CN116232586A - Image encryption method based on fractional order memristor neural network time feedback control - Google Patents
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Abstract
The invention relates to the technical field of digital image encryption, in particular to an image encryption method based on fractional order memristor neural network time feedback control and an image encryption device using the image encryption method. The invention is based on a fractional order memristor neural network, forms a new network model by adding a time feedback control item, and can convert a periodic state into a chaotic state under the action of the time feedback item, thereby generating a chaotic sequence for image encryption and ensuring the use effect of the network model. The invention is based on the fractional order memristor neural network design, the randomness and the sensitivity to the initial value are improved, the key space is large, and the invention has good practical application prospect.
Description
Technical Field
The invention relates to the technical field of digital image encryption, in particular to an image encryption method based on fractional order memristor neural network time feedback control and an image encryption device using the image encryption method.
Background
With the development of computer technology, images are widely used as an information carrier. However, due to the characteristics of large information quantity and high redundancy, the safety of the system is also an increasingly focused problem. In the field of image information security, encrypting an image is one of the most effective means, which is also an important subject in the field of information security.
Fractional calculus equations can improve modeling accuracy for physical applications and systems. Compared with integer-order calculus, the fractional order is more suitable for describing physical history features and genetic features, so that modeling of a fractional order nonlinear system is more accurate and has stronger universality.
The memristor is proposed by Cai Shaotang in 1971 for the first time, and has become an irreplaceable fourth basic circuit element for removing resistance, inductance and capacitance due to the nonlinearity and unique memory characteristics, and has important application prospects in chaotic circuits, secret communication and neural networks. Based on the characteristics of the memristor, a memristor neural network suitable for simulating the human brain is constructed by replacing the resistor in the traditional neural network circuit. In recent years, the advantages of memristive neural networks have emerged and have become of great interest to scientists.
Fractional order memristor neural networks are prone to multistation, i.e. can present periodic states, and also can present chaotic states. The fractional order memristive neural network is in a periodic state, and is not suitable for image encryption due to low safety.
The inventor considers the condition of fractional order memristor neural network, changes multistable into monostable through time feedback control, and even though fractional order memristor neural network model is in a periodic state through parameter control, the target chaotic state can still be obtained, so that the method is better used for image encryption.
Disclosure of Invention
Based on the above, it is necessary to provide an image encryption method based on fractional memristive neural network time feedback control, aiming at the problem that the existing fractional memristive neural network model is in a periodic state and is not suitable for image encryption.
The invention is realized by adopting the following technical scheme:
in a first aspect, the invention discloses an image encryption method based on fractional order memristor neural network time feedback control, which is used for encrypting a plaintext image into an encrypted image.
The image encryption method based on fractional order memristor neural network time feedback control comprises the following steps:
step S1, constructing a fractional order memristor neural network model I;
step S2, adding a time feedback control item serving as a state transition controller to the constructed model I to form a fractional order memristor neural network model II after adding the time feedback controller, so that the periodic state of the model I is converted into a chaotic state;
step S3, providing a secret key to be substituted into the second model according to the plaintext image to obtain a chaotic sequence;
and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
Implementation of such fractional memristive neural network time feedback control-based image encryption methods is in accordance with methods or processes of embodiments of the present disclosure.
In a second aspect, the invention discloses an image encryption device, and the image encryption method based on fractional order memristor neural network time feedback control disclosed in the first aspect is used.
The image encryption device comprises a basic model module, a model perfecting module and an image encryption module. The basic model module is used for constructing a fractional order memristive neural network model I. The model perfecting module is used for adding a time feedback control item serving as a state conversion controller to the constructed model I to form a fractional order memristor neural network model II after the time feedback controller is added, so that the periodic state of the model I is converted into a chaotic state. The image encryption module is used for providing a secret key according to the plaintext image to be substituted into the second model to obtain a chaotic sequence, and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
Implementation of such an image encryption device is in accordance with a method or process of an embodiment of the present disclosure.
Compared with the prior art, the invention has the following beneficial effects:
1, the invention is based on a fractional order memristor neural network, forms a new network model by adding a time feedback control item, and can convert a periodic state into a chaotic state under the action of the time feedback item, thereby generating a chaotic sequence for image encryption and ensuring the use effect of the network model.
2, processing a part of the chaotic sequence by a nonlinear method, and then performing exclusive or to obtain an index sequence which is used in an image encryption scrambling process; and then the other part of the chaotic sequence is used for diffusing the disordered image in the forward and reverse directions, so that the encryption method has higher safety, and the obtained ciphertext image can resist typical attack and has strong robustness to noise or disturbance.
The invention is based on the fractional order memristor neural network design, the randomness and the sensitivity to the initial value are improved, the key space is large, and the invention has good practical application prospect.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the solutions in the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the drawings provided without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of an image encryption method based on fractional order memristor neural network time feedback control in embodiment 1 of the present disclosure;
FIG. 2 is a schematic diagram of a second embodiment of the model in FIG. 1;
FIG. 3 is a periodic state that is presented during a model time-free feedback control of FIG. 1;
FIG. 4 is a graph of the chaotic state exhibited by model two of FIG. 1 with time feedback control;
FIG. 5 shows a plaintext image, an encrypted image, and a successfully decrypted image as verified in example 2 of the present invention;
FIG. 6 is a histogram of the plaintext image and the encrypted image of FIG. 5;
FIG. 7 is a correlation of the plaintext image and the encrypted image of FIG. 5;
FIG. 8 shows that the key is (-1+10) in embodiment 2 of the present invention -17 0, -0.5,0, -1, 0) decrypting the failed image;
fig. 9 is a decrypted image of the encrypted image of fig. 5 at two salt and pepper noise intensities of 0.05 and 0.1.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It is noted that when an element is referred to as being "mounted to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "disposed on" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "secured to" another element, it can be directly secured to the other element or intervening elements may also be present.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or/and" as used herein includes any and all combinations of one or more of the associated listed items.
Example 1
Referring to fig. 1, fig. 1 is a schematic flowchart of an image encryption method based on fractional order memristive neural network time feedback control in embodiment 1 of the present disclosure, which is used for encrypting a plaintext image into an encrypted image.
As shown in fig. 1, the image encryption method based on fractional order memristive neural network time feedback control includes:
and S1, constructing a fractional order memristor neural network model I.
The S1 aims to introduce a fractional order memristor neural network, and the network has the characteristics of randomness and high sensitivity to initial values.
Referring to fig. 2, model one includes three neurons and memristors. The first neuron is a FitzHugh-Naguso neuron (abbreviated as FN), the second neuron is a Hindmarsh-Rose neuron (abbreviated as HR), and the third neuron is a FitzHugh-Naguso neuron (abbreviated as FN), wherein one FN is connected to the HR through a memristor.
Specifically, step S1 includes:
step S11, a memristor is constructed, wherein the memristor is a fractional order local active memristor:
the fractional order local active memristor is:
wherein I represents the output current，ω q () Representing the function of the memristive function,
represents magnetic flux, v represents input voltage, g () represents memristor internal state function, a, c represent memristor internal state parameter, D q Indicating that q-order leads are performed.
Step S12, constructing a fractional order neural network with three neurons. Wherein the triple neurons comprise one HR and two FNs.
And connecting one FN with HR through fractional order local active memristor connection to obtain a fractional order memristor neural network model I.
Will be the first 1 Neurons and the first 2 The electrical coupling coefficient between the individual neurons is set to
It should be noted that->
And->
Not necessarily the same.
The model one is abbreviated as D q Z=ψ (Z), specifically:
where Z characterizes the variable, ψ () characterizes the vector field describing its kinetic behavior.
x 1 、x 2 、x 3 、y 1 、y 2 、y 3 、
Is a seven-dimensional variable;
x z represents membrane potential in the z-th neuron, y z Representing the z-th recovery variable, the value of the recovery variable,
representing magnetic flux; z=1, 2,3.
k represents memristor coupling strength between heterogeneous neurons; a, a 1 、b 1 、c 1 、ε 1 Is an internal parameter of the first neuron, a 2 、b 2 、c 2 、d 2 Is an internal parameter of the second neuron, a 3 、b 3 、c 3 、ε 3 Is an internal parameter of the third neuron; i.e 1 、i 2 、i 3 Representing an external input current; m is m 11 、m 21 、m 13 、m 31 、m 23 、m 32 Representing the electrical coupling coefficient between neurons.
Based on the existing study and experimental verification, the parameters are specifically set as follows:
a 1 ＝0.6，b 1 ＝1/3，c 1 ＝0.1，ε 1 ＝10；a 2 ＝1，b 2 ＝3，c 2 ＝1，d 2 ＝5；a 3 ＝0.6，b 3 ＝1/3，c 3 ＝0.1，ε 3 ＝10；i 1 ＝-3，i 2 ＝2，i 3 ＝-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。
the first model is a bistable system, and can present a periodic state or a chaotic state according to different initial values.
And S2, adding a time feedback control item serving as a state transition controller to the constructed model I to form a fractional order memristor neural network model II after adding the time feedback controller, so that the periodic state of the model I is converted into a chaotic state.
Step S2 is an improved embodiment of the present invention, including:
step S21, constructing a time feedback control item:
the time feedback control term is-h (tau) GX (Z-A);
theoretically, G is an identity matrix of n×n; z is a matrix of n-dimensional variables.
A is a vector, a= (α) 1 ,α 2 ,...,α n ) T ；
The elements in a are critical to effectively positioning the bistable system to monostable,
can be taken as a constant value near the ideal state, l 3 =1, 2, …, n. Wherein (1)>
Maximum value of>
And minimum->
Respectively the upper and lower boundary values of the target chaotic attractor, then->
h () represents a rectangular function, h (τ) is a time-dependent term, τ represents a time variable, where τ min Indicating the instantaneous state τ c Representing the time range for which the state transition controller is active, then:
in particular, in this example 1, G is a unit matrix of 7*7;
z represents a matrix of seven-dimensional variables:
A＝(0,α 2 ,...,0) T ；τ min ＝0，τ c ＝3；
α 2 also denoted as α, is a parameter related to the target chaotic attractor location.
Since G is the identity matrix of 7*7, the time feedback control term is effectively-h (τ) (y 1 - α) corresponding to D of model one q y 1 。y 1 max and y 1 min is the upper and lower boundary values of the target chaotic attractor respectively, namely,
step S22, the time feedback control item is added into the first model to generate a second model.
Model two can be expressed as: d (D) q Z＝ψ(Z)-h(τ)G(Z-A)；
From the above analysis, the time feedback control term complements D of model one q y 1 Thus, model two is specifically expressed as:
for model one, take
The initial values of (1, 0, -0.5,0, -1, 0) are (-1, 0), resulting in a phase diagram as shown in fig. 3, indicating that model one is in a periodic state.
The value of alpha affects the transition of the periodic state and two methods of determination are available:
the first is to adjust the value of α by adopting a test mode until the periodic state is changed into the chaotic state, as shown in the phase diagram of fig. 4.
The second is a reverse method, which changes the initial value to make the model in a chaotic state when no time feedback term exists. For example, take
The initial values of (1) are (0.5, 0, -0.5,0, -1, 10), and a phase diagram as shown in fig. 4 is obtained, which indicates that model one is in a chaotic state.
Then the position interval [ y ] of the target chaotic attractor is obtained according to the chaotic state 1 min，y 1 max]And according to
In this example 1, y is obtained from the position of the target attractor of FIG. 4 1 max≈0.743，y 1 min≈0.537。
/>
Through verification, alpha E (0.635,0.645) can realize the transition of the periodic state, and in the following steps
The state of fig. 4 is still obtained when the initial value is (-1, 0, -0.5,0, -1, 0), and can be applied to image encryption. Where α=0.64, the effect is optimal.
Step S3, providing a secret key to be substituted into the second model according to the plaintext image to obtain a chaotic sequence; and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
Step S3, encrypting the plaintext image based on the model II to obtain an encrypted image:
first, since the plaintext images are different in size, the specification thereof is to be taken as a basis for generating the chaotic sequence.
In general, a plaintext image is read according to pixel points to obtain an image matrix P composed of m×n pixel points M*N . M x N corresponds to the size of the plaintext image.
Providing a group of initial values as a secret key, substituting the initial values into a second model, and iterating to obtain a chaotic data group with the length of at least 3M x N. The key of this embodiment 1 employs (-1, 0, -0.5,0, -1, 0), and the key involves 7 dimensions, and the key space is large and the security is high.
Intercepting 3M-N mixture from chaotic data setChaotic sequence R and nonlinear processing to obtain chaotic sequence W 1 、W 2 、W 3 、S 1 、S 2 。
Since the iteration has an initial state effect, the data in the earlier stage of the chaotic data set can be removed to eliminate the initial state effect. Therefore, the length of the chaotic data set is generally 500+3m×n, and the first 500 data are removed, so as to obtain a chaotic sequence R of 3m×n.
For the chaotic sequence R, the following formula is adopted for processing, and the numerical range is adjusted to the range requirements met by different encryption stages:
W＝mod(floor(R+100*10 10 )，256)+1；
S＝mod(floor(R*pow2(16))，256)。
then, W is obtained by adopting the following formula 1 、W 2 、W 3 、S 1 、S 2 ：
W 1 ＝W(1：M*N)；
W 2 ＝W((M*N+1)：2M*N)；
W 3 ＝W((2M*N+1)：3M*N)；
S 1 ＝S(1：M*N)；
S 2 ＝S((M*N+1)：2M*N)。
Next, a chaotic sequence W is used 1 、W 2 、W 3 、S 1 、S 2 For image matrix P M*N And (3) performing treatment:
first, the chaotic sequence W 1 、W 2 、W 3 Binarization is carried out respectively, and the index sequence B is obtained by carrying out exclusive OR operation and then decimal operation:
Then, P is compared according to the index sequence B M*N And carrying out pixel level scrambling to obtain a scrambled image C:
c (j) =p (B (j)), where j=1, …, m×n.
Then, according to the mixingChaotic sequence S 1 And chaotic sequence S 2 And respectively carrying out two rounds of forward and reverse diffusion on the disordered image C, and finally obtaining an encrypted image E.
The diffusion sequence of the two rounds of forward and reverse directions is not rigidly defined, and the diffusion uses a remainder operator to introduce a ciphertext feedback mechanism.
If forward diffusion encryption is carried out on the first round, introducing the scrambled image C as input to obtain a first round diffusion result D:
the second round of reverse diffusion encryption is carried out, a first round of diffusion result D is introduced as input, and a second round of diffusion result E is obtained, namely an encrypted image:
similarly, the number of the devices to be used in the system,
if the first round of reverse diffusion encryption is performed, introducing the scrambled image C as input to obtain a first round of diffusion result E:
the second round of forward diffusion encryption is carried out, a first round of diffusion result E is introduced as input, and a second round of diffusion result D is obtained, namely an encrypted image:
of course, the decryption of the encrypted image generated by the method is realized through the encryption inverse process:
taking forward diffusion encryption in the first round and backward diffusion encryption in the second round as examples: the decryption process needs to input the secret key according to the same rule to obtain an index sequenceB. Chaotic sequence S 1 And chaotic sequence S 2 The image can be decrypted.
In the first round of reverse diffusion reduction, introducing an encrypted image E as the input of the first round of reverse diffusion to obtain a result F after the first round of reverse diffusion:
and in the second round of reverse diffusion reduction, introducing a result F after the first round of reverse diffusion as an input of the second round of reverse diffusion to obtain a result G after the second round of reverse diffusion:
then, scrambling and restoring the result G after the second round of reverse diffusion to obtain a decrypted image P':
P′(j)＝G(B(j))。
the embodiment 1 also synchronously discloses an image encryption device, which uses the image encryption method based on fractional order memristor neural network time feedback control. The image encryption device comprises a basic model module, a model perfecting module and an image encryption module. The basic model module is used for constructing a fractional order memristive neural network model I. The model perfecting module is used for adding a time feedback control item serving as a state conversion controller to the constructed model I to form a fractional order memristor neural network model II after the time feedback controller is added, so that the periodic state of the model I is converted into a chaotic state. The image encryption module is used for providing a secret key according to the plaintext image to be substituted into the second model to obtain a chaotic sequence, and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
Of course, embodiment 1 also discloses an image decryption device that decrypts an encrypted image according to the reverse process of the above-described image encryption method to obtain a decrypted image. Specifically, the image decryption device includes an image decryption module. For image decryption modulesAccording to the chaos sequence S 1 And chaotic sequence S 2 And performing diffusion restoration on the encrypted image for two times, and performing scrambling restoration on a diffusion restoration result according to the index sequence B to obtain a decrypted image.
Example 2
This embodiment 2 discloses a specific example of the image encryption method based on embodiment 1, in which the sample image is subjected to encryption processing using the image encryption method of embodiment 1, and then also subjected to decryption processing.
In this example 2, the plain text image (Lena image) of fig. 5 (a) is used, and the size of the plain text image is 256×256 as the original grayscale image.
The parameters are selected as follows: a, a 1 ＝0.6，b 1 ＝1/3，c 1 ＝0.1，ε 1 ＝10；a 2 ＝1，b 2 ＝3，c 2 ＝1，d 2 ＝5；a 3 ＝0.6，b 3 ＝1/3，c 3 ＝0.1，ε 3 ＝10；ε＝10；i 1 ＝-3，i 2 ＝2，i 3 ＝-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，α＝0.64。
The key was selected to be (-1, 0, -0.5,0, -1, 0), and the encrypted image shown in fig. 5 (b) was obtained after processing using the encryption method of example 1. As a result, the original information is completely lost from the encrypted image, which means that the encryption algorithm of embodiment 1 can encrypt the image well.
Analysis was performed in combination with histogram and correlation:
fig. 6 (d) is a histogram of the plain image in fig. 5, and fig. 6 (e) is a histogram of the encrypted image in fig. 5. The histogram reflects the distribution of the overall pixel values, and it is known that the plain text image is unevenly distributed, and the encrypted image loses the original statistical characteristics.
Fig. 7 (f) is the correlation of the plain images in fig. 5, and fig. 7 (g) is the correlation of the encrypted images in fig. 5. It can be seen that the plaintext image has a strong correlation; while the encrypted image exhibits a disordered state with substantially no correlation. And the combination table is a table of the phase relation between the plaintext image and the encrypted image in the horizontal, vertical and diagonal directions.
Table-correlation coefficient table
It can be seen that the correlation coefficient of the plain image is large, whereas the correlation coefficient of the encrypted image is close to 0, with little correlation.
In addition, the information entropy reflects the randomness of the image, when the information entropy is close to the theoretical value 8, the randomness of the encrypted image is strong, the information entropy of the plaintext image before encryption is 7.4451 as known by information entropy calculation of the image before encryption and the image after encryption, the information entropy of the encrypted image after encryption is obviously increased to 7.9993 and is close to the theoretical value 8, and the image encryption is proved to obtain a good effect.
Further, the encrypted image of fig. 5 (b) is decrypted by selecting a key (-1, 0, -0.5,0, -1, 0), and the decrypted image shown in fig. 5 (c) is successfully obtained, which is the same as the plaintext image of fig. 5 (a), indicating that the decryption was successful.
In addition, the key is trimmed (-1+10) -17 0, -0.5,0, -1, 0) cannot decrypt the encrypted image of fig. 6, and still only the image shown in fig. 6 which fails decryption. It is explained that even if there is a very small change in the key (10 -17 Magnitude) is also sufficient to fail decryption, and the initial value sensitivity of the encryption method is high, so that the encrypted image is difficult to crack. Through experiments, when the key change is more than 10 -17 When the encrypted image cannot be correctly decrypted. Therefore, the key space of embodiment 1 is (10 17 ) 7 ＝10 119 ≈2 357 It is believed that it is resistant to all types of brute force attacks.
In addition, fig. 9 (h) is a decrypted image of the encrypted image of fig. 5 at a salt and pepper noise intensity of 0.05. Fig. 9 (l) is a decrypted image of the encrypted image of fig. 5 at a salt and pepper noise intensity of 0.1. The results show that the decrypted image can still identify most of the valid information despite the use of salt and pepper noise of different intensities, indicating that the encryption method of example 1 is very robust to noise or disturbances.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (10)
1. An image encryption method based on fractional order memristor neural network time feedback control is used for encrypting a plaintext image into an encrypted image, and is characterized by comprising the following steps:
step S1, constructing a fractional order memristor neural network model I;
the model I comprises three neurons and a memristor, wherein the first neuron is a FitzHugh-Nagumo neuron, the second neuron is a Hindmarsh-Rose neuron, the third neuron is a FitzHugh-Nagumo neuron, and one FitzHugh-Nagumo neuron is connected with the Hindmarsh-Rose neuron through the memristor;
step S2, adding a time feedback control item serving as a state transition controller to the constructed model I to form a fractional order memristor neural network model II after adding the time feedback controller, so that the periodic state of the model I is converted into a chaotic state;
the second model is as follows:
wherein x is 1 、x 2 、x 3 、y 1 、y 2 、y 3 、
Is a seven-dimensional variable; x is x z Represents membrane potential in the z-th neuron, y z Represents the z-th recovery variable,>
representing magnetic flux; z=1, 2,3; d (D) q Representing q-order derivative; k represents memristor coupling strength between heterogeneous neurons; a. c is the internal state parameter of the memristor; a, a 1 、b 1 、c 1 、ε 1 Is an internal parameter of the first neuron, a 2 、b 2 、c 2 、d 2 Is an internal parameter of the second neuron, a 3 、b 3 、c 3 、ε 3 Is an internal parameter of the third neuron; i.e 1 、i 2 、i 3 Representing an external input current; m is m 11 、m 21 、m 13 、m 31 、m 23 、m 32 Representing the electrical coupling coefficient between neurons; h () represents a rectangular function, τ represents a time variable, and α represents a parameter related to the target chaotic attractor location;
step S3, providing a secret key to be substituted into the second model according to the plaintext image to obtain a chaotic sequence;
and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
2. The image encryption method based on fractional order memristive neural network time feedback control of claim 1, wherein step S1 comprises:
step S11, a memristor is constructed, wherein the memristor is a fractional order local active memristor;
step S12, constructing a fractional order neural network with three neurons, wherein the three neurons comprise a Hindmarsh-Rose neuron and two FitzHugh-Nagulo neurons;
and connecting one of the FitzHugh-Nagumo neurons with a Hindmarsh-Rose neuron through fractional order local active memristor connection to obtain a fractional order memristor neural network model I.
3. The image encryption method based on fractional order memristor neural network time feedback control of claim 2, wherein the fractional order local active memristor is:
wherein I represents the output current, ω q () Representing the memristive function, v representing the input voltage, g () representing the memristor internal state function.
4. The image encryption method based on fractional order memristive neural network time feedback control of claim 2, wherein the model one is:
5. the image encryption method based on fractional order memristive neural network time feedback control of claim 1, wherein step S2 comprises:
s21, constructing a time feedback control item;
step S22, the time feedback control item is added into the first model to generate a second model.
6. The image encryption method based on fractional order memristive neural network time feedback control of claim 5, wherein the time feedback control term is-h (τ) gx (Z-a);
wherein G is the identity matrix of 7*7,
7. the image encryption method based on fractional order memristive neural network time feedback control of claim 1, wherein a 1 ＝0.6，b 1 ＝1/3，c 1 ＝0.1，ε 1 ＝10；a 2 ＝1，b 2 ＝3，c 2 ＝1，d 2 ＝5；a 3 ＝0.6，b 3 ＝1/3，c 3 ＝0.1，ε 3 ＝10；ε＝10；i 1 ＝-3，i 2 ＝2，i 3 ＝-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；α∈(0.635,0.645)。
8. The image encryption method based on fractional order memristor neural network time feedback control of claim 1, wherein in step S3, the chaotic sequence generation method is as follows:
reading the plaintext image according to the pixel points to obtain an image matrix P M*N Wherein m×n represents the size of the plain image;
providing a group of initial values as keys, substituting the initial values into a second model for iteration to obtain a chaotic data group with the length of at least 3M x N;
intercepting a 3M x N chaotic sequence R from a chaotic data set, and performing nonlinear processing to obtain a chaotic sequence W 1 、W 2 、W 3 、S 1 、S 2 。
9. The image encryption method based on fractional order memristive neural network time feedback control of claim 8, wherein in step S3, the encrypted image acquisition method is as follows:
for chaos sequence W 1 、W 2 、W 3 Exclusive-or is carried out to obtain an index sequence B, and P is paired according to the index sequence B M*N Performing pixel level scrambling to obtain a scrambled image C;
according to the chaotic sequence S 1 And chaotic sequence S 2 And respectively carrying out two rounds of forward and reverse diffusion on the disordered image C, and finally obtaining the encrypted image.
10. An image encryption device, characterized in that the image encryption method based on fractional order memristive neural network time feedback control according to any one of claims 1-9 is used;
the basic model module is used for constructing a fractional order memristive neural network model I;
the model perfecting module is used for adding a time feedback control item serving as a state conversion controller to the constructed model I to form a fractional order memristor neural network model II after the time feedback controller is added, so that the periodic state of the model I is converted into a chaotic state;
and
The image encryption module is used for providing a secret key according to the plaintext image to be substituted into the second model to obtain a chaotic sequence, and scrambling and diffusing the plaintext image by adopting the generated chaotic sequence to obtain an encrypted image.
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| CN116760933A (en) * | 2023-07-03 | 2023-09-15 | 盐城工学院 | Image encryption method and system based on neural network with reactive diffusion |
| CN116827519A (en) * | 2023-07-28 | 2023-09-29 | 常州大学 | Hyperchaotic memristor Chialvo neuron mapping encryption method and system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116760933A (en) * | 2023-07-03 | 2023-09-15 | 盐城工学院 | Image encryption method and system based on neural network with reactive diffusion |
| CN116760933B (en) * | 2023-07-03 | 2024-02-27 | 盐城工学院 | Image encryption method and system based on neural network with reactive diffusion |
| CN116827519A (en) * | 2023-07-28 | 2023-09-29 | 常州大学 | Hyperchaotic memristor Chialvo neuron mapping encryption method and system |
| CN116827519B (en) * | 2023-07-28 | 2024-05-28 | 常州大学 | Hyperchaos memristor Chialvo neuron mapping encryption method and system |
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