CN116760933B - Image encryption method and system based on neural network with reactive diffusion - Google Patents
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- H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
- H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
- H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
- H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
- H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
- H04N1/32272—Encryption or ciphering
Abstract
The invention belongs to the technical field of new generation information, and particularly discloses an image encryption method and system based on a neural network with reactive diffusion, wherein the method comprises the following steps: establishing a driving system and a response system based on a memristive neural network with reaction diffusion terms and distribution time lags; setting an anti-synchronization error, and designing an anti-synchronization controller by adopting an event trigger control strategy; the response system is in anti-synchronization with the driving system under the action of the anti-synchronization controller, so that image encryption is realized. The invention solves the problem that the memristor neural network with reaction diffusion term and distribution time lag is difficult to realize anti-synchronization, and provides a novel image encryption method and system, which remarkably 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 a neural network with reactive diffusion.
Background
Memristors have the advantages of small volume, high density, good expandability and the like. Unlike resistance, memristors can remember the last charge value passed when the circuit is open. This characteristic is similar to the memory characteristics of biological neuron synapses, so memristors are often used to simulate synapses in artificial neural networks. Such a neural network with memristors is referred to as a memristive neural network. Compared with the traditional neural network, the memristive neural network has the advantages that the connection weight is not fixed, so that the memristive neural network has the nonlinear switching jump characteristic and the dynamic behavior is more complex. Analysis of the dynamic behavior of memristive neural networks is also important in practical applications, including machine learning, signal processing, image processing, and the like.
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 desynchronization of memristive neural networks with reaction diffusion items and distribution time lags, and provides an image encryption method and system based on the neural networks with reaction diffusion, 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 a neural network with reactive diffusion, comprising the steps of:
step S1: establishing a driving system and a response system based on a memristive neural network with reaction diffusion terms and distribution time lags;
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 that the image encryption and decryption are realized.
Further, the step S1 specifically includes the following steps:
step S11: the driving system is established based on the memristive neural network with reaction diffusion term and distribution time lag, and comprises the following steps:
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 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; 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; a, a 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 of normal number>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 is a constant; c ij (x i (t,r))、d ij (x i (t, r)) and ε ij (x i (t, r)) represents the driveMemristor connection weights in a dynamic system are in the following form:
in which the switching interval T i >0；And->Is a constant; is provided with-> The boundary conditions and initial conditions of the drive system are: x is x i (t,r)＝0，/>x i (h,r)＝φ i (h,r)，/>Wherein phi is i (h, r) is defined as +.>A continuous and bounded function, Ω being a tight set with smooth boundaries;
step S12: the memristive neural network building response system based on the reaction diffusion term and the distribution time lag comprises the following components:
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;and->State variables at time t and space r of an ith neuron and a jth neuron in the response system, respectively; a, a 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 of normal number>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 is a constant; u (u) i (t, r) is the controller to be designed; />And->And representing the memristor connection weight in the response system, wherein the form is as follows:
in which the switching interval T i >0；And->Is a constant; the boundary conditions and initial conditions of the response system are: /> Wherein->Is defined as +.>And a continuous and bounded function, Ω is a tight set with smooth boundaries.
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) i (t,r)＝-π i e i (t k h, r), where the gain pi is controlled i Is the normal number, t k h is an event trigger time, h is a sampling interval, tk is a positive integer, and the sequence of event trigger times can be described as {0, t 1 h,t 2 h,…,t k h}， For measuring error, when the measuring error range exceeds and is equal toWhen the threshold value related to the state is in violation of the event triggering condition, updating the anti-synchronous controller, wherein the specific event triggering condition is as follows: />Wherein time t e [ t ] k h,t k+1 h) Constant lambda is greater than or equal to 2, alpha is 0,1]，/> Control gain pi i To satisfy pi i ≥max{0,-η i +π i }。
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, 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) 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 to obtainTo three new signal sequences Z 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, and 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 e {1,2, …, M }, q e {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 matrixes r (p, q), g (p, q) and b (p, q) of the encrypted image, wherein p epsilon {1,2, …, M }, q epsilon {1,2, …, N }, and the elements of r (p, q), g (p, q) and b (p, q) are all a certain value of 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, …, M }, q e {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 systemSelecting and selecting z in step S32 1 (p,q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And-> Wherein->And->Is a value of 0,1, …,255, and 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 a neural network with reactive diffusion is provided, comprising:
the chaotic signal acquisition module is used for: based on a memristive 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) selecting three chaotic signal sequences z 1 (p,q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemSelecting and z 1 (p,q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequence->And->
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 obtained in step S33Novel signal sequence Z 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->Elements 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), q (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 T 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 neural network model, a more complex network model is formed by particularly introducing a reaction diffusion term according to the characteristics of a 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, an event triggering control strategy is adopted, an event triggering anti-synchronization controller is designed, and event triggering conditions are given, and the control scheme 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 and system based on the neural network with reactive diffusion provided by the invention combine the advantages of scrambling and replacement with the use of absorbing, so that a better encryption effect is obtained, the method and system are more effective in resisting noise and data loss, and are not easy to suffer from statistical attack.
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 flow chart of an image encryption method based on a neural network with reactive diffusion;
FIG. 2 is an uncontrolled time anticynchronous error e i A trace of (t, r), wherein (a) is e when uncontrolled 1 A locus of (t, r), e when (b) is uncontrolled 2 A trajectory of (t, r);
FIG. 3 is an anti-synchronization error e under event-triggered conditions i (t, r), wherein (a) is e under event trigger condition 1 A trace of (t, r), and (b) is e under event trigger condition 2 A trajectory of (t, r);
fig. 4 is an event trigger timing chart under an event trigger condition, in which (a) is an event trigger timing when i=1 and (b) is an event trigger timing when i=2;
fig. 5 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. 6 is a flowchart of an image encryption system based on a neural network with reactive diffusion according to the present invention.
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.
As shown in fig. 1, the present embodiment provides an image encryption method based on a neural network with reactive diffusion. The image encryption method comprises the following steps:
step S1: establishing a driving system and a response system based on a memristive neural network with reaction diffusion terms and distribution time lags;
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: the driving system is established based on the memristive neural network with reaction diffusion term and distribution time lag, and comprises the following steps:
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 denotes the spatial dimension, iota=1, 2, …, K, spatial variable r= (r) 1 ,r 2 ,…,r K ) T And satisfy |r ι |<μ l ，μ l 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; a, a 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 of normal number>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 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 drive system in the form:
in which the switching interval T i >0；And->Is a constant. Is provided with-> The boundary conditions and initial conditions of the drive system are: x is x i (t,r)＝0，/>x i (h,r)＝φ i (h,r)，/>Wherein phi is i (h, r) is defined as +.>A continuous and bounded function, Ω being a tight set with smooth boundaries;
step S12: the memristive neural network building response system based on the reaction diffusion term and the distribution time lag comprises the following components:
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, l=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;and->State variables at time t and space r of an ith neuron and a jth neuron in the response system, respectively; a, a 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 of normal number>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 is a constant; u (u) i (t, r) is the controller to be designed; />And->And representing the memristor connection weight in the response system, wherein the form is as follows:
in which the switching interval T i >0；And->Is a constant; the boundary conditions and initial conditions of the response system are: /> Wherein->Is defined as +.>And a continuous and bounded function, Ω is a tight set with smooth boundaries.
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) i (t,r)＝-π i e i (t k h, r), where the gain pi is controlled i Is the normal number, t k h is an event trigger time, h is a sampling interval, tk is a positive integer, and the sequence of event trigger times can be described as {0, t 1 h,t 2 h,…,t k h}， 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: />Wherein time t e [ t ] k h,t k+1 h) Constant lambda is greater than or equal to 2, alpha is 0,1]，/> Control gain pi i To satisfy pi i ≥max{0,-η i +π i }。
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 is based on the fact that the response system is anti-synchronized with the driving system under the action of the anti-synchronization controller, so as to implement 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, 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) 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 each a value of 0,1, …,255, the particular transition used in step S33The formula is changed as follows:
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 e {1,2, …, M }, q e {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 the encrypted image, extracting three color component matrixes r (p, q) of the encrypted image,
g (p, q), b (p, q), p e {1,2, …, M }, q e {1,2, …, N }, wherein the elements of r (p, q), g (p, q) and b (p, q) are all some value of 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, …, M }, q e {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 systemSelecting and selecting z in step S32 1 (p,q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequenceAnd->
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And-> Wherein->And->Is a value of 0,1, …,255, and 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 a neural network with reactive diffusion is provided, and the flow of the image encryption system is shown in fig. 6, and the image encryption system includes:
the chaotic signal acquisition module is used for: based on a memristive 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) selecting three chaotic signal sequences z 1 (p,q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemSelecting and z 1 (p,q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequence->And->
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) are respectively associated with three color component matrices R (p, q), G (p, q), B (p,performing exclusive OR operation on the corresponding position elements in q);
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->Elements 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, a reaction diffusion term is 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 scheme 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 neural network with reactive diffusion provided by the invention combines the advantages of scrambling and substitution and using suction, thereby obtaining better encryption effect, being more effective in resisting noise and data loss and being not easy to suffer statistical attack.
Example 2:
the embodiment mainly comprises two parts of contents:
one is to carry out theoretical demonstration on the effectiveness of the designed desynchronized controller in the desynchronized control method of the memristive neural network with reaction diffusion term and distribution time lag, which is proposed in the embodiment 1.
Secondly, whether the constructed driving system and the response system reach the desynchronization or not and whether the image encryption method is effective or not are aimed at the memristive neural network with the reaction diffusion term and the distribution time lag in the embodiment 1 through a numerical simulation method.
(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 i And (t, r) is a controller to be designed.
Defining the anti-synchronization error between the drive system and the response system asThe 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 boundary condition and initial condition of the anti-synchronous error system are e i (t,r)＝0，
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 i (t,r)| λ-1 |F j (e j (t,r))|≤(λ-1)|e i (t,r)| λ +|F j (e j (t,r))| λ
λ|e i (t,r)| λ-1 |F j (e j (t-τ(t),r))|
≤(λ-1)|e i (t,r)| λ +|F j (e j (t-τ(t),r))| λ
λ|e i (t,r)| λ-1 |F j (e j (s,r))|≤(λ-1)|e i (t,r)| λ +|F j (e j (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 reach the anti-synchronization.
2. Numerical simulation
In this embodiment, the memristive neural network driving system with the reaction diffusion term and the distribution time lag is selected as follows:
the memristive neural network response system model with the response diffusion term and the distribution time lag corresponding to the memristive neural network response system model is as follows:
wherein i, j=1, 2; the time t is more than or equal to 0; the space dimension K=1, Ω= { r| -5.ltoreq.r.ltoreq.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 a 1 ＝0.2，a 2 ＝0.8，b 1 ＝1，b 2 =1. Liposchitz constant ρ 1 ＝ρ 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 1 >3.6，π 2 >5.56. Selecting the gain pi of the controller 1 ＝4，π 2 =6, and η can be calculated 1 ＝0.4，η 2 =0.44. In the numerical simulation, the initial value of a driving system is taken as x 1 (h,r)＝0.5，x 2 (h,r)＝0.7，(h,r)∈[-1,0]×[-5,5]The method comprises the steps of carrying out a first treatment on the surface of the Taking initial value of response system
From the above parameters, the event trigger condition can be obtained:/>under event-triggered conditions, the drive system may be desynchronized with the response system.
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. 4 (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 a certain value of 0,1, …, 255;
step S32: after the driving system and the response system reach the anti-synchronization, obtaining a chaotic signal x according to the driving system 1 (t,r)、x 2 (t,r)、Three chaotic signal sequences z are respectively selected 1 (p,q)、z 2 (p, q) and z 3 (p,q)，p∈{1,2,…,256}，q∈{1,2,…,256}；
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 conversionThree new signal sequences Z are obtained 1 (p,q)、Z 2 (p, q) and Z 3 (p, q), p ε {1,2, …,256}, q ε {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, and 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: 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 as follows:
step S37: reading the encrypted image, extracting three color component matrixes r (p, q) of the encrypted image,
g (p, q), b (p, q), p e {1,2, …,256}, q e {1,2, …,256}, wherein the elements of r (p, q), g (p, q) and b (p, q) are each a value of 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, obtaining the chaotic signal according to 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->
Step S310: the chaotic signal sequence obtained in the step S39And->After specific conversion, three new signal sequences +.>And-> Wherein->And->Is a value of 0,1, …,255, and 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) to restore to obtain an original color imageThree color component matrices r 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.
Fig. 2 shows the evolution trace of the desynchronized error without the controller. Obviously, the desynchronization error is continuously oscillating and does not converge to 0 without the action of the controller, which means that the driving system and the response system do not reach desynchronization. The controller acts on the response system, and when alpha=0.6, the evolution track of the anti-synchronization error under the event triggering condition is shown in fig. 3. 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. 4 shows the event trigger time at α=0.6 in the event trigger condition, where fig. 4 (a) and 4 (b) are the event trigger time at i=1 and i=2, respectively. As shown in fig. 5, the image encryption effects are fig. 5 (a), 5 (b), and 5 (c) are an original image, an encrypted image, and a decrypted image, respectively. Fig. 5 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.
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 a neural network with reactive diffusion, comprising the steps of:
step S1: based on memristive 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: the driving system is established based on the memristive neural network with reaction diffusion term and distribution time lag, and comprises the following steps:
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; a, a 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 of normal number>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 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 drive system in the form:
in which the switching interval T i ＞0；And->Is a constant; is provided with-> The boundary conditions and initial conditions of the drive system are: x is x i (t，r)＝0，/>x i (h，r)＝φ i (h，r)，/>Wherein phi is i (h, r) is defined as +.>A continuous and bounded function, Ω being a tight set with smooth boundaries;
step S12: the memristive neural network building response system based on the reaction diffusion term and the distribution time lag comprises the following components:
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;and->State variables at time t and space r of an ith neuron and a jth neuron in the response system, respectively; a, a 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 of normal number>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 is a constant; u (u) i (t, r) is the controller to be designed; />And->And representing the memristor connection weight in the response system, wherein the form is as follows:
in which the switching interval T i ＞0；And->Is a constant; the boundary conditions and initial conditions of the response system are: /> Wherein->Is defined as +.>A continuous and bounded function, Ω being a tight set with smooth boundaries;
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, 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) 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, & gt, 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 systemSelecting 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 obtained in the step S39Sequence(s)And->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) 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) i (t，r)＝-π i e i (t k h, r), where the gain pi is controlled i 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}， For measuring errors, the anti-synchronous controller is updated in violation of event triggering conditions when the measuring error range exceeds a threshold value related to the state, in particularThe event triggering conditions of (1) are: />Wherein time t e [ t ] k h，t k+1 h) Constant lambda is greater than or equal to 2, alpha is 0,1]，/> Control gain pi i To satisfy pi i ≥max{0，-η i +π i }。
2. An image encryption system based on a neural network with reactive diffusion, comprising:
the chaotic signal acquisition module is used for: based on a memristive 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) selecting three chaotic signal sequences z 1 (p，q)、z 2 (p, q) and z 3 (p, q) based on chaotic signal of response systemSelecting and z 1 (p，q)、z 2 (p, q) and z 3 (p, q) corresponding chaotic signal sequence->And->
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->Elements 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.
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