Image Encryption Method Based on Time Feedback Control of Fractional-Order Memristive Neural Networks

Abstract

The present invention relates to the field of digital image encryption technology, and particularly to an image encryption method based on time feedback control of a fractional-order memristive neural network, and an image encryption device using the image encryption method. The present invention is based on a fractional-order memristive neural network. By adding a time feedback control term, a new network model is formed. Under the action of the time feedback term, the periodic state can be converted into a chaotic state, thereby generating a chaotic sequence for image encryption, ensuring the use effect of the network model. The present invention is designed based on a fractional-order memristive neural network, with improved randomness and sensitivity to initial values, a large key space, and has good practical application prospects.

Description

Technical Field

[0001] The present invention relates to the field of digital image encryption technology, and specifically relates to an image encryption method based on time feedback control of a fractional-order memristive neural network, and an image encryption device using the image encryption method. Background Art

[0002] With the development of computer technology and network technology, images are widely used as an information carrier. However, due to its large amount of information and high redundancy, its security has also become an issue that people pay more and more attention to. In the field of image information security, encrypting images is one of the most effective means, which has also become an important topic in the field of information security.

[0003] Fractional calculus equations can improve the modeling accuracy of physical applications and systems. Compared with integer-order calculus, fractional order is more suitable for describing physical historical characteristics and genetic characteristics. Therefore, the modeling of fractional-order nonlinear systems is more accurate and more general.

[0004] The memristor was first proposed by Chua in 1971. Due to its nonlinearity and unique memory characteristics, it has become an irreplaceable fourth basic circuit element in addition to resistors, inductors, and capacitors, and has important application prospects in chaotic circuits, secure communications, and neural networks. Based on the characteristics of the memristor, a memristive neural network suitable for simulating the human brain is constructed by replacing the resistors in traditional neural network circuits. In recent years, the advantages of memristive neural networks have gradually emerged and have attracted great attention from scientists.

[0005] Fractional-order memristive neural networks are prone to multi-stability, that is, they may exhibit periodic states or chaotic states. Among them, the fractional-order memristive neural network exhibits a periodic state, which is not suitable for image encryption due to its low security.

[0006] Considering the situation of fractional-order memristive neural networks, the inventor changes the multi-stability to mono-stability through time feedback control. Through parameter control, even if the fractional-order memristive neural network model exhibits a periodic state, the target chaotic state can still be obtained, thus being better used for image encryption. Summary of the Invention

[0007] Based on this, it is necessary to provide an image encryption method based on time feedback control of a fractional-order memristive neural network for the problem that the existing fractional-order memristive neural network model exhibits a periodic state and is not suitable for image encryption.

[0008] The present invention is implemented by the following technical solutions:

[0009] In a first aspect, the present invention discloses an image encryption method based on time feedback control of a fractional-order memristive neural network, which is used to encrypt a plaintext image into an encrypted image.

[0010] An image encryption method based on time feedback control of a fractional-order memristive neural network includes:

[0011] Step S1, constructing a first fractional-order memristive neural network model;

[0012] Step S2, adding a time feedback control term as a state conversion controller to the constructed first model to form a second fractional-order memristive neural network model after adding the time feedback controller, converting the periodic state of the first model into a chaotic state;

[0013] Step S3, providing a key according to the plaintext image and substituting it into the second model to obtain a chaotic sequence;

[0014] Then, using the generated chaotic sequence to scramble and diffuse the plaintext image to obtain an encrypted image.

[0015] The implementation of this image encryption method based on time feedback control of a fractional-order memristive neural network is based on the method or process of the embodiments of the present disclosure.

[0016] In a second aspect, the present invention discloses an image encryption device that uses the image encryption method based on time feedback control of a fractional-order memristive neural network disclosed in the first aspect.

[0017] The image encryption device includes a basic model module, a model improvement module, and an image encryption module. The basic model module is used to construct a first fractional-order memristive neural network model. The model improvement module is used to add a time feedback control term as a state conversion controller to the constructed first model to form a second fractional-order memristive neural network model after adding the time feedback controller, converting the periodic state of the first model into a chaotic state. The image encryption module is used to provide a key according to the plaintext image and substitute it into the second model to obtain a chaotic sequence, and then use the generated chaotic sequence to scramble and diffuse the plaintext image to obtain an encrypted image.

[0018] The implementation of this image encryption device is based on the method or process of the embodiments of the present disclosure.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. The present invention is based on a fractional-order memristive neural network. By adding a time feedback control term, a new network model is formed. Under the action of the time feedback term, the periodic state can be converted into a chaotic state, thereby generating a chaotic sequence for image encryption, ensuring the use effect of the network model.

[0021] 2. In the present invention, a part of the chaotic sequence is first processed by a non-linear method and then XORed to obtain an index sequence, which is used in the image encryption scrambling process. Then, another part of the chaotic sequence is used to perform diffusion in opposite forward and reverse directions on the scrambled image, so that the encryption method of the present invention has higher security, and the obtained ciphertext image can resist typical attacks and has strong robustness to noise or perturbation.

[0022] 3. The present invention is designed based on a fractional-order memristive neural network, with improved randomness and sensitivity to initial values, a large key space, and good practical application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings according to the provided drawings without creative efforts.

[0024] Figure 1 It is a flowchart of the image encryption method based on time feedback control of a fractional-order memristive neural network in Embodiment 1 of the present invention;

[0025] Figure 2 For Figure 1 it is a schematic structural diagram of Model 2 in

[0026] Figure 3 For Figure 1 it is the periodic state presented by Model 1 without time feedback control in

[0027] Figure 4 For Figure 1 it is the chaotic state presented by Model 2 with time feedback control in

[0028] Figure 5 It is the plaintext image, encrypted image, and successfully decrypted image verified in Embodiment 2 of the present invention;

[0029] Figure 6 For Figure 5 it is the histogram of the plaintext image and the histogram of the encrypted image in

[0030] Figure 7 For Figure 5 it is the correlation of the plaintext image and the correlation of the encrypted image in

[0031] Figure 8 It is the image with decryption failure when the key is (-1 + 10 -17 , 0, 0, -0.5, 0, -1, 0) in Embodiment 2 of the present invention;

[0032] Figure 9 For Figure 5 The decrypted images of the encrypted image under two salt-and-pepper noise intensities of 0.05 and 0.1 Detailed implementation manners

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0034] It should be noted that when a component is referred to as being "installed on" another component, it can be directly on the other component or there may also be an intermediate component. When a component is considered to be "disposed on" another component, it can be directly disposed on the other component or there may be an intermediate component at the same time. When a component is considered to be "fixed to" another component, it can be directly fixed to the other component or there may be an intermediate component at the same time.

[0035] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "or / and" used herein includes any and all combinations of one or more of the related listed items.

[0036] Embodiment 1

[0037] Please refer to Figure 1 , Figure 1 which is a brief flowchart of the image encryption method based on time feedback control of a fractional-order memristive neural network in Embodiment 1 of the present invention, and is used to encrypt a plaintext image into an encrypted image.

[0038] As Figure 1 , the image encryption method based on time feedback control of a fractional-order memristive neural network includes:

[0039] Step S1, constructing a first fractional-order memristive neural network model.

[0040] The purpose of S1 is to first introduce a fractional-order memristive neural network, which itself has the characteristics of randomness and high sensitivity to initial values.

[0041] Refer to Figure 2, Model 1 includes three neurons and a memristor. The first neuron is a FitzHugh-Nagumo neuron (abbreviated as FN), the second neuron is a Hindmarsh-Rose neuron (abbreviated as HR), and the third neuron is a FitzHugh-Nagumo neuron (abbreviated as FN). One of the FNs is connected to the HR through a memristor.

[0042] Specifically, step S1 includes:

[0043] Step S11, construct a memristor, which is a fractional-order local active memristor:

[0044] The fractional-order local active memristor is:

[0045]

[0046] where I represents the output current, ω q () represents the memductance function, represents the magnetic flux, v represents the input voltage, g() represents the internal state function of the memristor, a and c represent the internal state parameters of the memristor, D q represents taking the q-th derivative.

[0047] Step S12, construct a fractional-order neural network with three neurons. Among them, the three neurons include one HR and two FNs.

[0048] Then connect one of the FNs to the HR through the connection of the fractional-order local active memristor to obtain the fractional-order memristive neural network model 1.

[0049] Set the electrical coupling coefficient between the l1-th neuron and the l2-th neuron as l1, l2 = 1, 2, 3. It should be noted that and are not necessarily the same.

[0050] The model 1 is abbreviated as D q Z = ψ(Z), specifically:

[0051]

[0052] where Z represents the variable, and ψ() represents the vector field describing its dynamic behavior.

[0053] x1, x2, x3, y1, y2, y3, are seven-dimensional variables;

[0054] x z represents the membrane potential in the z-th neuron, and y z represents the z-th recovery variable, represents the magnetic flux; z = 1, 2, 3.

[0055] k represents the memristor coupling strength between heterogeneous neurons; a1, b1, c1, ε1 are the internal parameters of the first neuron, a2, b2, c2, d2 are the internal parameters of the second neuron, a3, b3, c3, ε3 are the internal parameters of the third neuron; i1, i2, i3 represent the external input currents; m 11 , m 21 , m 13 , m 31 , m 23 , m 32 represents the electrical coupling coefficient between neurons.

[0056] Based on existing research and experimental verification, the above parameters are specifically set as:

[0057] a1 = 0.6, b1 = 1 / 3, c1 = 0.1, ε1 = 10; a2 = 1, b2 = 3, c2 = 1, d2 = 5; a3 = 0.6, b3 = 1 / 3, c3 = 0.1, ε3 = 10; i1 = -3, i2 = 2, i3 = -2; α = -0.2, c = 10; m 12 = 4.2, m 21 = -4.5, m 31 = 1, m 13 = -3.5, m 32 = 0.1, m 23 = 1, q = 0.9, k = 0.3.

[0058] The model one at this time is a bistable system, and according to different initial values, it can present a periodic state or a chaotic state.

[0059] Step S2, add a time feedback control term as a state conversion controller to the constructed model one to form the fractional-order memristive neural network model two after adding the time feedback controller, so that the periodic state of model one changes to a chaotic state.

[0060] Step S2 is the improvement embodiment of the present invention, including:

[0061] Step S21, construct the time feedback control term:

[0062] The time feedback control term is -h(τ)G×(Z - A);

[0063] Theoretically, G is an n*n identity matrix; Z is a matrix composed of n-dimensional variables.

[0064] A is a vector, A = (α1, α2,..., α n ) T ;

[0065] The elements in A are crucial for effectively positioning the bistable system into a monostable state, which can be taken as a certain constant value near the ideal state, l3 = 1, 2, …, n. Among them, the maximum value max and the minimum value are respectively the upper and lower boundary values of the target chaotic attractor, then

[0066] h() represents the rectangle function, h(τ) is a time-related term, τ represents the time variable, where τmin represents the instantaneous state and τc represents the time range when the state transition controller is activated, then:

[0067]

[0068] Specifically in this Embodiment 1, G is a 7×7 identity matrix;

[0069] Z represents a matrix composed of seven-dimensional variables:

[0070] A = (0, α2, ..., 0) T ; τ min = 0, τ c = 3;

[0071]

[0072] α2 is also denoted as α, which is a parameter related to the position of the target chaotic attractor.

[0073] Since G is a 7×7 identity matrix, therefore, the time feedback control term is actually -h(τ)(y1 - α), which corresponds to D q y1 in Model 1. y1 max and y1 min are respectively the upper and lower boundary values of the target chaotic attractor, that is,

[0074] Step S22, supplement the time feedback control term into Model 1 to generate Model 2.

[0075] Model 2 can be expressed as: D q Z = ψ(Z) - h(τ)G(Z - A);

[0076] According to the above analysis, the time feedback control term is supplemented into D q y1 of Model 1. Therefore, Model 2 is specifically expressed as:

[0077]

[0078] For Model 1, take The initial value of is (-1, 0, 0, -0.5, 0, -1, 0), and the phase diagram as shown in Figure 3 is obtained, indicating that Model 1 is in a periodic state.

[0079] The value of α affects the transition of the periodic state, and there are two methods to determine it:

[0080] The first method is to use the experimental method to adjust the value of α until the periodic state changes to a chaotic state, as shown in the Figure 4 phase diagram.

[0081] The second method is the backstepping method. Change the initial value so that Model 1 is also in a chaotic state without the time feedback term. For example, take the initial value of as (0.5, 0, 0, -0.5, 0, -1, 10), and the phase diagram as shown in Figure 4 is obtained, indicating that Model 1 is in a chaotic state.

[0082] Then, based on this chaotic state, obtain the position interval [y1min, y1 max] of the target chaotic attractor, and according to

[0083] In this Example 1, from the Figure 4 position of the target attractor, it is obtained that y1 max≈0.743 and y1 min≈0.537.

[0084] After verification, when α∈(0.635, 0.645), the transition of the periodic state can be achieved. When the initial value is (-1, 0, 0, -0.5, 0, -1, 0), the Figure 4 state can still be obtained, which can be applied to image encryption. Among them, α = 0.64 has the best effect.

[0085] Step S3: According to the plaintext image, provide the key and substitute it into Model 2 to obtain a chaotic sequence; then use the generated chaotic sequence to scramble and diffuse the plaintext image to obtain the encrypted image.

[0086] Step S3 is to encrypt the plaintext image based on the above-mentioned Model 2 to obtain the encrypted image:

[0087] First, since the sizes of plaintext images are different, their specifications should be used as the basis for generating the chaotic sequence.

[0088] Generally, read the plaintext image according to pixel points to obtain an image matrix P composed of M*N pixel points M*N . M*N corresponds to the size of the plaintext image.

[0089] Provide a set of initial values as the key, substitute it into Model 2 for iteration to obtain a chaotic data set with a length of at least 3M*N. The key in this Embodiment 1 is (-1, 0, 0, -0.5, 0, -1, 0). The key involves 7 dimensions, has a large key space, and high security.

[0090] Intercept a chaotic sequence R of 3M*N from the chaotic data set, and perform non-linear processing to obtain chaotic sequences W1, W2, W3, S1, and S2.

[0091] Due to the initial state effect in iteration, the data in the early stage of the chaotic data set will be removed to eliminate the initial state effect. Therefore, the length of the chaotic data set generally adopts 500 + 3M*N, and the first 500 data are removed to obtain a chaotic sequence R of 3M*N.

[0092] For the chaotic sequence R, first process it with the following formula to adjust the numerical range to meet the range requirements of different encryption stages:

[0093] W = mod(floor(R + 100 * 10 10 ), 256) + 1;

[0094] S = mod(floor(R * pow2(16)), 256).

[0095] Then, use the following formula to obtain W1, W2, W3, S1, and S2:

[0096] W1 = W(1:M*N);

[0097] W2 = W((M*N + 1):2M*N);

[0098] W3 = W((2M*N + 1):3M*N);

[0099] S1 = S(1:M*N);

[0100] S2 = S((M*N + 1):2M*N).

[0101] Next, use the chaotic sequences W1, W2, W3, S1, and S2 to process the image matrix P M*N as follows:

[0102] First, binaryize the chaotic sequences W1, W2, and W3 respectively, perform exclusive OR operations and then decimalize them to obtain the index sequence B:

[0103] where j = 1,..., M*N.

[0104] Then, perform pixel-level scrambling on P M*N according to the index sequence B to obtain the scrambled image C:

[0105] C(j) = P(B(j)), where j = 1,..., M*N.

[0106] Next, perform two rounds of diffusion in opposite forward and reverse directions on the scrambled image C according to the chaotic sequence S1 and the chaotic sequence S2 respectively, and finally obtain the encrypted image E.

[0107] The order of the two rounds of diffusion in opposite forward and reverse directions is not strictly specified. The diffusion uses the modulo operator and introduces a ciphertext feedback mechanism.

[0108] If the first round performs forward diffusion encryption, introduce the scrambled image C as the input to obtain the first-round diffusion result D:

[0109]

[0110] The second round performs reverse diffusion encryption, introduce the first-round diffusion result D as the input to obtain the second-round diffusion result E, which is the encrypted image:

[0111]

[0112] Similarly,

[0113] If the first round performs reverse diffusion encryption, introduce the scrambled image C as the input to obtain the first-round diffusion result E:

[0114]

[0115] The second round performs forward diffusion encryption, introduce the first-round diffusion result E as the input to obtain the second-round diffusion result D, which is the encrypted image:

[0116]

[0117] Of course, to decrypt the encrypted image generated by this method, it is achieved through the reverse process of encryption:

[0118] Taking the first round of forward diffusion encryption and the second round of reverse diffusion encryption as an example: The decryption process needs to input the key according to the same rules to obtain the index sequence B, the chaotic sequence S1, and the chaotic sequence S2, and then the image can be decrypted.

[0119] When performing the first-round reverse diffusion reduction, introduce the encrypted image E as the input of the first-round reverse diffusion to obtain the result F after the first-round reverse diffusion:

[0120]

[0121] When performing the second-round reverse diffusion reduction, introduce the result F after the first-round reverse diffusion as the input of the second-round reverse diffusion to obtain the result G after the second-round reverse diffusion:

[0122]

[0123] After that, the result G after the second-round inverse diffusion is scrambled and restored to obtain the decrypted image P':

[0124] P'(j) = G(B(j)).

[0125] This Embodiment 1 also synchronously discloses an image encryption device, which uses the above-mentioned image encryption method based on time feedback control of a fractional-order memristive neural network. The image encryption device includes a basic model module, a model improvement module, and an image encryption module. The basic model module is used to construct a fractional-order memristive neural network model one. The model improvement module is used to add a time feedback control term as a state transition controller to the constructed model one to form a fractional-order memristive neural network model two after adding the time feedback controller, so that the periodic state of model one changes to a chaotic state. The image encryption module is used to provide a key according to the plaintext image and substitute it into model two to obtain a chaotic sequence, and then use the generated chaotic sequence to scramble and diffuse the plaintext image to obtain an encrypted image.

[0126] Of course, this Embodiment 1 also discloses an image decryption device, which decrypts the encrypted image according to the inverse process of the above-mentioned image encryption method to obtain a decrypted image. Specifically, the image decryption device includes an image decryption module. The image decryption module is used to perform two diffusion restorations on the encrypted image according to the chaotic sequence S1 and the chaotic sequence S2, and then perform a scrambling restoration on the diffusion restoration result according to the index sequence B to obtain a decrypted image.

[0127] Embodiment 2

[0128] This Embodiment 2 discloses a specific example of the image encryption method based on Embodiment 1. The sample image is encrypted using the image encryption method of Embodiment 1, and then decryption processing is also performed.

[0129] This Embodiment 2 uses Figure 5 the plaintext image (Lena image) in the (a) area in

[0130] The parameter selection is as follows: a1 = 0.6, b1 = 1 / 3, c1 = 0.1, ε1 = 10; a2 = 1, b2 = 3, c2 = 1, d2 = 5; a3 = 0.6, b3 = 1 / 3, c3 = 0.1, ε3 = 10; ε = 10; i1 = -3, i2 = 2, i3 = -2; α = -0.2, c = 10; m 12 = 4.2, m 21 = -4.5, m 31 = 1, m 13 = -3.5, m32 = 0.1, m 23 = 1, q = 0.9, k = 0.3, α = 0.64.

[0131] The secret key was selected as (-1, 0, 0, -0.5, 0, -1, 0), and after being processed by the encryption method of Example 1, the encrypted image as shown in the Figure 5 region (b) was obtained. It can be seen from the results that the encrypted image completely lost the original information, indicating that the encryption algorithm of Example 1 can encrypt the image well.

[0132] Analysis was carried out by combining the histogram and correlation:

[0133] Figure 6 The region (d) in Figure 5 is the histogram of the plaintext image in the region (a) in Figure 6 The region (e) in Figure 5 is the histogram of the encrypted image in the region (b) in

[0134] Figure 7 The region (f) in Figure 5 is the correlation of the plaintext image in the region (a) in Figure 7 The region (g) in Figure 5 is the correlation of the encrypted image in the region (b) in

[0135] Table 1 Correlation coefficient table

[0136]

[0137] It can be seen that the correlation coefficient of the plaintext image is relatively large, while the correlation coefficient of the encrypted image is close to 0, with almost no correlation.

[0138] In addition, the information entropy reflects the randomness of the image. When the information entropy is close to the theoretical value of 8, it indicates that the randomness of the encrypted image is very strong. By calculating the information entropy of the image before and after encryption, it can be known that the information entropy of the plaintext image before encryption is 7.4451, and the information entropy of the encrypted image after encryption increases significantly to 7.9993, which is very close to the theoretical value of 8, indicating that good results have been achieved in image encryption.

[0139] Furthermore, the secret key (-1, 0, 0, -0.5, 0, -1, 0) was selected, and the encrypted image in the Figure 5 region (b) was decrypted, and the Figure 5The decrypted image shown in region (c) is the same as the plaintext image in region (a) of Figure 5 , indicating successful decryption.

[0140] In addition, when the key is finely tuned (-1 + 10 -17 , 0, 0, -0.5, 0, -1, 0), the encrypted image in region (b) of Figure 5 cannot be decrypted, and there is still only the image showing decryption failure as shown in Figure 8 . This shows that even with a very small change (10 -17 magnitude) in the key, it is sufficient to cause decryption failure, indicating that the initial value of this encryption method is highly sensitive, making it difficult to crack the encrypted image. After testing, when the change in the key is greater than 10 -17 , the encrypted image cannot be correctly decrypted. Therefore, the key space of Embodiment 1 is (10 17 ) 7 = 10 119 ≈2 357 , and it can be considered able to resist all types of brute-force attacks.

[0141] In addition, Figure 9 region (h) in Figure 5 is the decrypted image of the encrypted image in region (b) of Figure 9 under a salt-and-pepper noise intensity of 0.05. Figure 5 Region (l) in

[0142] is the decrypted image of the encrypted image in region (b) of Figure 5 under a salt-and-pepper noise intensity of 0.1. The results show that although different intensities of salt-and-pepper noise are used, most of the effective information can still be recognized in the decrypted image, indicating that the encryption method of Embodiment 1 has strong robustness to noise or perturbations.

[0142] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0143] The above-described embodiments only represent several implementation manners of the present invention. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. An image encryption method based on time feedback control of fractional-order memristive neural networks for encrypting a plaintext image into an encrypted image, characterized in that, The described image encryption method includes: Step S1, constructing a fractional-order memristive neural network model one; The model one includes three neurons and a memristor. The first neuron is a FitzHugh-Nagumo neuron, the second neuron is a Hindmarsh-Rose neuron, and the third neuron is a FitzHugh-Nagumo neuron. One of the FitzHugh-Nagumo neurons is connected to the Hindmarsh-Rose neuron through a memristor; Step S2, adding a time feedback control term as a state transition controller to the constructed model one to form a fractional-order memristive neural network model two after adding the time feedback controller, and changing the periodic state of model one to a chaotic state; The model two is: Among them, x1, x2, x3, y1, y2, y3, are seven-dimensional variables; x z represents the membrane potential in the z-th neuron, y z represents the z-th recovery variable, represents the magnetic flux; z = 1, 2, 3; D q represents taking the q-th derivative; k represents the memristor coupling strength between heterogeneous neurons; a, c are internal state parameters of the memristor; a1, b1, c1, ε1 are internal parameters of the first neuron, a2, b2, c2, d2 are internal parameters of the second neuron, a3, b3, c3, ε3 are internal parameters of the third neuron; i1, i2, i3 represent external input currents; m 12 , m 21 , m 13 , m 31 , m 23 , m 32 represent the electrical coupling coefficients between neurons; h() represents the rectangular function, τ represents the time variable, and α represents a parameter related to the position of the target chaotic attractor; Step S3, according to the plaintext image, providing a key and substituting it into model two to obtain a chaotic sequence; Then using the generated chaotic sequence to scramble and diffuse the plaintext image to obtain an encrypted image.

2. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 1, characterized in that, Step S1 includes: Step S11, constructing a memristor, and the memristor is a fractional-order locally active memristor; Step S12, constructing a fractional-order neural network with three neurons, where the three neurons include one Hindmarsh-Rose neuron and two FitzHugh-Nagumo neurons; Then connecting one of the FitzHugh-Nagumo neurons to the Hindmarsh-Rose neuron through a fractional-order locally active memristor connection to obtain a fractional-order memristive neural network model one.

3. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 2, wherein The fractional-order locally active memristor is: where I represents the output current, ω q () represents the memductance function, v represents the input voltage, and g() represents the internal state function of the memristor.

4. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 2, wherein The model one is:

5. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 1, wherein Step S2 includes: Step S21, constructing a time feedback control term; Step S22, supplementing the time feedback control term into model one to generate model two.

6. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 5, characterized in that, The time feedback control term is -h(τ)G×(Z - A); Among them, G is a 7×7 identity matrix, 7. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 1, characterized in that, a1 = 0.6, b1 = 1 / 3, c1 = 0.1, ε1 = 10; a2 = 1, b2 = 3, c2 = 1, d2 = 5; a3 = 0.6, b3 = 1 / 3, c3 = 0.1, ε3 = 10; i1 = -3, i2 = 2, i3 = -2; c = 10; m 12 = 4.2, m 21 = -4.5, m 31 = 1, m 13 = -3.5, m 32 = 0.1, m 23 = 1, q = 0.9, k = 0.3; α ∈ (0.635, 0.645).

8. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 1, characterized in that, In step S3, the generation method of the chaotic sequence is: Read the plaintext image according to the pixel points to obtain the image matrix P M*N , where M*N represents the size of the plaintext image; Providing a set of initial values as a key, substituting it into model two for iteration to obtain a chaotic data set with a length of at least 3M*N; Intercepting a chaotic sequence R of 3M*N from the chaotic data set and performing non-linear processing to obtain chaotic sequences W1, W2, W3, S1, and S2.

9. The image encryption method based on time feedback control of fractional-order memristive neural network according to claim 8, wherein In step S3, the acquisition method of the encrypted image is: The XOR operation is performed on the chaotic sequences W1, W2, and W3 to obtain the index sequence B, and based on the index sequence B, P M*N is pixel-level scrambled to obtain the scrambled image C; According to the chaotic sequence S1 and the chaotic sequence S2, respectively performing two rounds of diffusion in opposite forward and reverse directions on the scrambled image C, and finally obtaining the encrypted image.

10. An image encryption device, characterized in that, Using the image encryption method based on time feedback control of fractional-order memristive neural network as described in any one of claims 1-9; The described image encryption device includes: A basic model module, which is used to construct a fractional-order memristive neural network model one; A model improvement module, which is used to add a time feedback control term as a state transition controller to the constructed model one to form a fractional-order memristive neural network model two after adding the time feedback controller, and changing the periodic state of model one to a chaotic state; And An image encryption module, which is used to, according to the plaintext image, provide a key and substitute it into model two to obtain a chaotic sequence, and then use the generated chaotic sequence to scramble and diffuse the plaintext image to obtain an encrypted image.

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