor neural network, the ODE45 Runge-Kutta algorithm is used and continuously iterated to generate a chaotic sequence.

[0023] Step 3: Select the original image ORI, whose size is (A×B), and serialize the 2D image in a column-first scanning manner to obtain a 1D image sequence O(i), with a sequence length of (A×B).

[0024] Step 4: Extract a sequence K(i) of length (A×B) from the chaotic sequence. Then, randomly select two numbers Ki and Li from K(i) for use in the subsequent encryption process.

[0025]

[0026] Where floor(x) represents the largest integer less than or equal to x, randi(x, y) represents returning a random integer between [x, y], and length(K(i)) returns the length of the K(i) sequence.

[0027] Step 4: Use Ki and Li to construct the Anorld Cat Map (ACM) scrambling mapping expression as follows:

[0028]

[0029] Where I and J represent the original pixel positions, I' and J' represent the scrambled pixel positions, Ki and Li are system parameters of ACM, and N is equal to min(A, B).

[0030] All elements in the image sequence O(i) are traversed and scrambled, and the ACM scrambling mapping is performed a total of abs(Ki-Li) / 2 times until the scrambling is completed, and the scrambled sequence P(i) is obtained.

[0031] Step 5: Perform bitwise XOR operation on P(i) and K(i) to realize the diffusion of the image encryption process and obtain the encrypted sequence E(i).

[0032] Step 6: Arrange E(i) by columns to form an encrypted image ENC of size (A×B).

[0033] The decryption process is the reverse process of the encryption process. The encryption-related effects are shown in Figure 6.

[0034] In the information entropy analysis of different encrypted images, the entropy values ​​of the encrypted images are very close to the ideal value 8 when the same initial value is set. In the histogram analysis of different encrypted images, the histogram distribution of the encrypted image is very uniform, and the distribution characteristics of the image pixel values ​​are well hidden, and it is difficult for the cracker to obtain any useful information in the histogram. In the correlation analysis, the correlation coefficient of the encrypted image in the horizontal, vertical and diagonal directions is almost close to 0, indicating that there is almost no correlation between adjacent pixels of the encrypted image. In addition, the image encryption and image decryption times on the FPGA platform are 0.240443s and 0.217897s, respectively. These times are much lower than the corresponding times of 0.762345s and 0.671635s in MATLAB numerical simulation. The present invention can quickly and effectively encrypt images, and can be successfully applied to FPGA hardware chips, and has good development prospects in the future in terms of large-scale Internet of Things multimedia communication confidentiality. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a work flow chart of the present invention;

[0036] Figure 2(a) is a characteristic diagram of the new memristor model;

[0037] Figure 2(b) is a characteristic diagram of the new memristor model;

[0038] Figure 2(c) is a characteristic diagram of the new memristor model;

[0039] Figure 2(d) is a characteristic diagram of the new memristor model;

[0040] Figure 3This is the topological structure diagram of the dynamic characteristics of the memristor neural network;

[0041] Figure 4(a) is a characteristic diagram of a memristor neural network;

[0042] Figure 4(b) is a characteristic diagram of a memristor neural network;

[0043] Figure 4(c) is a characteristic diagram of a memristor neural network;

[0044] Figure 4(d) is a characteristic diagram of a memristor neural network;

[0045] Figure 5(a) is a characteristic diagram of a memristor neural network;

[0046] Figure 5(b) is a characteristic diagram of a memristor neural network;

[0047] Figure 6(a) is the Lena plaintext image;

[0048] Figure 6(b) is the Lena ciphertext image;

[0049] Figure 6(c) is the Lena decrypted image;

[0050] Figure 6(d) is the plaintext image of Airplane;

[0051] Figure 6(e) is the Airplane ciphertext image;

[0052] Figure 6(f) is the decrypted image of Airplane;

[0053] Figure 6(g) is the Pepper plaintext image;

[0054] Figure 6(h) is the Pepper ciphertext image;

[0055] Figure 6(i) is the Pepper decrypted image. DETAILED DESCRIPTION

[0056] The specific embodiments of the present invention are described in detail below in conjunction with the technical scheme and the accompanying drawings.

[0057] Step 1: Select a 512×512 image and serialize the 2D image in a column-first scanning manner to obtain a 1D image sequence O(i) with a sequence length of (262144).

[0058] Step 2: According to formula (4), select a set of real numbers (1 1,1,1,7π,π), ρ 1 =2.8,ρ 2 =0.008 is used as the initial state of the memristor neural network, and the ODE45 Runge-Kutta algorithm is used to solve equation (3), and it is continuously iterated to generate a chaotic sequence.

[0059] Step 3: Using formula (5), we get a sequence K(i) with a length of (262144) and two random numbers. By rounding, we get Ki and Li.

[0060] Step 4: Use Ki and Li to traverse and scramble all elements in the image sequence O(i) using formula (6), and perform ACM scrambling mapping a total of abs(Ki-Li) / 2 times until all scrambling is completed to obtain the scrambled sequence P(i).

[0061] Step 5: Perform bitwise XOR operation on P(i) and K(i) to realize the diffusion of the image encryption process and obtain the encrypted sequence E(i).

[0062] Step 6: Deserialize E(i) according to the original image size of 512×512 to obtain the encrypted image ENC.

[0063] The decryption process is the reverse process of the encryption process.

[0064] Embodiment 2:

[0065] The image encryption and decryption times on the FPGA platform are 0.240443s and 0.217897s, respectively, which are much lower than the corresponding times of 0.762345s and 0.671635s in the MATLAB numerical simulation.

Claims

1. An image encryption method based on multi-stable memristor and four-dimensional chaotic neural network, It is characterized in that The following steps are involved: Step 1: Design a new type of multi-stable memristor, the mathematical expression is: i=G(x)v=(cx+dcos(x))v, (1) dx / dt=g(x, υ)=abcos(x)tanh(x)-v, (2) Under sinusoidal external stimulation, the parameters of equations (1) and (2) are set as follows: a is set to 10; b is set to 0.3, c is set to 500, and d is set to 0.4; Assuming v = 0, the memristor state equation (2) becomes dx / dt = g(x, 0) = abcos(x)tanh(x). Through the "POP" steady-state point analysis method, it is found that this memristor has infinite discrete steady-state points, which can be expressed as The equilibrium steady-state point is expressed as Step 2: By coupling the memristor proposed in the previous step with the traditional Hopfield neural network, a memristor neural network is designed. The mathematical expression is: Among them G 1 =500z 1 +0.4cos(z 1 ), G 2 =500z 2 +0.4cos(z 2 ), represents a multi-stable universal memristor, used to simulate neural synapses, and ρ 1 , 2 is the system coupling coefficient, representing the coupling strength of the memristor to the neural network, x i It is used to represent the membrane voltage between the outside and inside of neuron i, tanh(x i ) is the activation function of the neuron; At the same time, by setting the right side of equation (3) to 0, it is found that the memristor neural network has infinite discrete steady-state points, see equation (4); Where i = 1, 2, 3, 4; k∈(0, 1, 2, 3, ...) According to formula (4), select a set of real numbers As the initial state of the memristor neural network, the ODE45 Runge-Kutta algorithm is used to iterate continuously to generate a chaotic sequence; Step 3: Select the original image ORI, the image size is (A×B), and serialize the 2D image in a column-first scanning manner to obtain a 1D image sequence O(i), the sequence length is (A×B); Step 4: Extract a sequence K(i) of length (A×B) from the chaotic sequence; then, randomly select two numbers Ki and Li from K(i) to be used in the subsequent encryption process; Where floor(x) represents the largest integer less than or equal to x, randi(x,y) represents returning a random integer between [x,y], and length(K(i)) returns the length of the K(i) sequence; Step 4: Use Ki and Li to construct the Anorld Cat Map ACM scrambling mapping expression as follows: Where I and J represent the original pixel positions, while I' and J' represent the scrambled pixel positions, and Ki, Li are the system parameters of ACM, and N is equal to min(A, B); All elements in the image sequence O(i) are traversed and scrambled, and the ACM scrambling mapping is performed a total of abs(Ki-Li) / 2 times until the scrambling is completed, and the scrambled sequence P(i) is obtained; Step 5: Perform bitwise XOR operation on P(i) and K(i) to realize the diffusion of the image encryption process and obtain the encrypted sequence E(i); Step 6: Arrange E(i) by columns to form an encrypted image ENC of size (A×B).

Images