CN116847033B - Image encryption method and system based on inertial memristor neural network desynchronization - Google Patents
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Abstract
The invention belongs to the technical field of new generation information, and particularly discloses an image encryption method and system based on inertial memristor neural network desynchronization, wherein the method comprises the following steps: firstly, establishing a driving system and a response system based on an inertial memristor neural network with reaction diffusion terms and distribution time lags; secondly, setting an anti-synchronization error, and designing an anti-synchronization controller by adopting an event trigger control strategy; and then the response system realizes the anti-synchronization of the response system and the driving system under the action of the anti-synchronization controller, thereby realizing the image encryption method. The invention solves the problem that the inertial memristor neural network with reaction diffusion term and distribution time lag is difficult to realize event triggering desynchronization, and applies the inertial memristor neural network to the field of image encryption, and provides that the image encryption system can obviously improve the security of image encryption.
Description
Technical Field
The invention relates to the technical field of new generation information, in particular to an image encryption method and system based on inertial memristor neural network desynchronization.
Background
Neural networks are a complex nonlinear system and also a highly intelligent information processing system. Humans have been under the dream of studying neural networks with computational, human reasoning and recognition capabilities to simulate the mechanisms of brain neurons. In recent decades, research in the field of biology has been advancing dramatically, leading to a growing search for neural networks. The types of neural networks are also endless, such as fractional order neural networks, feed forward neural networks, stochastic neural networks, competing neural networks, recurrent neural networks. Currently, neural networks have become marginal leading-edge disciplines in the fields of biology, computer science, artificial intelligence, and the like. In addition, neural networks have been applied to fields of natural language processing, image recognition, signal processing, pattern recognition, and the like, due to their excellent associative memory function and information storage capability.
Memristor is a nonvolatile storage device and has the characteristics of small volume, high density, good expandability and the like. As a result, memristors are often used to replace resistances in traditional artificial neural networks, thereby better simulating synapses of neurons. Such a neural network is called a memristive neural network, and reflects a more complex dynamic behavior of the neural network than a conventional artificial neural network.
With the deep research on memristive neural networks, the continuous expansion of network scale and the rapid growth of information data make bandwidth resources of communication networks increasingly scarce. Therefore, in order to maintain good control performance, it is necessary to select an appropriate control method to reduce the transmission amount in the memristive neural network. It is well known that the use of state feedback control methods to achieve desynchronization can be broadly divided into two categories. One is a continuous control method that requires the controller to constantly change as the state error changes. A disadvantage of this approach is that the constant updating of the controller results in a huge energy consumption. The other is a discontinuous control method, which can avoid unnecessary communication and power consumption in the network. Event-triggered control is a typical discontinuous control method, and is currently receiving extensive attention from researchers.
In addition, with the widespread use of smartphones, social media has become an important channel of people's communication, where a large number of images and videos need to be securely transmitted. Therefore, research on image encryption has great practical significance. The neural network system can generate chaotic signals, and the chaotic signals have the characteristics of random like, non-periodic like, unpredictable like and the like. The chaotic signal is applied to the image encryption method, so that the encrypted image can effectively resist noise and data loss, and is not easy to suffer from statistical attack.
Disclosure of Invention
The invention aims to solve the problem of event-triggered desynchronization of an inertial memristor neural network with reaction diffusion terms and distribution time lags, and provides an image encryption method and system based on the desynchronization of the inertial memristor neural network, so that the security of image encryption is improved.
In order to achieve the above purpose, the present invention provides the following technical solutions: an image encryption method based on inertial memristor neural network desynchronization comprises the following steps:
step S1: based on an inertial memristor neural network with reaction diffusion terms and distribution time lags, a driving system and a response system are established;
step S2: setting an anti-synchronization error according to the driving system and the response system established in the step S1, and designing an anti-synchronization controller;
step S3: and the response system realizes the anti-synchronization of the response system and the driving system under the action of the anti-synchronization controller, so as to realize an image encryption method.
Further, the step S1 specifically includes the following steps:
step S11: establishing a driving system based on an inertial memristor neural network with reaction diffusion terms and distribution time lags;
the state equation for establishing the inertial memristor neural network with the reaction diffusion term and the distribution time lag is as follows:
Wherein the time t is more than or equal to 0; n is the number of neurons in the drive system, i, j=1, 2, n; k represents the spatial dimension, iota=1, 2,..k, spatial variable r= (r 1 ，r 2 ，...，r K ) T And satisfy |r ι |<μ ι ，μ ι Is a positive constant; x is x i (t, r) and x j (t, r) are state variables of the f-th and j-th neurons in the drive system at time t and space r, respectively; alpha il 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,0≤δ(t)≤δ，/>wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant ρ j ；b i ＞0，a i > 0 is a constant; c ij (x i (t，r))、d ij (x i (t, r)) and ε ij (x i (t, r)) represents memristor connection weights in the form:
in which the switching interval T i ＞0；And->Is a constant; is provided with->
And performing variable substitution order reduction processing on a state equation of the inertial memristor neural network with a reaction diffusion term and a distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein the method comprises the steps ofβ i ＝b i -a i -1，γ i ＝b i -1；
Step S12: the corresponding response system is established according to the driving system:
wherein the time t is more than or equal to 0; n is the number of neurons in the response system, i, j=1, 2, n; k represents the spatial dimension, iota=1, 2,..k, spatial variable r= (r 1 ，r 2 ，...，r K ) t And satisfy |r ι |<μ ι ，μ ι Is a positive constant;in response to the state variables of the ith neuron in the system at time t and space r,/and> α iι 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,0≤δ(t)≤δ，/>wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant ρ j ；β i ＝b i -a i -1，γ i ＝b i -1；u 1i (t, r) and u 2i (t, r) is the controller to be designed; />And->Representing memristor connection weights in the form:
in which the switching interval T i ＞0；And->Is a constant.
Further, the step S2 specifically includes the following steps:
step S21: the anti-synchronization error between the driving system and the response system is set as follows:
step S22: according to the anti-synchronization error between the driving system and the response system set in the step S21, designing an anti-synchronization controller based on an event trigger control strategy as follows: u (u) 1i (t，r)＝-π 1i e 1i (t k h, r) and u 2i (t，r)＝-π 2i e 2i (t k h, r), where the gain pi is controlled 1i And pi 2i Is the normal number, t k h is an event trigger time, h is a sampling interval, t k The sequence of event trigger times can be described as {0, t 1 h，t 2 h，...，t k h}， And->For measuring errors, when the measuring error range exceeds a threshold value related to a state, an event triggering condition is violated, and the anti-synchronous controller is updated, wherein the specific event triggering condition is as follows: And->Wherein time t e [ t ] k h，t k+1 h) Constant lambda is greater than or equal to 2, omega is 0,1]，/> Control gain pi 1i To satisfy pi 1i ≥max{0，-η 1i +π 1i Control gain pi 2i To satisfy pi 2i ≥max{0，-η 2i +π 2i }。
And applying the anti-synchronization controller to the response system so that the response system is anti-synchronized with the driving system.
Further, step S3 is based on the response system being inversely synchronized with the driving system under the action of the anti-synchronization controller, so as to further realize image encryption and decryption, and the specific implementation steps are as follows:
the encryption process comprises the following steps:
step S31: reading an original color image, extracting a red component matrix R (p, q), a green component matrix G (p, q) and a blue component matrix B (p, q), wherein p is {1,2, M, q is {1,2, N, and elements of R (p, q), G (p, q) and B (p, q) are all 0,1, 255;
step S32: when the driving system and the response system reach the inverse directionAfter synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S33: three chaotic signal sequences z obtained in the step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z are obtained 1 (p，q)、Z 2 (p, q) and Z 3 (p, q), p e {1,2,., M }, q e {1,2,., N }, where Z 1 (p，q)、Z 2 (p, q) and Z 3 The elements of (p, q) are all 0, 1..255, the specific conversion formula used in step S33 is:
Z 1 (p，q)＝mod(10000*(z 1 (p，q)-floor(z 1 (p，q)))，256)，
Z 2 (p，q)＝mod(10000*(z 2 (p，q)-floor(z 1 (p，q)))，256)，
Z 3 (p，q)＝mod(10000*(z 3 (p，q)-floor(z 1 (p，q)))，256)；
step S34: three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) performing exclusive OR operation with corresponding position elements in three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image respectively to obtain three color component matrixes R after replacement 1 (p，q)、G 1 (p，q)、B 1 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S35: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
step S36: the three color component matrices R after being scrambled in the step S35 2 (p，q)、G 2 (p，q)、B 2 (p, q) as three color component matrices of the encrypted image, combining the color component matrices of the encrypted image to generate the encrypted image;
the decryption process is the inverse of the encryption process, and specifically comprises the following steps:
step S37: reading an encrypted image, and extracting three color component matrices r (p, q), g (p, q), b (p, q), p epsilon {1,2,., M }, q epsilon {1, 2., N }, wherein elements of r (p, q), g (p, q), and b (p, q) are all 0, 1., 255;
Step S38: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold inverse transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
step S39: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal of the response systemOr->Selecting and selecting z in step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And->p.epsilon.1, 2, M, q.epsilon.1, 2, N, where ∈>And->Is 0,1,..255, the specific conversion formula used in step S310 is:
step S311: three new signal sequences obtained in step S310 Respectively with the three color component matrices r restored in step S38 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q), and recovering to obtain three color component matrixes r of the original color image 2 (p，q)、g 2 (p，q)、b 2 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S312: three color component matrices r of the original color image restored in step S311 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, decryption to obtain the original color image.
In a second aspect of the present invention, an image encryption system based on inertial memristor neural network desynchronization is provided, including:
the chaotic signal acquisition module is used for: based on an inertial memristor neural network with reaction diffusion terms and distribution time lags, a driving system and a response system are established, an anti-synchronization error is set, and an anti-synchronization controller is designed to enable the driving system and the response system to achieve anti-synchronization; after the driving system and the response system reach the anti-synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemOr->Selecting and z 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->
The encryption chaotic signal processing module: for sequencing a chaotic signal z 1 (p，q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z can be obtained 1 (p，q)、Z 2 (p, q) and Z 3 (p, q) wherein Z 1 (p，q)、Z 2 (p，q)、Z 3 Elements of (p, q) are all 0,1, a value of 255;
an encryption component reading module: for reading an original color image, extracting a red component matrix R (p, q), a green component matrix G (p, q), and a blue component matrix B (p, q) of the original color image;
Encryption replacement operation module: for combining the three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) exclusive-or operation is carried out on the three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image and corresponding position elements;
scrambling operation module: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p，q)；
An encryption component combining module: three color component matrices R for combining encrypted images 2 (p，q)、G 2 (p，q)、B 2 (p, q) generating an encrypted image;
the decryption chaotic signal processing module: for sequencing chaotic signalsAnd->After specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofElements of (a) are all 0, 1..255;
decryption component reading module: for reading the encrypted image, extracting three color component matrices r (p, q), g (p, q), b (p, q) of the encrypted image;
the reverse scrambling operation module is as follows: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p，q)；
Decryption replacement operation module: for combining the three new signal sequences obtained in step S310 Respectively with the three color component matrices r restored in step S38 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q);
decryption component combination module: three color component matrices r for restoring the original color image 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, decryption to obtain the original color image.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the memristor circuit, in the selection of the memristor neural network model, an inertia term, a reaction diffusion term and a distribution time lag are particularly introduced to form a more complex network model according to the characteristics of the memristor circuit, and the complexity and the cracking difficulty of an image encryption scheme are remarkably improved.
2. In the invention, in order to enable the response system to be inversely synchronized with the driving system, the control method can reduce the cost of information exchange and controller updating.
3. The principle of image encryption is generally divided into scrambling and permutation. The image encryption method using scrambling and the image encryption method using substitution each have merits and merits. The image encryption method based on the anti-synchronization of the inertial memristor neural network has the advantages of combining scrambling and replacement with the use of absorbing, so that a better encryption effect is achieved, noise resistance and data loss are more effective, and statistical attack is not easy to suffer.
Drawings
The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate the invention and together with the description of the embodiment 1 of the invention serve to explain the invention.
In the drawings:
FIG. 1 is a schematic diagram of an image encryption and decryption process;
FIG. 2 is an anti-synchronization error e under event-triggered conditions 11 (t, r) a trace plot;
FIG. 3 is an anti-synchronization error e under event-triggered conditions 12 (t, r) a trace plot;
FIG. 4 is an anti-synchronization error e under event-triggered conditions 21 (t, r) a trace plot;
FIG. 5 is an anti-synchronization error e under event-triggered conditions 22 (t, r) a trace plot;
FIG. 6 is e 11 (t k h, r);
FIG. 7 e 12 (t k h, r);
FIG. 8 is e 21 (t k h, r);
FIG. 9 is e 22 (t k h, r);
fig. 10 is an image encryption effect display diagram in which (a) is an original image, (b) is an encrypted image, and (c) is a decrypted image;
fig. 11 is a pixel distribution histogram of each component of an original image and an encrypted image, wherein (a) is an original image red component histogram, (b) is an original image green component histogram, (c) is an original image blue component histogram, (d) is an encrypted image red component histogram, (e) is an encrypted image green component histogram, and (f) is an encrypted image blue component histogram;
Fig. 12 is a flowchart of an image encryption system.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
The embodiment provides an image encryption method and system based on inertial memristor neural network desynchronization, wherein the image encryption and decryption process is shown in fig. 1. The image encryption method comprises the following steps:
step S1: based on an inertial memristor neural network with reaction diffusion terms and distribution time lags, a driving system and a response system are established;
step S2: setting an anti-synchronization error according to the driving system and the response system established in the step S1, and designing an anti-synchronization controller;
step S3: and the response system realizes the anti-synchronization of the response system and the driving system under the action of the anti-synchronization controller, so as to realize an image encryption method.
In this embodiment, the step S1 specifically includes the following steps:
step S11: establishing a driving system based on an inertial memristor neural network with reaction diffusion terms and distribution time lags;
the state equation for establishing the inertial memristor neural network with the reaction diffusion term and the distribution time lag is as follows:
Wherein the time ist is more than or equal to 0; n is the number of neurons in the drive system, i, j=1, 2, n; k represents the spatial dimension, iota=1, 2,..k, spatial variable r= (r 1 ，r 2 ，...，r K ) T And satisfy |r ι |<μ ι ，μ ι Is a positive constant; x is x i (t, r) and x j (t, r) are state variables of the ith and jth neurons in the drive system at time t and space r, respectively; alpha iι 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,0≤δ(t)≤δ，/>wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant ρ j ；b i ＞0，a i > 0 is a constant; c ij (x i (t，r))、d ij (x i (t, r)) and ε ij (x i (t, r)) represents memristor connection weights in the form:
in which the switching interval T i ＞0；And->Is a constant; is provided with->
And performing variable substitution order reduction processing on a state equation of the inertial memristor neural network with a reaction diffusion term and a distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein the method comprises the steps ofβ i ＝b i -a i -1，γ i ＝b i -1；
Step S12: the corresponding response system is established according to the driving system:
wherein the time t is more than or equal to 0; n is the number of neurons in the response system, i, j=1, 2, n; k represents the spatial dimension, iota=1, 2,..k, spatial variable r= (r 1 ，r 2 ，...，r K ) T And satisfy |r ι |<μ ι ，μ ι Is a positive constant;in response to the state variables of the ith neuron in the system at time t and space r,/and> α iι 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,0≤δ(t)≤δ，/>wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant of p j ；β i ＝b i -a i -1，γ i ＝b i -1；u 1i (t, r) and u 2i (t, r) is the controller to be designed; />And->Representing memristor connection weights in the form:
in which the switching interval T i ＞0；And->Is a constant.
In this embodiment, the step S2 specifically includes the following steps:
step S21: the anti-synchronization error between the driving system and the response system is set as follows:
step S22: according to the anti-synchronization error between the driving system and the response system set in the step S21, designing an anti-synchronization controller based on an event trigger control strategy as follows: u (u) 1i (t，r)＝-π 1i e 1i (t k h, r) and u 2i (t，r)＝-π 2i e 2i (t k h, r), where the gain pi is controlled 1i And pi 2i Is the normal number, t k h is an event trigger time, h is a sampling interval, t k The sequence of event trigger times can be described as {0, t 1 h，t 2 h，...，t k h}， And->For measuring errors, when the measuring error range exceeds a threshold value related to a state, an event triggering condition is violated, and the anti-synchronous controller is updated, wherein the specific event triggering condition is as follows: And->Wherein time t e [ t ] k h，t k+1 h) Constant lambda is greater than or equal to 2, omega is 0,1]，/> Control gain pi 1i To satisfy pi 1i ≥max{0，-η 1i +π 1i Control gain pi 2i To satisfy pi 2i ≥max{0，-η 2i +π 2i }。
And applying the anti-synchronization controller to the response system so that the response system is anti-synchronized with the driving system.
In this embodiment, step S3: based on the response system, the driving system is reversely synchronized under the action of the anti-synchronization controller, and further, the image encryption and decryption are realized, and the specific implementation steps are as follows:
the encryption process comprises the following steps:
step S31: reading an original color image, extracting a red component matrix R (p, q), a green component matrix G (p, q) and a blue component matrix B (p, q), wherein p is {1,2, M, q is {1,2, N, and elements of R (p, q), G (p, q) and B (p, q) are all 0,1, 255;
step S32: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S33: three chaotic signal sequences z obtained in the step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z are obtained 1 (p，q)、Z 2 (p, q) and Z 3 (p, q), p e {1,2,., M }, q e {1,2,., N }, where Z 1 (p，q)、Z 2 (p, q) and Z 3 The elements of (p, q) are all 0, 1..255, the specific conversion formula used in step S33 is:
Z 1 (p，q)＝mod(10000*(z 1 (p，q)-floor(z 1 (p，q)))，256)，
Z 2 (p，q)＝mod(10000*(z 2 (p，q)-floor(z 1 (p，q)))，256)，
Z 3 (p，q)＝mod(10000*(z 3 (p，q)-floor(z 1 (p，q)))，256)；
step S34: three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) are respectively associated with three color component matrices R (p, q), G (p, q), R (p, q),B (p, q) to obtain three color component matrixes R after substitution 1 (p，q)、G 1 (p，q)、B 1 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S35: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
step S36: the three color component matrices R after being scrambled in the step S35 2 (p，q)、G 2 (p，q)、B 2 (p, q) as three color component matrices of the encrypted image, combining the color component matrices of the encrypted image to generate the encrypted image;
the decryption process is the inverse of the encryption process, and specifically comprises the following steps:
step S37: reading an encrypted image, and extracting three color component matrices r (p, q), g (p, q), b (p, q), p epsilon {1,2,., M }, q epsilon {1, 2., N }, wherein elements of r (p, q), g (p, q), and b (p, q) are all 0, 1., 255;
Step S38: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold inverse transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
step S39: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal of the response systemOr->Selecting and selecting z in step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And->p.epsilon.1, 2, M, q.epsilon.1, 2, N, where ∈>And->Is 0,1,..255, the specific conversion formula used in step S310 is:
step S311: three new signal sequences obtained in step S310 Respectively with the three color component matrices r restored in step S38 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q), and recovering to obtain three color component matrixes r of the original color image 2 (p，q)、g 2 (p，q)、b 2 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S312: three color component matrices r of the original color image restored in step S311 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, decryption to obtain the original color image.
In addition, the invention provides an image encryption system based on the anti-synchronization of the inertial memristive neural network, the image encryption system is shown in fig. 12, and the image encryption system comprises:
the chaotic signal acquisition module is used for: based on the inertial memristor neural network with reaction diffusion term and distribution time lag, a driving system and a response system are established, an anti-synchronization error is set, an anti-synchronization controller is designed,the driving system and the response system are in anti-synchronization; after the driving system and the response system reach the anti-synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemOr->Selecting and z 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->
The encryption chaotic signal processing module: for sequencing a chaotic signal z 1 (p，q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z can be obtained 1 (p，q)、Z 2 (p, q) and Z 3 (p, q) wherein Z 1 (p，q)、Z 2 (p，q)、Z 3 Elements of (p, q) are all 0,1, a value of 255;
An encryption component reading module: for reading an original color image, extracting a red component matrix R (p, q), a green component matrix G (p, q), and a blue component matrix B (p, q) of the original color image;
encryption replacement operation module: for combining the three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) exclusive-or operation is carried out on the three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image and corresponding position elements;
scrambling operation module: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p，q)；
An encryption component combining module: three color component matrices R for combining encrypted images 2 (p，q)、G 2 (p，q)、B 2 (p, q) generating an encrypted image;
the decryption chaotic signal processing module: for sequencing chaotic signalsAnd->After specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofElements of (a) are all 0, 1..255;
decryption component reading module: for reading the encrypted image, extracting three color component matrices r (p, q), g (p, q), b (p, q) of the encrypted image;
the reverse scrambling operation module is as follows: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p，q)；
Decryption replacement operation module: for combining the three new signal sequences obtained in step S310 Respectively with the three color component matrices r restored in step S38 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q);
decryption component combination module: three color component matrices r for restoring the original color image 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, decryption to obtain the original color image.
It is worth to say that, in the selection of the memristor neural network model, according to the characteristics of the memristor circuit, an inertia term, a reaction diffusion term and a distribution time lag are particularly introduced to form a more complex network model, so that the complexity and the cracking difficulty of an image encryption scheme are remarkably improved. In order to enable the response system to be inversely synchronized with the driving system, the invention adopts an event triggering control strategy, designs an event triggering anti-synchronization controller and gives event triggering conditions, and the control method can reduce the cost of information exchange and controller updating. The principle of image encryption is generally divided into scrambling and permutation. The image encryption method using scrambling and the image encryption method using substitution each have merits and merits. The image encryption method based on the anti-synchronization of the inertial memristor neural network has the advantages of combining scrambling and replacement with the use of absorbing, so that a better encryption effect is achieved, noise resistance and data loss are more effective, and statistical attack is not easy to suffer.
Example 2:
the embodiment mainly comprises two parts of contents:
the effectiveness of the designed desynchronized controller in the event-triggered desynchronized control method of the inertial memristor neural network with the reaction diffusion term and the distribution time lag, which is proposed in the embodiment 1, is theoretically proved.
Secondly, aiming at the fact that in the embodiment 1, based on the inertial memristor neural network with reaction diffusion term and distribution time lag, whether a driving system and a response system which are constructed reach event triggering desynchronization or not is achieved through a numerical simulation method, and whether an image encryption method is effective or not is judged.
(neither theoretical demonstration nor simulation experiment is intended to limit the invention, in other embodiments, simulation experiments may be omitted, or other experimental schemes may be used to verify the performance of the neural network system.)
1. Proof of theory
Because the driving system contains memristive connection weight and is a discontinuous switching system, the driving system only has solutions in the Filipply meaning, and can be written as follows according to set value mapping and differential inclusion theory:
wherein the method comprises the steps of
Because the response system contains memristive connection weight and is a discontinuous switching system, the response system only has solutions in the Filipply meaning, and can be written into the following form according to set value mapping and differential inclusion theory:
Wherein u is 1i (t, r) and u 2i And (t, r) is a controller to be designed.
Defining the anti-synchronization error between the drive system and the response system as The anti-synchronization error system is obtained by the rewritten driving system and response system as follows:
wherein the method comprises the steps ofAccording to the measurable choice theorem, there is +.> So that the error system rewrites as: />
The following gives the quotation that will be adopted.
Lemma 1: omega represents a set with smooth boundaries, C 1 (Ω) represents a set of functions that are continuously-conductive, 1 st order defined on Ω, for a function belonging to the order C 1 A real value function v (x) of (Ω) satisfyingThe following inequality holds
Wherein |x ι |<μ ι (ι＝1，2，...，K)，μ ι Is a positive constant, and the constant lambda is more than or equal to 2.
The lyapunov function was constructed as:
dini derivatives with respect to time t are taken for V (t) along an anti-synchronization error system (4.9), and are obtained:
because the discrete time lag tau (t) is less than or equal to 0 and less than or equal to tau (t) and less than or equal to tau,the distribution time lag delta (t) is 0-delta (t) delta, and the distribution time lag delta (t) delta is 0-delta, and the distribution time lag delta (t) is 0-delta>Inequality can be obtained
And then can obtain:
from the lemma 1 and green's formula, the following inequality can be obtained:
wherein div represents a divergence operator;
according to Young's inequality:
wherein w is 1 ＞0，w 2 ＞0，1/w 1 +1/w 2 =1. The following inequality can be obtained:
λ|e 1i (t，r)| λ-1 |e 2i (t，r)|≤(λ-1)|e 1i (t，r)| λ +|e 2i (t，r)| λ
λ|e 2i (t，r)| λ-1 |e 1i (t，r)|≤(λ-1)|e 2i (t，r)| λ +|e 1i (t，r)| λ
λ|e 2i (t，r)| λ-1 |F j (e 1j (t，r))|≤(λ-1)|e 2i (t，r)| λ +|F j (e 1j (t，r))| λ
λ|e 2i (t，r)| λ-1 |F j (e 1j (t-τ(t)，r))|
≤(λ-1)|e 2i (t，r)| λ +|F j (e 1j (t-τ(t)，r))| λ
λ|e 2i (t，r)| λ-1 |F j (e 1j (s，r))|≤(λ-1)|e 2i (t，r)| λ +|F j (e 1j (s，r))| λ
from the above inequality, it is further derived that:
thus, under event-triggered conditions, D can be obtained + V (t) is less than or equal to 0, and the driving system and the response system can achieve event triggering anti-synchronization.
2. Numerical simulation
In this embodiment, the inertial memristor neural network driving system with the reaction diffusion term and the distribution time lag is selected as follows:
the response system model corresponding to the drive system is:
wherein i, j=1, 2; the time t is more than or equal to 0; the space dimension K=1, Ω= { r| -0.5.ltoreq.r.ltoreq.0.5 }; the activation function is set to f j (·) =tanh (·); time lag τ (t) =δ (t) =e t /1+e t The method comprises the steps of carrying out a first treatment on the surface of the Remaining System parameters alpha 11 ＝0.3，α 21 ＝0.1，a 1 ＝a 2 ＝0.5，b 1 ＝b 2 =2. Liposchitz constant ρ 1 ＝p 2 ＝1；τ＝1，τ 0 ＝0.25，δ＝1，δ 0 =0.25. Switching interval T p =1, memristive connection weight set to Available according to memristive connection weights>/>
Let λ=2, calculate the range pi of the control gain available 11 ＞6.733，π 12 ＞6.067，π 21 ＞3.45，π 22 > 4.2. Selecting the gain pi of the controller 11 ＝7，π 12 ＝7，π 11 ＝4，π 12 =5, and η can be calculated 11 ＝0.267，η 12 ＝0.933，η 21 ＝0.55，η 22 =0.8. In the numerical simulation, the initial value of a driving system is taken as x 1 (h，r)＝0，x 2 (h，r)＝0，y 1 (h，r)＝0.5，y 2 (h，r)＝0.5，(h，r)∈[-1，0]×[-0.5，0.5]The method comprises the steps of carrying out a first treatment on the surface of the Taking initial value of response system (h，r)∈[-1，0]×[-0.5，0.5]。
From the above parameters, the event trigger condition can be obtained: under event-triggered conditions, the driving system may reach event-triggered desynchronization with the responding system.
Applying an anti-synchronization controller to the response system, when ω=0.8, fig. 2 is an anti-synchronization error e under event-triggered conditions 11 (t, r) trace diagram, FIG. 3 is an anti-synchronization error e under event trigger condition 12 (t, r) trace diagram, FIG. 4 is an anti-synchronization error e under event trigger condition 21 (t, r) trace diagram, FIG. 5 is an anti-synchronization error e under event trigger condition 22 (t, r). Obviously, the anti-synchronization error converges to 0 under the event-triggered condition, which means that the driving system and the response system reach anti-synchronization. FIG. 6 is e 11 (t k h, r), FIG. 7 is e 12 (t k h, r), FIG. 8 is e 21 (t k h, r), FIG. 9 is e 22 (t k h, r), e 11 (t k h，r)、e 12 (t k h，r)、e 21 (t k h, r) and e 22 (t k h, r) converges to 0 in a stepwise manner, verifying the effectiveness of the controller under event-triggered conditions.
Based on the fact that the response system in the embodiment is reversely synchronized with the driving system under the action of the anti-synchronization controller, image encryption and decryption are achieved, and the method comprises the following specific implementation steps:
the encryption process is as follows:
step S31: reading a lena color image as shown in fig. 10 (a), wherein the image size is 256×256×3, extracting a red component matrix R (p, q) of the original lena color image, a green component matrix G (p, q), a blue component matrix B (p, q), p e {1, 2..256 }, q e {1, 2..256 }, wherein elements of R (p, q), G (p, q) and B (p, q) are all 0, 1..255;
step S32: after the driving system and the response system reach the anti-synchronization, three chaotic signals x of the driving system are used for generating 1 (t，r)、x 2 (t，r)、y 1 (t, r) respectively selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p，q)，p∈{1，2，...，256}，q∈{1，2，...，256}；
Step S33: three chaos obtained in step S32Signal sequence z 1 (p，q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z are obtained 1 (p，q)、Z 2 (p, q) and Z 3 (p, q), p e {1,2,., 256}, q e {1,2,., 256}, where Z 1 (p，q)、Z 2 (p, q) and Z 3 The elements of (p, q) are all 0, 1..255, the specific conversion formula used in step S33 is:
Z 1 (p，q)＝mod(10000*(z 1 (p，q)-floor(z 1 (p，q)))，256)，
Z 2 (p，q)＝mod(10000*(z 2 (p，q)-floor(z 1 (p，q)))，256)，
Z 3 (p，q)＝mod(10000*(z 3 (p，q)-floor(z 1 (p，q)))，256)；
step S34: three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) performing exclusive OR operation with corresponding position elements in three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image respectively to obtain three color component matrixes R after replacement 1 (p，q)、G 1 (p，q)、B 1 (p，q)，p∈{1，2，...，256}，q∈{1，2，...，256}；
Step S35: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p, q), p e {1,2,..256 }, q e {1,2,..256 }, the arnold transform algorithm is:
where (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, a=2, b=3;
step S36: three of the steps S35 are arrangedSeed color component matrix R 2 (p，q)、G 2 (p，q)、B 2 (p, q) as three color component matrices of the encrypted image, combining the color component matrices of the encrypted image to generate the encrypted image;
the decryption process is as follows:
step S37: reading an encrypted image, and extracting three color component matrices r (p, q), g (p, q), b (p, q), p epsilon {1, 2..256 }, q epsilon {1, 2..256 }, wherein elements of r (p, q), g (p, q) and b (p, q) are all 0, 1..255;
step S38: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p, q), p e {1,2,..256 }, q e {1,2,..256 }, the arnold inverse transform algorithm is:
where (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, a=2, b=3;
step S39: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal of the response systemSelecting and selecting z in step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequence->And->p∈{1，2，...，256}，q∈{1，2，...，256}；
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +. >And->p.e {1, 2..256 }, q.e {1, 2..256 }, where +.>And->Is 0,1,..255, the specific conversion formula used in step S310 is:
step S311: three new signal sequences obtained in step S310 Respectively with the three color component matrices r restored in step S38 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q), and recovering to obtain three color component matrixes r of the original color image 2 (p，q)、g 2 (p，q)、b 2 (p，q)，p∈{1，2，...，256}，q∈{1，2，...，256}；
Step S312: three color component matrices r of the original color image restored in step S311 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, restoring the original lena color image.
As shown in fig. 10, (a), (b), and (c) are an original image, an encrypted image, and a decrypted image, respectively. Fig. 10 shows the encryption effect in a visual way, and the encrypted image has no similarity with the original image, so that the purpose of image encryption is achieved. Fig. 11 shows the pixel distribution histograms of the respective color components of the original image and the encrypted image, and fig. 11 shows the pixel distribution histograms of the respective color components of the original image, and fig. 11 shows the pixel distribution histograms of the respective color components of the encrypted image. As can be seen from fig. 11, the original image pixels are unevenly distributed and are easily attacked by statistical analysis, and the encrypted image pixels are relatively evenly distributed, so that the statistical attack can be effectively resisted, and a good encryption effect is realized.
Finally, it should be noted that: the foregoing is merely a preferred example of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. An image encryption method based on inertial memristor neural network desynchronization is characterized by comprising the following steps:
step S1: based on an inertial memristor neural network with reaction diffusion term and distribution time lag, a driving system and a response system are established, and the method specifically comprises the following steps:
step S11: establishing a driving system based on an inertial memristor neural network with reaction diffusion terms and distribution time lags;
the state equation for establishing the inertial memristor neural network with the reaction diffusion term and the distribution time lag is as follows:
wherein the time t is more than or equal to 0; n is the number of neurons in the drive system, i, j=1, 2, n; k represents the spatial dimension, iota=1, 2,..k, spatial variable r= (r 1 ，r 2 ，...，r K ) T And satisfy |r ι |<μ ι ，μ ι Is a positive constant; x is x i (t, r) and x j (t, r) are state variables of the ith and jth neurons in the drive system at time t and space r, respectively; x is x j (s, r) represents x when time t=s j The value of (t, r), s being an integral variable; alpha iι 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,0≤δ(t)≤δ，/>wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant ρ j ；b i ＞0，a i > 0 is a constant; c ij (x i (t，r))、d ij (x i (t, r)) and ε ij (x i (t, r)) represents memristor connection weights in the form:
in which the switching interval T i >0；And->Is a constant; is provided with->
And performing variable substitution order reduction processing on a state equation of the inertial memristor neural network with a reaction diffusion term and a distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein the method comprises the steps ofβ i ＝b i -a i -1，γ i ＝b i -1；
Step S12: the corresponding response system is established according to the driving system:
wherein the time t is more than or equal to 0; n is the number of neurons in the response system, i, j=1, 2, …, n; k denotes the spatial dimension, iota=1, 2, …, K, spatial variable r= (r) 1 ,r 2 ,…,r K ) T And satisfy |r ι |<μ ι ，μ ι Is a positive constant;in response to the state variables of the ith neuron in the system at time t and space r,/and > In response to state variables of the jth neuron in the system at time t and space r; />Represents +.>Is a value of (2); alpha iι 0 or more represents a transmission diffusion parameter; τ (t) and δ (t) represent discrete time lags and distributed time lags, respectively, and satisfy 0.ltoreq.τ (t). Ltoreq.τ,/v>0≤δ(t)≤δ，/>Wherein τ, τ 0 Delta and delta 0 Is a positive constant; f (f) j (. Cndot.) represents the activation function of the j-th neuron and satisfies the Lipohsh condition, which has a Lipohsh constant ρ j ；β i ＝b i -a i -1，γ i ＝b i -1；u 1i (t, r) and u 2i (t, r) is the controller to be designed; />And->Representing memristor connection weights in the form:
in which the switching interval T i >0；And->Is a constant;
step S2: setting an anti-synchronization error according to the driving system and the response system established in the step S1, and designing an anti-synchronization controller;
step S3: based on the response system, the driving system is reversely synchronized under the action of the anti-synchronization controller, and further, the image encryption and decryption are realized, and the specific implementation steps are as follows:
the encryption process comprises the following steps:
step S31: reading an original color image, wherein the image size M multiplied by N multiplied by 3, extracting a red component matrix R (p, q), a green component matrix G (p, q) and a blue component matrix B (p, q), p epsilon {1,2, …, M }, q epsilon {1,2, …, N }, wherein the elements of R (p, q), G (p, q) and B (p, q) are all certain values of 0,1, …, 255;
Step S32: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p,q)、z 2 (p, q) and z 3 (p,q)，p∈{1,2,…,M}，q∈{1,2,…,N}；
Step S33: three chaotic signal sequences z obtained in the step S32 1 (p,q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z are obtained 1 (p,q)、Z 2 (p, q) and Z 3 (p, q), p ε {1,2, …, M }, q ε {1,2, …, N }, where Z 1 (p,q)、Z 2 (p, q) and Z 3 The elements of (p, q) are all 0, 1..255, the specific conversion formula used in step S33 is:
Z 1 (p，q)＝mod(10000*(z 1 (p，q)-floor(z 1 (p，q)))，256)，
Z 2 (p，q)＝mod(10000*(z 2 (p，q)-floor(z 1 (p，q)))，256)，
Z 3 (p，q)＝mod(10000*(z 3 (p，q)-floor(z 1 (p，q)))，256)；
step S34: three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) performing exclusive OR operation with corresponding position elements in three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image respectively to obtain three color component matrixes R after replacement 1 (p，q)、G 1 (p，q)、B 1 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S35: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
Step S36: the three color component matrices R after being scrambled in the step S35 2 (p，q)、G 2 (p，q)、B 2 (p, q) as three color component matrices of the encrypted image, combining the color component matrices of the encrypted image to generate the encrypted image;
the decryption process is the inverse of the encryption process, and specifically comprises the following steps:
step S37: reading an encrypted image, and extracting three color component matrices r (p, q), g (p, q), b (p, q), p epsilon {1,2,., M }, q epsilon {1, 2., N }, wherein elements of r (p, q), g (p, q), and b (p, q) are all 0, 1., 255;
step S38: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p, q), p.epsilon.1, 2, M, q.epsilon.1, 2, n., the arnold inverse transform algorithm is:
wherein (m, n) is the original position of the pixel, (m ', n') is the position of the pixel after scrambling, and a and b are constants;
step S39: after the driving system and the response system reach the anti-synchronization, according to the chaotic signal of the response systemOr->Selecting and selecting z in step S32 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequence And->p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And->p.epsilon.1, 2, M, q.epsilon.1, 2, N, where ∈>And->Is 0,1,..255, the specific conversion formula used in step S310 is:
step S311: three new signal sequences obtained in step S310 Respectively with step S38Three color component matrices r for reduction 1 (p，q)、g 1 (p，q)、b 1 Performing exclusive OR operation on the corresponding position elements in (p, q), and recovering to obtain three color component matrixes r of the original color image 2 (p，q)、g 2 (p，q)、b 2 (p，q)，p∈{1，2，...，M}，q∈{1，2，...，N}；
Step S312: three color component matrices r of the original color image restored in step S311 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombining, decrypting to obtain an original color image;
the step S2 specifically comprises the following steps:
step S21: the anti-synchronization error between the driving system and the response system is set as follows:
step S22: according to the anti-synchronization error between the driving system and the response system set in the step S21, designing an anti-synchronization controller based on an event trigger control strategy as follows: u (u) 1i (t，r)＝-π 1i e 1i (t k h, r) and u 2i (t,r)＝-π 2i e 2i (t k h, r), where the gain pi is controlled 1i And pi 2i Is the normal number, t k h is an event trigger time, h is a sampling interval, t k The sequence of event trigger times can be described as {0, t 1 h,t 2 h,…,t k h}， And->For measuring errors, when the measuring error range exceeds a threshold value related to a state, an event triggering condition is violated, and the anti-synchronous controller is updated, wherein the specific event triggering condition is as follows:and->Wherein time t e [ t ] k h,t k+1 h) Constant lambda is greater than or equal to 2, omega is 0,1]，/> Control gain pi 1i To satisfy pi 1i ≥max{0,-η 1i +π 1i Control gain pi 2i To satisfy pi 2i ≥max{0,-η 2i +π 2i }。
2. An inertial memristive neural network-based anti-synchronization image encryption system applied to the method of claim 1, comprising:
the chaotic signal acquisition module is used for: based on an inertial memristor neural network with reaction diffusion terms and distribution time lags, a driving system and a response system are established, an anti-synchronization error is set, and an anti-synchronization controller is designed to enable the driving system and the response system to achieve anti-synchronization; after the driving system and the response system reach the anti-synchronization, according to the chaotic signal x of the driving system i (t, r) or y i (t, r) selecting three chaotic signal sequences z 1 (p,q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemOr->Selecting and z 1 (p,q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->
The encryption chaotic signal processing module: for sequencing a chaotic signal z 1 (p,q)、z 2 (p, q) and z 3 (p, q) after a specific conversion, three new signal sequences Z can be obtained 1 (p,q)、Z 2 (p, q) and Z 3 (p, q) wherein Z 1 (p,q)、Z 2 (p,q)、Z 3 The elements of (p, q) are each a value of 0,1, …, 255;
an encryption component reading module: for reading an original color image, extracting a red component matrix R (p, q), a green component matrix G (p, q), and a blue component matrix B (p, q) of the original color image;
encryption replacement operation module: for combining the three new signal sequences Z obtained in step S33 1 (p，q)、Z 2 (p，q)、Z 3 (p, q) exclusive-or operation is carried out on the three color component matrixes R (p, q), G (p, q) and B (p, q) of the original color image and corresponding position elements;
scrambling operation module: the three color component matrixes R after the replacement are subjected to the arold transformation 1 (p，q)、G 1 (p，q)、B 1 (p, q) scrambling to obtain three color component matrixes R after scrambling 2 (p，q)、G 2 (p，q)、B 2 (p，q)；
An encryption component combining module: three color components for combining encrypted imagesQuantity matrix R 2 (p，q)、G 2 (p，q)、B 2 (p, q) generating an encrypted image;
the decryption chaotic signal processing module: for sequencing chaotic signalsAnd->After specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofElements of (a) are all 0, 1..255;
decryption component reading module: for reading the encrypted image, extracting three color component matrices r (p, q), g (p, q), b (p, q) of the encrypted image;
The reverse scrambling operation module is as follows: the inverse scrambling operation is carried out on three color component matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image by adopting the inverse Arnold transformation, and three color component matrixes r are restored 1 (p，q)、g 1 (p，q)、b 1 (p，q)；
Decryption replacement operation module: for combining the three new signal sequences obtained in step S310 Respectively with the three color component matrices r1 (p, q), g restored in step S38 1 (p，q)、b 1 Exclusive-or operation of corresponding position elements in (p, q)；
Decryption component combination module: three color component matrices r for restoring the original color image 2 (p，q)、g 2 (p，q)、b 2 (p, q) recombination, decryption to obtain the original color image.
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