CN117436098B - Image encryption method and system based on unknown disturbance inertial fuzzy neural network - 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 an unknown disturbance inertial fuzzy neural network, comprising the following steps: firstly, establishing a driving system and a response system based on an inertial memristor fuzzy neural network with unknown disturbance; secondly, setting a synchronous error, and designing an aperiodic intermittent adjustment synchronous controller by adopting an aperiodic intermittent adjustment control strategy; and then the response system realizes the finite time synchronization of the response system and the driving system under the action of the non-periodic intermittent adjustment synchronous controller, thereby realizing the image encryption method. The invention solves the problem that the inertial memristor fuzzy neural network with unknown disturbance is difficult to realize the finite time synchronization, and the invention is applied to the field of image encryption, and the proposed 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 an unknown disturbance inertial fuzzy neural network.
Background
With the development of science and technology, people are eager to explore the complex neuronal activity mechanisms of the brain. Since the advent of Hopfield neural networks, humans have realized applications such as image denoising, image encryption, associative memory, and the like through a variety of neural networks.
In real life, the fuzzy theory is valued in life due to a large number of uncertain factors and the existence of fuzziness. The fuzzy logic is introduced into the traditional neural network, so that the continuity between cells can be maintained, and the fuzzy logic is added between the fuzzy input and the fuzzy output besides the sum of output operations, so that the traditional neural network is better in image processing.
Compared with the traditional continuous control strategy, the intermittent control strategy can save a large amount of control resources, consider most phenomena in real life, such as wind energy and solar power generation, non-periodic starting of a heating system and the like, have uncertainty, and the non-periodic intermittent control can eliminate the defects and the limitations of periodic intermittent control.
With the development of the internet, countless picture information is transmitted in the internet, and whether the picture information is transmitted through secure encryption is widely paid attention to. Therefore, research on image encryption is of great practical importance. Because the neural network can generate complex chaotic signals, the quasi-randomness, non-periodicity and unpredictable characteristics of the chaotic signals can be combined in the image encryption method, so that the effectiveness of the image encryption method is improved.
Disclosure of Invention
The invention aims to solve the problem that the inertial memristor fuzzy neural network with unknown disturbance is difficult to realize finite time synchronization, and provides an image encryption method and system based on the inertial memristor fuzzy neural network with unknown disturbance, 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 an unknown disturbance inertial fuzzy neural network comprises the following steps:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unknown disturbance are constructed, and the method specifically comprises the following steps:
Step S11: the driving system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
step S12: the response system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
In step S11 and step S12, time t is not less than 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, x i (t) represents the state of the ith neuron of the driving system at the time t, and y i (t) represents the state of the ith neuron of the response system at the time t; a i denotes the damping coefficient of the ith neuron, b i denotes the rate at which the ith neuron resets its potential to a rest state when the network is disconnected from an external input, a i and b i satisfy a i >0 and b i>0;fj(xj (t), respectively), an activation function that the jth neuron of the drive system does not contain a time lag, f j(xj(t-τj (t)) denotes an activation function that the jth neuron of the drive system contains a time-varying discrete time lag, f j(yj (t)) denotes an activation function that the jth neuron of the response system does not contain a time lag, f j(yj(t-τj (t))) represents an activation function of a j-th neuron of the response system that contains a time-varying discrete time lag that is a discontinuous activation function and satisfies |f j(.)|≤Mj, where M j is a positive constant; τ j (t) and δ j (t) are time-varying discrete time lag and time-varying distributed time lag, respectively, and satisfy 0.ltoreq.τ j(t)≤τ,0≤δj (t). Ltoreq.δ, wherein τ and δ are positive constants, and ζ=max { τ, δ }; η is an integral variable; z ij represents a feed-forward element; And q ij represents the elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules, respectively; h ij and ρ ij represent the elements of the minimum and maximum fuzzy feedback modules, respectively; m j (t) represents the input of the jth neuron; v and V respectively represent fuzzy and fuzzy or operators, and the following conditions are satisfied:
And/> Unknown disturbances in the drive system and the response system, respectively, satisfy/> Wherein σ i is a positive constant; u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x i(s)＝φi (s)/> cij(xi(t))、dij(xi(t))、wij(xi(t))、cij(yi(t))、dij(yi(t))、wij(yi(t)) The memristor connection weights are expressed, and respectively satisfy:
Wherein Γ i is a switching threshold and Γ i >0; Are all constant;
Since the right side of the equal sign of the driving system and the response system is discontinuous, the solutions of the driving system and the response system need to be considered in the Filippov sense, and then the driving system and the response system are respectively rewritten as follows by adopting the set value mapping and the differential inclusion theory:
In the method, in the process of the invention, AndSatisfy/> And/>Satisfy/> Χ j and iota j are constants ;K[cij(xi(t))]、K[dij(xi(t))]、K[wij(xi(t))]、K[cij(yi(t))]、K[dij(yi(t))]、K[wij(yi(t))]、K[fj(xj(t))]、K[fj(yj(t))]、K[fj(xj(t-τj(t)))] and K [ f j(yj(t-τj (t))) respectively:
Wherein,
Step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing an aperiodic intermittent adjusting synchronous controller;
Step S3: based on the response system, the drive system is synchronized with limited time under the action of the non-periodic intermittent adjustment synchronous controller, so that the image encryption and decryption are realized, and the method comprises the following specific implementation steps:
The encryption process comprises the following steps:
step S31: reading unencrypted color image, image size Extracting the red channel component matrix/>, of an unencrypted color imageGreen channel component matrix/>And blue channel/> Wherein/>And/>The value ranges are all one value in (0, 1, …, 255);
Step S32: after the driving system and the response system reach limited time synchronization, three chaotic signal sequences are selected according to discrete time sequence chaotic signals x i (t) of the driving system And
Step S33: three chaotic signal sequences obtained in the step S32 After specific conversion, three new signal sequences/>, are obtainedAnd/> Wherein/>And/>The value ranges are all one value in (0, 1, …, 255); the specific conversion formula used in step S33 is:
step S34: three new signal sequences obtained in step S33 And/>Three color channel component matrices/>, respectively with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes/>, and obtaining three color channel component matrixes/>, wherein the three color channel component matrixes/>, the three color channel component matrixes are replaced by the three color channel component matrixes/>, and the three color channel component matrixes/> areobtained by the three color channel component matrixesAnd
Step S35: the arnold transformation is adopted to replace the three color channel component matrixes And/>Scrambling to obtain a scrambled three-color channel component matrix/>AndThe arnold transform algorithm is:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S36: the three color channel component matrices after being scrambled in step S35 As three color channel component matrixes of the encrypted image, combining the color component matrixes 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 channel component matrixes of the encrypted image And/>Wherein the method comprises the steps ofAnd/>The value ranges are all one value in (0, 1, …, 255);
Step S38: three color channel component matrices for encrypted images using arnold inverse transforms And/>Performing inverse scrambling treatment and restoring to obtain three color channel component matrixesAnd/>The arnold inversion algorithm is as follows:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S39: after the driving system and the response system reach the limited time synchronization, selecting and in step S32 according to the discrete time sequence chaotic signal y i (t) of the response system And/>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/>The value ranges are all one 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 And/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive or operation on the corresponding position elements of the image to obtain three color channel component matrixes/>, of the decrypted image, wherein the three color channel component matrixes/>, of the decrypted image are obtained through decryptionAnd
Step S312: three color channel component matrices of the decrypted image obtained in step S311 areAnd/>And (5) recombining to obtain a decrypted image.
Further, the step S2 specifically includes the following steps:
Step S21: the synchronization error of the driving system and the response system is set as follows:
ei(t)＝yi(t)-xi(t)
Step S22: according to the synchronization error between the driving system and the response system set in step S21, the non-periodic intermittent adjustment synchronization controller is designed to:
Where k is the number of control cycles, i.e., k=0, 1,2, …; t k is the start-up time of the first subinterval controller in the kth period, s k represents the start-up time of the second subinterval controller in the kth period, and t k and s k are required to satisfy: Omega and/> Is constant and meetsΖ i、εi、θi、∈i、λ1i、λ2i is positive controller gain; l e (0, 1); /(I)Expressed as derivative of synchronization error/>Is a sign function of (2); e i(t-τi (t)) represents the synchronization error of the state variable of the driving system i-th neuron comprising a time-varying discrete time lag and the state variable of the response system i-th neuron comprising a time-varying discrete time lag, and the controller gain ζ i、εi、θi、∈i、λ1i、λ2i satisfies the following inequality:
ζi≧1-ai
Wherein ψ is a constant and E represents a natural constant e; /(I)
And enabling the non-periodic intermittent adjustment synchronous controller to act on the response system so that the response system is synchronous with the driving system for a limited time.
Further, the response system is synchronized with the drive system for a limited time, and an upper bound T of the limited time is:
wherein T 1 is Is a smaller solution to that.
In a second aspect of the present invention, an image encryption system based on an unknown disturbance inertial fuzzy neural network is provided, the image encryption system comprising:
the chaotic signal acquisition module is used for: the method comprises the steps of establishing a driving system and a response system based on an inertial memristor fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjustment synchronous controller so that the driving system and the response system are synchronous in a limited time; after the driving system and the response system are synchronous, the chaotic signal acquisition module selects three chaotic signal sequences according to the discrete time sequence chaotic signal x i (t) of the driving system And/>The chaotic signal acquisition module selects and/>, according to the discrete time sequence chaotic signal y i (t) of the response systemAndCorresponding chaotic signal sequence/>And/>
The chaotic signal processing module: the system is particularly subdivided into a driving system chaotic signal processing module and a response system chaotic signal processing module, wherein the driving system chaotic signal processing module is used for sequencing a chaotic signal AndAfter specific conversion, three new signal sequences/> And/>The response system chaotic signal processing module is used for converting the chaotic signal sequence/> And/>After specific conversion, three new signal sequences/>And/>Wherein the method comprises the steps ofAnd/>The value ranges are all one value in (0, 1, …, 255);
Channel color component extraction module: the method comprises the steps of specifically subdividing an unencrypted color image component extraction module and an encrypted image component extraction module; the unencrypted color image component extraction module is used for reading an unencrypted color image in the encryption process and extracting a red channel component matrix of the color image Green channel component matrix/>And blue channel component matrix/>The encryption image component extraction module is used for reading the encryption image in the decryption process and extracting three color channel component matrixes/>, of the encryption image And/>
A signal replacement processing module: used in the encryption process for the three new signal sequences obtained in step S33And/>Three color channel components respectively associated with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the table; in the decryption process, three new signal sequences/>, obtained in step S310, are obtainedAnd/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive OR operation on the corresponding position elements in the table;
the signal scrambling processing module: the method is particularly subdivided into a signal scrambling processing module and a signal inverse scrambling processing module, wherein the signal scrambling processing module is used for encrypting, and arnold transformation is adopted to perform the matrix of the three color channel components after the substitution And/>Scrambling to obtain three color channel component matrixes after scramblingAnd/>The signal inverse scrambling processing module is used for adopting arnold inverse transformation to encrypt three color channel component matrixes/>, of the image in the decryption processAnd/>Performing inverse scrambling processing and restoring to obtain a color channel component matrix/>And/>
Channel color component combining module: the method comprises the steps of dividing the image into an encrypted image component combination module and a decrypted image component combination module, wherein the encrypted image component combination module is used for combining three color channel component matrixes of an encrypted image in an encryption processAnd/>Generating an encrypted image; the decryption image component combination module is used for combining three color channel component matrixes/>, of the decryption image in the decryption process And/>And (3) recombining and restoring to a color image.
Compared with the prior art, the invention has the beneficial effects that:
1. In the invention, the fuzzy logic item is introduced into the traditional inertial memristor neural network, compared with the traditional neural network model, the fuzzy logic item is introduced, so that the fuzzy logic item has the functions of qualitative analysis and reasoning of a fuzzy theory, processing natural language and the like, has strong learning capacity of the neural network, can better process the boundary problem of fuzzy data, and considers the interference of external disturbance to the model, so that the designed controller has strong robustness.
2. Compared with a reduced-order method, the method directly uses a non-reduced-order method to directly analyze the dynamic behavior of the second-order differential system, so that the obtained synchronization criterion is simpler and easier to understand.
3. In the invention, in order to synchronize the limited time of the response system with the driving system, an aperiodic intermittent adjustment synchronous controller is designed, and compared with a continuous feedback controller, the aperiodic intermittent adjustment synchronous controller can effectively reduce the control cost and the resource consumption.
4. The image encryption method based on the unknown disturbance inertial fuzzy neural network provided by the invention adopts two methods of replacement and scrambling at the same time, and compared with the traditional method, the encryption effect can be better improved, and the method has better effects in the aspects of noise resistance and statistical cracking.
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 according to the present invention;
FIG. 2 is a flow chart of the image encryption system of the present invention;
FIG. 3 is a trace map of drive system state x 1 (t) and response system state y 1 (t) without controller action;
FIG. 4 is a trace map of drive system state x 2 (t) and response system state y 2 (t) without controller action;
FIG. 5 is a graph of the variation of synchronization errors e 1 (t) and e 2 (t) without controller;
FIG. 6 is a graph of a trace of the drive system state x 1 (t) and the response system state y 1 (t) under the influence of an aperiodic intermittent mode synchronous controller;
FIG. 7 is a graph of trace contrast for drive system state x 2 (t) and responsive system state y 2 (t) under the influence of an aperiodic intermittent mode synchronous controller;
FIG. 8 is a graph of the variation of synchronization errors e 1 (t) and e 2 (t) under the influence of an aperiodic intermittently adjusting synchronization controller;
Fig. 9 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. 10 is a graph of adjacent pixels of an original image R color channel component and an encrypted image R color channel component, wherein (a) is a graph of adjacent pixels of the original image R color channel component in a horizontal direction, (b) is a graph of adjacent pixels of the original image R color channel component in a vertical direction, (c) is a graph of adjacent pixels of the original image R color channel component in a diagonal direction, (d) is a graph of adjacent pixels of the encrypted image R color channel component in a horizontal direction, (e) is a graph of adjacent pixels of the encrypted image R color channel component in a vertical direction, and (f) is a graph of adjacent pixels of the encrypted image R color channel component in a diagonal direction;
Fig. 11 is a graph of adjacent pixels of an original image G color channel component and an encrypted image G color channel component, wherein (a) is a graph of adjacent pixels of the original image G color channel component in a horizontal direction, (b) is a graph of adjacent pixels of the original image G color channel component in a vertical direction, (c) is a graph of adjacent pixels of the original image G color channel component in a diagonal direction, (d) is a graph of adjacent pixels of the encrypted image G color channel component in a horizontal direction, (e) is a graph of adjacent pixels of the encrypted image G color channel component in a vertical direction, and (f) is a graph of adjacent pixels of the encrypted image G color channel component in a diagonal direction;
fig. 12 is a neighboring pixel statistic diagram of an original image B color channel component and an encrypted image B color channel component, wherein (a) is a neighboring pixel statistic diagram of the original image B color channel component in the horizontal direction, (B) is a neighboring pixel statistic diagram of the original image B color channel component in the vertical direction, (c) is a neighboring pixel statistic diagram of the original image B color channel component in the diagonal direction, (d) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the horizontal direction, (e) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the vertical direction, and (f) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the diagonal direction.
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.
Example 1:
the embodiment provides an image encryption method and system based on an unknown disturbance inertial fuzzy neural network, wherein the image encryption and decryption process is shown in fig. 1. The image encryption method comprises the following steps:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unknown disturbance are constructed;
Step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing an aperiodic intermittent adjusting synchronous controller;
step S3: based on the response system, the driving system is synchronized with limited time under the action of the non-periodic intermittent adjustment synchronous controller, so that an image encryption method is realized.
In this embodiment, the step S1 specifically includes the following steps:
Step S11: the driving system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
step S12: the response system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
In step S11 and step S12, time t is not less than 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, x i (t) represents the state of the ith neuron of the driving system at the time t, and y i (t) represents the state of the ith neuron of the response system at the time t; a i denotes the damping coefficient of the ith neuron, b i denotes the rate at which the ith neuron resets its potential to a rest state when the network is disconnected from an external input, a i and b i satisfy a i >0 and b i>0;fj(xj (t), respectively), an activation function that the jth neuron of the drive system does not contain a time lag, f j(xj(t-τj (t)) denotes an activation function that the jth neuron of the drive system contains a time-varying discrete time lag, f j(yj (t)) denotes an activation function that the jth neuron of the response system does not contain a time lag, f j(yj(t-τj (t))) represents an activation function of a j-th neuron of the response system that contains a time-varying discrete time lag that is a discontinuous activation function and satisfies |f j(.)|≤Mj, where M j is a positive constant; τ j (t) and delta j (t) are time-varying discrete time lag and time-varying distributed time lag, respectively, and satisfy 0.ltoreq.τ j(t)≤τ,0≤δj (t.ltoreq.delta), wherein τ and delta are positive constants, and are set Η is an integral variable; z ij represents a feed-forward element; /(I)And q ij represents the elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules, respectively; h ij and ρ ij represent the elements of the minimum and maximum fuzzy feedback modules, respectively; m j (t) represents the input of the jth neuron; Λ and V represent fuzzy and fuzzy or operators respectively, satisfying the following conditions: /(I)
And/>Unknown disturbances in the drive system and the response system, respectively, satisfy/> Wherein σ i is a positive constant; u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x i(s)＝φi (s)/> cij(xi(t))、dij(xi(t))、wij(xi(t))、cij(yi(t))、dij(yi(t))、wij(yi(t)) The memristor connection weights are expressed, and respectively satisfy:
Wherein Γ i is a switching threshold and Γ i >0; Are all constant;
Since the right side of the equal sign of the driving system and the response system is discontinuous, the solutions of the driving system and the response system need to be considered in the Filippov sense, and then the driving system and the response system are respectively rewritten as follows by adopting the set value mapping and the differential inclusion theory:
/>
In the method, in the process of the invention, And/>Satisfy/> AndSatisfy/> Χ j and iota j are constants ;K[cij(xi(t))]、K[dij(xi(t))]、K[wij(xi(t))]、K[cij(yi(t))]、K[dij(yi(t))]、K[wij(yi(t))]、K[fj(xj(t))]、K[fj(yj(t))]、K[fj(xj(t-τj(t)))] and K [ f j(yj(t-τj (t))) respectively: /(I)
Wherein,
In this embodiment, the step S2 specifically includes the following steps:
Step S21: the synchronization error of the driving system and the response system is set as follows:
ei(t)＝yi(t)-xi(t)
Step S22: according to the synchronization error between the driving system and the response system set in step S21, the non-periodic intermittent adjustment synchronization controller is designed to:
Where k is the number of control cycles, i.e., k=0, 1,2, …; t k is the start-up time of the first subinterval controller in the kth period, s k represents the start-up time of the second subinterval controller in the kth period, and t k and s k are required to satisfy: Omega and/> Is constant and meetsΖ i、εi、θi、∈i、λ1i、λ2i is positive controller gain; l e (0, 1); /(I)Expressed as derivative of synchronization error/>Is a sign function of (2); e i(t-τi (t)) represents the synchronization error of the state variable of the driving system i-th neuron comprising a time-varying discrete time lag and the state variable of the response system i-th neuron comprising a time-varying discrete time lag, and the controller gain ζ i、εi、θi、∈i、λ1i、λ2i satisfies the following inequality: /(I)
ζi≧1-ai
Wherein ψ is a constant and E represents a natural constant e; /(I)
And enabling the non-periodic intermittent adjustment synchronous controller to act on the response system so that the response system is synchronous with the driving system for a limited time.
In the present embodiment, ifThe upper bound of the finite timeIf/>The upper bound t=t 1,T1 of the finite time is In the middle of the smaller solution.
In this embodiment, step S3: based on the response system, the driving system is synchronized for a limited time under the action of the non-periodic intermittent adjustment synchronous controller, so that the image encryption and decryption are realized, and the method comprises the following specific implementation steps:
The encryption process comprises the following steps:
step S31: reading unencrypted color image, image size Extracting the red channel component matrix/>, of an unencrypted color imageGreen channel component matrix/>And blue channel component matrixWherein/>And/>The value ranges are all one value in (0, 1, …, 255);
Step S32: after the driving system and the response system reach limited time synchronization, three chaotic signal sequences are selected according to discrete time sequence chaotic signals x i (t) of the driving system And
Step S33: three chaotic signal sequences obtained in the step S32And/>After specific conversion, three new signal sequences/>, are obtainedAnd/> Wherein/>And/>The value ranges are all one value in (0, 1, …, 255); the specific conversion formula used in step S33 is: /(I)
Step S34: three new signal sequences obtained in step S33And/>Three color channel component matrices/>, respectively with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes/>, and obtaining three color channel component matrixes/>, wherein the three color channel component matrixes/>, the three color channel component matrixes are replaced by the three color channel component matrixes/>, and the three color channel component matrixes/> areobtained by the three color channel component matrixesAnd
Step S35: the arnold transformation is adopted to replace the three color channel component matrixes And/>Scrambling to obtain a scrambled three-color channel component matrix/>AndThe arnold transform algorithm is:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S36: the three color channel component matrices after being scrambled in step S35 AndAs three color channel component matrixes of the encrypted image, combining the color component matrixes 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 channel component matrixes of the encrypted image And/>Wherein the method comprises the steps ofAnd/>The value ranges are all one value in (0, 1, …, 255);
Step S38: three color channel component matrices for encrypted images using arnold inverse transforms And/>Performing inverse scrambling treatment and restoring to obtain three color channel component matrixesAnd/>The arnold inversion algorithm is as follows:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S39: after the driving system and the response system reach the limited time synchronization, selecting and in step S32 according to the discrete time sequence chaotic signal y i (t) of the response system And/>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/>The value ranges are all one 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 And/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive or operation on the corresponding position elements of the image to obtain three color channel component matrixes/>, of the decrypted image, wherein the three color channel component matrixes/>, of the decrypted image are obtained through decryptionAnd
Step S312: three color channel component matrices of the decrypted image obtained in step S311 areAnd/>And (5) recombining to obtain a decrypted image.
In addition, the invention provides an inertial fuzzy neural network image encryption system based on unknown disturbance, the flow of the image encryption system is shown in figure 2, and the image encryption system comprises:
the chaotic signal acquisition module is used for: the method comprises the steps of establishing a driving system and a response system based on an inertial memristor fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjustment synchronous controller so that the driving system and the response system are synchronous in a limited time; after the driving system and the response system are synchronous, the chaotic signal acquisition module selects three chaotic signal sequences according to the discrete time sequence chaotic signal x i (t) of the driving system And/>The chaotic signal acquisition module selects and/>, according to the discrete time sequence chaotic signal y i (t) of the response systemAndCorresponding chaotic signal sequence/>And/>
The chaotic signal processing module: the system is particularly subdivided into a driving system chaotic signal processing module and a response system chaotic signal processing module, wherein the driving system chaotic signal processing module is used for sequencing a chaotic signal AndAfter specific conversion, three new signal sequences/> And/>The response system chaotic signal processing module is used for converting the chaotic signal sequence/> And/>After specific conversion, three new signal sequences/>And/>Wherein the method comprises the steps ofAnd/>The value ranges are all one value in (0, 1, …, 255);
Channel color component extraction module: the method comprises the steps of specifically subdividing an unencrypted color image component extraction module and an encrypted image component extraction module; the unencrypted color image component extraction module is used for reading an unencrypted color image in the encryption process and extracting a red channel component matrix of the color image Green channel component matrix/>And blue channel component matrix/>The encryption image component extraction module is used for reading the encryption image in the decryption process and extracting three color channel component matrixes/>, of the encryption image And/>
A signal replacement processing module: in the encryption process, three new signal sequences obtained in step S33 are used forAnd/>Three color channel components respectively associated with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the table; in the decryption process, three new signal sequences/>, obtained in step S310, are obtainedAnd/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive OR operation on the corresponding position elements in the table;
the signal scrambling processing module: the method is particularly subdivided into a signal scrambling processing module and a signal inverse scrambling processing module, wherein the signal scrambling processing module is used for encrypting, and arnold transformation is adopted to perform the matrix of the three color channel components after the substitution And/>Scrambling to obtain three color channel component matrixes after scramblingAnd/>The signal inverse scrambling processing module is used for adopting arnold inverse transformation to encrypt three color channel component matrixes/>, of the image in the decryption processAnd/>Performing inverse scrambling processing and restoring to obtain a color channel component matrix/>And/>
Channel color component combining module: the method comprises the steps of dividing the image into an encrypted image component combination module and a decrypted image component combination module, wherein the encrypted image component combination module is used for combining three color channel component matrixes of an encrypted image in an encryption processAnd/>Generating an encrypted image; the decryption image component combination module is used for combining three color channel component matrixes/>, of the decryption image in the decryption process And/>And (3) recombining and restoring to a color image.
It is worth noting that the fuzzy logic item is introduced into the traditional inertial memristor neural network, compared with the traditional neural network model, the fuzzy logic item is introduced, so that the fuzzy logic item has the functions of qualitative analysis and reasoning of a fuzzy theory, processing natural language and the like, has the strong learning ability of the neural network, can better process the boundary problem of fuzzy data, and in order to enable the response system to be in time synchronization with the driving system in a limited way and consider the interference of external disturbance to the model, an aperiodic intermittent adjustment synchronous controller is designed, and compared with a continuous feedback controller, the controller can effectively reduce the control cost and resource consumption and has strong robustness. The image encryption method based on the unknown disturbance inertial fuzzy neural network combines the replacement and scrambling in the image encryption, thereby obtaining better encryption effect and having more effects in the aspects of noise resistance and statistical cracking.
Example 2:
the embodiment mainly comprises two parts of contents:
one is to carry out theoretical demonstration on the effectiveness of the non-periodic intermittent adjustment synchronous controller designed in the finite time synchronous control method of the inertial memristor fuzzy neural network with unknown disturbance, which is proposed in the embodiment 1.
Secondly, aiming at the inertia memristor fuzzy neural network with unknown disturbance in the embodiment 1 by a numerical simulation method, whether a constructed driving system and a response system achieve limited time synchronization or not, and whether an image encryption method is effective or not.
(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
Defining a synchronization error between the drive system and the response system as: e i(t)＝yi(t)-xi (t), the synchronization error system available from the drive system and the response system is as follows:
Wherein,
The quotation that will be adopted in the certification process is given below:
Lemma 1: assume that The above is a continuous, non-negative function and satisfies the following condition:
Where k=0, 1,2, …, α >0, β >0,0< η <1, if the constant ψ e (0, 1) is present, the following inequality holds:
Wherein the upper bound T of the finite time has the value:
If it is If/>T=t 1,T1 is/>In the middle of the smaller solution.
And (4) lemma 2: let alpha 1,α2,…,αn be a normal number and 0<r 1 be 1 or less
Next, the lyapunov functional is constructed:
The established lyapunov functional is then solved for the dily derivative:
When t is E [ t k,sk ]
/>
Again because the controller gain ζ i、εi、θi、∈i satisfies the following four inequalities:
ζi≧1-ai
/>
Then it is further possible to obtain:
Wherein,
Then according to lemma 2, since l E (0, 1), we can get
Similarly, when t is E (s k,tk+1)
Wherein,
According to lemma 1, then we can get:
if/> Upper bound/>, of finite time If/>The upper bound of finite time t=t 1,T1 isIn the middle of the smaller solution. /(I)
2. Numerical simulation
In this embodiment, taking an inertial memristor fuzzy neural network containing two neurons as an example, the driving system is determined as follows:
the response system corresponding to the driving system is as follows:
wherein ,t≥0,i＝1,2;f1(x1(t))＝tanh(x1(t))+0.031*sign(x1(t))、f2(x2(t))＝tanh(x2(t))+0.031*sign(x2(t))、f1(x1(t-τ1(t)))＝tanh(x1(t-τ1(t)))+0.031*sign(x1(t-τ1(t)))、f2(x2(t-τ2(t)))＝tanh(x2(t-τ2(t)))+0.031*sign(x2(t-τ2(t)))、f1(y1(t))＝tanh(y1(t))+0.031*sign(y1(t))、f2(y2(t))＝tanh(y2(t))+0.031*sign(y2(t))、f1(y1(t-τ1(t)))＝tanh(y1(t-τ1(t)))+0.031*sign(y1(t-τ1(t)))、f2(y2(t-τ2(t)))＝tanh(y2(t-τ2(t)))+0.031*sign(y2(t-τ2(t))); constant χ1＝χ2＝1,ι1＝ι2＝0.062,M1＝M2＝1.031;a1＝a2＝0.55,b1＝b2＝2.2; Τ=δ=1, then/>z11＝z21＝-1,z12＝z22＝1,m1(t)＝m2(t)＝1，/>q11＝q12＝-1,q21＝q22＝1,h11＝h22＝0.1,h12＝h21＝-0.1,ρ11＝ρ22＝0.2,ρ12＝ρ21＝-0.2; External unknown disturbance Σ 1＝0.025,σ2 =0.02; memristor connection weights are selected as:
According to the above parameter settings, the inequality ζ i≧1-ai, And/> If the values of the non-periodic intermittent adjustment synchronous controller parameters are ：ζ1≧0.45、ζ2≧0.45、ε1≧3.8、ε2≧4.8、θ1≧4.6、θ2≧4.1、∈1≧3.6303、∈2≧3.9869,, the values of the non-periodic intermittent adjustment synchronous controller parameters can be ：ζ1＝ζ2＝1、ε1＝4、ε2＝5、θ1＝5、θ2＝4.5、∈1＝∈2＝4;, the values of the other non-periodic intermittent adjustment synchronous controller parameters are λ 11＝λ12＝λ21＝λ22 =4, l=0.6, and the non-periodic intermittent adjustment control time sequence is as follows: /(I) It can be known that ψ=0.1.
And the driving system, the response system and the non-periodic intermittent adjustment synchronous controller carry out numerical simulation experiments on the driving system, the response system and the non-periodic intermittent adjustment synchronous controller under the set parameters. The initial values of the drive system and the response system are set as follows: x 1(s)＝-0.1,x2(s)＝0.12,y1(s)＝0.2,y2(s) = -0.2, s e [ -1,0], according to the above parameter setting, the upper bound t=t 1 ≡12.31 of finite time can be calculated, and the specific simulation experiment results are as follows: FIG. 3 is a trace map of drive system state x 1 (t) and response system state y 1 (t) without controller action; FIG. 4 is a trace map of drive system state x 2 (t) and response system state y 2 (t) without controller action; FIG. 5 is a graph of the variation of synchronization errors e 1 (t) and e 2 (t) without controller; FIG. 6 is a graph of a trace of the drive system state x 1 (t) and the response system state y 1 (t) under the influence of an aperiodic intermittent mode synchronous controller; FIG. 7 is a graph of trace contrast for drive system state x 2 (t) and responsive system state y 2 (t) under the influence of an aperiodic intermittent mode synchronous controller; FIG. 8 is a graph of the variation of synchronization errors e 1 (t) and e 2 (t) under the influence of an aperiodic intermittently adjusting synchronization controller; 3-5 show that the driving system and the response system cannot realize synchronization under the action of no controller; the traces of fig. 6-8 demonstrate that the response system is synchronized with the drive system within a finite time under the action of the aperiodic intermittent adjustment synchronization controller, verifying synchronization performance.
Based on the fact that the response system in the embodiment is synchronized with the driving system for a limited time under the action of the non-periodic intermittent adjustment synchronous controller, the image encryption and decryption are achieved, and the method comprises the following specific implementation steps:
The encryption process comprises the following steps:
Step S31: reading an unencrypted color image, as shown in fig. 9 (a), the image size is 256×256×3, and extracting a red channel component matrix of the unencrypted color image Green channel component matrix/>And blue channel component matrix/>P.epsilon. {1,2, …,256}, q.epsilon.1, 2, …,256}, where/>And/>The value ranges are all one value in (0, 1, …, 255);
Step S32: after the driving system and the response system reach limited time synchronization, three chaotic signal sequences are selected according to discrete time sequence chaotic signals x 1(t)、x2 (t) and 0.5 (x 1(t)+x2 (t)) of the driving system And/>p∈{1,2,…,256}，q∈{1,2,…,256}；
Step S33: three chaotic signal sequences obtained in the step S32And/>After specific conversion, three new signal sequences/>, are obtainedAnd/>P.epsilon. {1,2, …,256}, q.epsilon.1, 2, …,256}, where/>And/>The value ranges are all one value in (0, 1, …, 255); the specific conversion formula used in step S33 is:
step S34: three new signal sequences obtained in step S33 And/>Three color channel component matrices/>, respectively with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes/>, and obtaining three color channel component matrixes/>, wherein the three color channel component matrixes/>, the three color channel component matrixes are replaced by the three color channel component matrixes/>, and the three color channel component matrixes/> areobtained by the three color channel component matrixesAndp∈{1,2,…,256}，q∈{1,2,…,256}；
Step S35: the arnold transformation is adopted to replace the three color channel component matrixes And/>Scrambling to obtain a scrambled three-color channel component matrix/>AndP epsilon {1,2, …,256}, q epsilon {1,2, …,256}, the arnold transformation algorithm is:
where (xx, yy) is the original position of the pixel, Is the position of the scrambled pixels;
Step S36: the three color channel component matrices after being scrambled in step S35 AndAs the three color channel component matrices of the encrypted image, combining the color component matrices of the encrypted image to generate an encrypted image, as shown in (b) of fig. 9;
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 channel component matrices of the encrypted image as shown in fig. 9 (b) And/>P.epsilon.1, 2, …,256, q.epsilon.1, 2, …,256, whereAnd/>The value ranges are all one value in (0, 1, …, 255);
Step S38: three color channel component matrices for encrypted images using arnold inverse transforms And/>Performing inverse scrambling treatment and restoring to obtain three color channel component matrixesAnd/>P epsilon {1,2, …,256}, q epsilon {1,2, …,256}, the arnold inverse transform algorithm is:
where (xx, yy) is the original position of the pixel, Is the position of the scrambled pixels;
Step S39: after the driving system and the response system reach the limited time synchronization, selecting and comparing in step S32 according to the discrete time sequence chaotic signals y 1(t)、y2 (t) and 0.5 (y 1(t)+y2 (t)) of the response system And/>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.epsilon. {1,2, …,256}, q.epsilon.1, 2, …,256}, where/>And/>The value ranges are all one 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 And/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive or operation on the corresponding position elements of the image to obtain three color channel component matrixes/>, of the decrypted image, wherein the three color channel component matrixes/>, of the decrypted image are obtained through decryptionAndp∈{1,2,…,256}，q∈{1,2,…,256}；
Step S312: three color channel component matrices of the decrypted image obtained in step S311 areAnd/>The decrypted image is obtained by recombination, as shown in fig. 9 (c).
Fig. 9 shows the encryption effect in a visual sense; fig. 10 is a graph of adjacent pixels of an original image R color channel component and an encrypted image R color channel component, wherein (a) is a graph of adjacent pixels of the original image R color channel component in a horizontal direction, (b) is a graph of adjacent pixels of the original image R color channel component in a vertical direction, (c) is a graph of adjacent pixels of the original image R color channel component in a diagonal direction, (d) is a graph of adjacent pixels of the encrypted image R color channel component in a horizontal direction, (e) is a graph of adjacent pixels of the encrypted image R color channel component in a vertical direction, and (f) is a graph of adjacent pixels of the encrypted image R color channel component in a diagonal direction; fig. 11 is a graph of adjacent pixels of an original image G color channel component and an encrypted image G color channel component, wherein (a) is a graph of adjacent pixels of the original image G color channel component in a horizontal direction, (b) is a graph of adjacent pixels of the original image G color channel component in a vertical direction, (c) is a graph of adjacent pixels of the original image G color channel component in a diagonal direction, (d) is a graph of adjacent pixels of the encrypted image G color channel component in a horizontal direction, (e) is a graph of adjacent pixels of the encrypted image G color channel component in a vertical direction, and (f) is a graph of adjacent pixels of the encrypted image G color channel component in a diagonal direction; fig. 12 is a neighboring pixel statistic diagram of an original image B color channel component and an encrypted image B color channel component, wherein (a) is a neighboring pixel statistic diagram of the original image B color channel component in the horizontal direction, (B) is a neighboring pixel statistic diagram of the original image B color channel component in the vertical direction, (c) is a neighboring pixel statistic diagram of the original image B color channel component in the diagonal direction, (d) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the horizontal direction, (e) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the vertical direction, and (f) is a neighboring pixel statistic diagram of the encrypted image B color channel component in the diagonal direction. As can be seen from fig. 10, 11 and 12, the correlation between adjacent pixels of the original image which is not encrypted is strong, and the original image is easily attacked by statistical analysis, etc., and the encrypted image is different, and is uniformly distributed in horizontal, vertical or diagonal directions, which means that the encrypted image effectively masks the statistical characteristics of the image, thereby improving the security.
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 (3)
1. The image encryption method based on the unknown disturbance inertial fuzzy neural network is characterized by comprising the following steps of:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unknown disturbance are constructed, and the method specifically comprises the following steps:
Step S11: the driving system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
step S12: the response system for constructing the inertial memristor fuzzy neural network with unknown disturbance is as follows:
In step S11 and step S12, time t is not less than 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, x i (t) represents the state of the ith neuron of the driving system at the time t, and y i (t) represents the state of the ith neuron of the response system at the time t; a i denotes the damping coefficient of the ith neuron, b i denotes the rate at which the ith neuron resets its potential to a rest state when the network is disconnected from an external input, a i and b i satisfy a i >0 and b i>0;fj(xj (t), respectively), an activation function that the jth neuron of the drive system does not contain a time lag, f j(xj(t-τj (t)) denotes an activation function that the jth neuron of the drive system contains a time-varying discrete time lag, f j(yj (t)) denotes an activation function that the jth neuron of the response system does not contain a time lag, f j(yj(t-τj (t))) represents an activation function of a j-th neuron of the response system that contains a time-varying discrete time lag that is a discontinuous activation function and satisfies |f j(.)|≤Mj, where M j is a positive constant; τ j (t) and delta j (t) are time-varying discrete time lag and time-varying distributed time lag, respectively, and satisfy 0.ltoreq.τ j(t)≤τ,0≤δj (t.ltoreq.delta), wherein τ and delta are positive constants, and are set Η is an integral variable; z ij represents a feed-forward element; And q ij represents the elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules, respectively; h ij and ρ ij represent the elements of the minimum and maximum fuzzy feedback modules, respectively; m j (t) represents the input of the jth neuron; v and V respectively represent fuzzy and fuzzy or operators, and the following conditions are satisfied:
And/> Unknown disturbances in the drive system and the response system, respectively, satisfy/> Wherein σ i is a positive constant; u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x i(s)＝φi (s)/> cij(xi(t))、dij(xi(t))、wij(xi(t))、cij(yi(t))、dij(yi(t))、wij(yi(t)) The memristor connection weights are expressed, and respectively satisfy:
Wherein Γ i is a switching threshold and Γ i >0; Are all constant;
Since the right side of the equal sign of the driving system and the response system is discontinuous, the solutions of the driving system and the response system need to be considered in the Filippov sense, and then the driving system and the response system are respectively rewritten as follows by adopting the set value mapping and the differential inclusion theory:
In the method, in the process of the invention, And/>Satisfy/> AndSatisfy/>τj(t)))|≤χj|yj(t-τj(t))-xj(t-τj(t))|+ιj,χj And iota j is a constant ;K[cij(xi(t))]、K[dij(xi(t))]、K[wij(xi(t))]、K[cij(yi(t))]、K[dij(yi(t))]、K[wij(yi(t))]、K[fj(xj(t))]、K[fj(yj(t))]、K[fj(xj(t-τj(t)))] and K [ f j(yj(t-τj (t))) respectively:
Wherein,
Step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing an aperiodic intermittent adjusting synchronous controller;
Step S3: based on the response system, the drive system is synchronized with limited time under the action of the non-periodic intermittent adjustment synchronous controller, so that the image encryption and decryption are realized, and the method comprises the following specific implementation steps:
The encryption process comprises the following steps:
step S31: reading unencrypted color image, image size Extracting the red channel component matrix/>, of an unencrypted color imageGreen channel component matrix/>And blue channel component matrixWherein/>And/>The value ranges are all one value in (0, 1, …, 255);
Step S32: after the driving system and the response system reach limited time synchronization, three chaotic signal sequences are selected according to discrete time sequence chaotic signals x i (t) of the driving system And
Step S33: three chaotic signal sequences obtained in the step S32And/>After specific conversion, three new signal sequences/>, are obtainedAnd/> Wherein/>And/>The value ranges are all one value in (0, 1, …, 255); the specific conversion formula used in step S33 is:
step S34: three new signal sequences obtained in step S33 And/>Three color channel component matrices/>, respectively with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes/>, and obtaining three color channel component matrixes/>, wherein the three color channel component matrixes/>, the three color channel component matrixes are replaced by the three color channel component matrixes/>, and the three color channel component matrixes/> areobtained by the three color channel component matrixesAnd
Step S35: the arnold transformation is adopted to replace the three color channel component matrixes AndScrambling to obtain a scrambled three-color channel component matrix/>AndThe arnold transform algorithm is:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S36: the three color channel component matrices after being scrambled in step S35 AndAs three color channel component matrixes of the encrypted image, combining the color component matrixes 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 channel component matrixes of the encrypted image And/>Wherein/>AndThe value ranges are all one value in (0, 1, …, 255);
Step S38: three color channel component matrices for encrypted images using arnold inverse transforms And/>Performing inverse scrambling treatment and restoring to obtain three color channel component matrixesAnd/>The arnold inversion algorithm is as follows:
where (xx, yy) is the original position of the pixel, For the position after pixel scrambling,/>And/>Is a constant;
Step S39: after the driving system and the response system reach the limited time synchronization, selecting and in step S32 according to the discrete time sequence chaotic signal y i (t) of the response system And/>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/>The value ranges are all one 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 And/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive or operation on the corresponding position elements of the image to obtain three color channel component matrixes/>, of the decrypted image, wherein the three color channel component matrixes/>, of the decrypted image are obtained through decryptionAnd
Step S312: three color channel component matrices of the decrypted image obtained in step S311 areAnd/>Recombining to obtain a decrypted image;
the step S2 specifically comprises the following steps:
Step S21: the synchronization error of the driving system and the response system is set as follows:
ei(t)＝yi(t)-xi(t)
Step S22: according to the synchronization error between the driving system and the response system set in step S21, the non-periodic intermittent adjustment synchronization controller is designed to:
Where k is the number of control cycles, i.e., k=0, 1,2, …; t k is the start-up time of the first subinterval controller in the kth period, s k represents the start-up time of the second subinterval controller in the kth period, and t k and sk are required to satisfy: Omega and/> Is constant and meetsΖ i、εi、θi、∈i、λ1i、λ2i is positive controller gain; l e (0, 1); /(I)Expressed as derivative of synchronization error/>Is a sign function of (2); e i(t-τi (t)) represents the synchronization error of the state variable of the driving system i-th neuron comprising a time-varying discrete time lag and the state variable of the response system i-th neuron comprising a time-varying discrete time lag, and the controller gain ζ i、εi、θi、∈i、λ1i、λ2i satisfies the following inequality:
ζi≧1-ai
Wherein ψ is a constant and E represents a natural constant e; /(I)
And enabling the non-periodic intermittent adjustment synchronous controller to act on the response system so that the response system is synchronous with the driving system for a limited time.
2. The image encryption method based on unknown disturbance inertial fuzzy neural network of claim 1, wherein the response system is time-synchronized to the drive system with a finite time, and the upper bound T of the finite time is:
wherein T 1 is Is a smaller solution to that.
3. An image encryption system based on an unknown disturbance-based inertial fuzzy neural network applied to the method of claim 1, the image encryption system comprising:
the chaotic signal acquisition module is used for: the method comprises the steps of establishing a driving system and a response system based on an inertial memristor fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjustment synchronous controller so that the driving system and the response system are synchronous in a limited time; after the driving system and the response system are synchronous, the chaotic signal acquisition module selects three chaotic signal sequences according to the discrete time sequence chaotic signal x i (t) of the driving system And/>The chaotic signal acquisition module selects and/>, according to the discrete time sequence chaotic signal y i (t) of the response systemAnd/>Corresponding chaotic signal sequence/>And/>
The chaotic signal processing module: the system is particularly subdivided into a driving system chaotic signal processing module and a response system chaotic signal processing module, wherein the driving system chaotic signal processing module is used for sequencing a chaotic signal And/>After specific conversion, three new signal sequences/> And/>The response system chaotic signal processing module is used for converting the chaotic signal sequence/> And/>After specific conversion, three new signal sequences/>And/>Wherein/>And/>The value ranges are all one value in (0, 1, …, 255);
Channel color component extraction module: the method comprises the steps of specifically subdividing an unencrypted color image component extraction module and an encrypted image component extraction module; the unencrypted color image component extraction module is used for reading an unencrypted color image in the encryption process and extracting a red channel component matrix of the color image Green channel component matrix/>And blue channel component matrixThe encryption image component extraction module is used for reading the encryption image in the decryption process and extracting three color channel component matrixes/>, of the encryption image And/>
A signal replacement processing module: used in the encryption process for the three new signal sequences obtained in step S33And/>Three color channel components respectively associated with an unencrypted color imageAnd/>Performing exclusive OR operation on the corresponding position elements in the table; in the decryption process, three new signal sequences/>, obtained in step S310, are obtainedAnd/>Three color channel component matrices respectively reduced in step S38/>And/>Performing exclusive OR operation on the corresponding position elements in the table;
the signal scrambling processing module: the method is particularly subdivided into a signal scrambling processing module and a signal inverse scrambling processing module, wherein the signal scrambling processing module is used for encrypting, and arnold transformation is adopted to perform the matrix of the three color channel components after the substitution And/>Scrambling to obtain three color channel component matrixes after scramblingAnd/>The signal inverse scrambling processing module is used for adopting arnold inverse transformation to encrypt three color channel component matrixes/>, of the image in the decryption processAnd/>Performing inverse scrambling processing and restoring to obtain a color channel component matrix/>And/>
Channel color component combining module: the method comprises the steps of dividing the image into an encrypted image component combination module and a decrypted image component combination module, wherein the encrypted image component combination module is used for combining three color channel component matrixes of an encrypted image in an encryption processAnd/>Generating an encrypted image; the decryption image component combination module is used for combining three color channel component matrixes/>, of the decryption image in the decryption process And/>And (3) recombining and restoring to a color image.
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