CN117454394A - Image encryption method and system based on fuzzy neural network fixed time synchronization - 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 fixed time synchronization of a fuzzy neural network, wherein the image encryption method is based on the fuzzy neural network, and a driving system and a response system are established; setting a synchronization error, and designing a synchronization controller by adopting an aperiodic intermittent adjustment control strategy; the response system is synchronous with the driving system in a fixed time under the action of the synchronous controller, so that image encryption is realized. The invention solves the problem that the fuzzy neural network is difficult to realize fixed time synchronization, and provides a novel image encryption method and system, which remarkably improve the security of image encryption.
Description
Technical Field
The invention belongs to the technical field of new generation information, and particularly relates to an image encryption method and system based on fixed time synchronization of a fuzzy neural network.
Background
The human brain is composed of about 100 to 1000 hundred million neurons, a very large and complex system, and numerous scientists and researchers are desirous of exploring the complex neuronal activity mechanisms of the brain. In 1982, the us scientist Hopfield neural network was proposed, from which the neural network research is carried out, and many achievements are achieved in the aspects of image denoising, image encryption and safety communication by using the neural networks such as the recurrent neural network and the memristive neural network.
The fuzzy neural network introduces fuzzy logic based on the traditional neural network, and compared with other neural networks, the fuzzy neural network can be used for maintaining continuity between cells, and the fuzzy logic is added between the fuzzy input and the fuzzy output besides the sum of output operations, so that the fuzzy neural network is better in the aspect of image processing.
Compared with a periodic intermittent adjustment control strategy, the non-periodic intermittent adjustment control strategy overcomes the defect that a first subinterval and a second subinterval of periodic intermittent adjustment are fixed, and is more suitable for most phenomena in real life, such as wind energy and solar energy power generation, non-periodic starting of a heating system and the like, and has uncertainty.
With the development of networks, people increasingly use networks to store personal photos of themselves, and whether personal privacy photos are transmitted in an encrypted manner receives more attention. The invention uses the characteristics of random-like, non-periodic and unpredictable chaotic signals of the neural network to greatly improve the effectiveness of the image encryption method.
Disclosure of Invention
The invention aims to solve the problem that the fuzzy neural network is difficult to realize fixed time synchronization, and provides an image encryption method and an image encryption system based on the fixed time synchronization of the fuzzy neural network, so that the security of image encryption is improved.
In order to achieve the above purpose, the present invention provides the following technical solutions: the image encryption method based on the fuzzy neural network fixed time synchronization comprises the following steps:
step S1: based on the fuzzy neural network, a driving system and a response system are established; the specific contents of the step S1 are as follows:
the establishment of a driving system and a response system based on the fuzzy neural network is respectively as follows:
wherein, the time t is more than or equal to 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, and x i (t) represents the state of the ith neuron of the driving system at time t, y i (t) represents the state of the ith neuron of the response system at time t; a, a i Represents the damping coefficient of the ith neuron, b i Represents the rate at which the ith neuron resets its potential to a quiescent state, a, when the network is disconnected from external inputs i And b i Respectively satisfy a i >0 and b i >0；f j (x j (t)) represents a time-lapse free activation function of the jth neuron of the drive system, f j (x j (t-τ j (t))) an activation function representing a time-varying discrete time lag of a jth neuron of the drive system, f j (y j (t)) represents a time-lapse free activation function of the jth neuron of the response system, f j (y j (t-τ j (t)) representing an activation function of the j-th neuron of the response system comprising a time-varying discrete time lag, said activation function being a discontinuous activation function and satisfying |f j (.)|≤M j Wherein M is j Is a positive constant; τ j (t) and delta j (t) is time-varying discrete time lag and time-varying distributed time lag respectively, and satisfies 0.ltoreq.τ j (t)≤τ，0≤δ j (t) is less than or equal to delta, wherein tau and delta are positive constants and are setη is an integral variable; z ij Representing a feed-forward element; />And q ij Elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules are represented respectively; h is a ij And ρ ij Elements of the minimum fuzzy feedback and maximum fuzzy feedback modules are respectively represented; m is m j (t) and I i (t) represents the input of the jth neuron and the bias of the ith neuron, respectively; v and V respectively represent fuzzy and fuzzy or operators, and the following conditions are satisfied:
u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x is x i (s)＝φ i (s)，c ij (x i (t))、d ij (x i (t))、w ij (x i (t))、c ij (y i (t))、d ij (y i (t))、w ij (y i (t)) represents memristor connection weights, respectively satisfying:
wherein Γ is 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, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
wherein, kc ij (x i (t))]、K[d ij (x i (t))]、K[w ij (x i (t))]、K[c ij (y i (t))]、K[d ij (y i (t))]、K[w ij (y i (t))]、K[f j (x j (t))]、K[f j (y j (t))]、K[f j (x j (t-τ j (t)))]And K [ f ] j (y j (t-τ j (t))) satisfy respectively:
Wherein,
according to the measurable choice theorem, there is And-> Then it is further possible to obtain:
wherein:and->Satisfy-> And->Satisfy-> χ j And iota (iota) j Is a constant;
step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing a synchronous controller;
step S3: based on the response system, under the action of the synchronous controller, the fixed time is synchronous with the driving system, so that the image encryption and decryption are realized, and the specific implementation steps are as follows:
the encryption process comprises the following steps:
step S31: original color image is read, image sizeExtracting red channel component matrix of original color image>Green channel component matrix->And blue channel component matrixWherein->And->The value ranges are all one value of (0, 1, …, 255);
step S32: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal x of the driving system i (t) selecting three chaotic signal sequencesAnd
step S33: three chaotic signal sequences obtained in the step S32And->After specific transformation, three new signal sequences are obtained +.>And-> Wherein->And->The value ranges are all one value of (0, 1, …, 255); the specific conversion formula used in step S33 is:
Step S34: three new signal sequences obtained in step S33And->Three color channel component matrices, each associated with an unencrypted color image> And->Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes after substitution to obtain +.>And->
Step S35: using the arnold variantThe three color channel component matrixes after the pair-changing and replacing And->Scrambling operation is carried out to obtain a scrambled three-color channel component matrixAnd->The arnold transformation algorithm is:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling;
step S36: the three color channel component matrices after being scrambled in step S35 And->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-> And->The value ranges are all one value of (0, 1, …, 255);
step S38: three color channel component matrices for encrypted images using inverse Arnold transformAnd->Performing inverse scrambling operation and recovering to obtain three color channel component matrixes And->The arnold inverse transformation algorithm is as follows:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling;
step S39: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal y of the response system i (t) selecting and in step S32And->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 as follows:
step S311: three new signal sequences obtained in step S310And->Three color channel component matrices restored in step S38, respectively>And->Exclusive or operation is carried out on the corresponding position elements of the decryption image to obtain three color channel component matrixes of the decryption imageAnd->
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:
e i (t)＝y i (t)-x i (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 is t k Starting working time s of the first subinterval controller in the kth period k Indicating the starting working time of the second subinterval controller in the kth period, t k Sum s k The requirements are as follows:omega and->Is constant and meetsε i 、θ i 、∈ i 、λ 1i 、λ 2i 、λ 3i 、λ 4i A positive controller gain; 0<l<1，γ>1；Derivative expressed as synchronization error ∈ ->Is a sign function of (2); e, e i (t-τ i (t)) represents the time when the ith neuron of the driving system is involvedA synchronization error of a state variable of varying discrete time lag and a state variable of varying discrete time lag contained in an ith neuron of the response system, and a controller gain +.>ε i 、θ i 、∈ i The following inequality is satisfied:
wherein,
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 at a fixed time.
Further, the response system is synchronized with the driving system at a fixed time, and an upper bound T of the fixed time is:
wherein ψ is a constant and
in a second aspect of the present invention, an image encryption system based on fixed time synchronization of a fuzzy neural network is provided, the image encryption system comprising:
Discrete time sequence chaotic signal acquisition module: the method is used for establishing a driving system and a response system based on a fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjusting synchronous controller so that the driving system and the response system are synchronous at a fixed time; after the driving system and the response system are synchronous, a driving system chaotic signal acquisition module acquires a discrete time sequence chaotic signal x according to the driving system i (t) selecting three chaotic signal sequencesAnd->The response system chaotic signal acquisition module acquires a discrete time sequence chaotic signal y according to the response system i (t) select and->And->Corresponding chaotic signal sequence->And->
The driving system chaotic signal conversion operation module: for sequencing chaotic signalsAndafter specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofAnd->The value ranges are all one value of (0, 1, …, 255);
and the response system chaotic signal conversion operation module: for sequencing chaotic signalsAndafter specific conversion, three new signal sequences are obtained>Wherein the method comprises the steps ofThe value ranges are all one value of (0, 1, …, 255);
the original color image component reading and extracting operation module comprises the following steps: used in the encryption process for reading the original color image and extracting the red component matrix of the original color image Green component matrix->And blue component matrix
The encrypted image component reading and extracting operation module comprises: in the decryption process, the method is used for reading the encrypted image and extracting three color channel component matrixes of the encrypted image
Signal replacement operation module: for use in encrypting a signal sequenceAndthree color component matrices respectively corresponding to the original color image>And->Performing exclusive OR operation on the corresponding position elements in the table; for inserting the signal sequence during decryption>Andrespectively with the reduced three color channel component matrices +.> And->Corresponding position element of (a) is performedExclusive-or operation;
signal scrambling operation module: used in encryption process, three color component matrixes after being replaced by arold transformationAnd->Scrambling operation is carried out to obtain a scrambled three-color channel component matrix +.>And->
The signal reverse scrambling operation module is as follows: three color channel component matrices for encrypted images using inverse Arnold transform for decryptionAnd->Performing inverse scrambling operation, and recovering to obtain color channel component matrix +.>And->
An encrypted image component combination operation module: three color channel component matrixes for combining encrypted images in encryption process And->Generating an encrypted image;
decrypting image componentsAnd the combined operation module is as follows: in the decryption process, three color channel component matrixes for combining decrypted imagesAnd (3) recombining and restoring to a color image.
Compared with the prior art, the invention has the beneficial effects that:
1. in the invention, in order to synchronize the response system with the driving system at a fixed time, an aperiodic intermittent adjustment synchronous controller is designed, and compared with the periodic intermittent adjustment synchronous controller, the controller effectively eliminates the defects and limitations of the periodic intermittent adjustment strategy.
2. In the invention, the synchronous control problem is analyzed directly by using a non-reduced-order method, so that the obtained synchronous criterion is more in line with the actual situation.
3. Compared with the limited time synchronous control method, the fixed time synchronous control method provided by the invention can effectively obtain the synchronous time of the system, does not depend on the initial condition of the system, and is more universal.
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 shows the state x of the drive system without the controller 1 (t) and responsive System status y 1 A trace map of (t);
FIG. 4 shows the state x of the drive system without the controller 2 (t) and responsive System status y 2 A trace map of (t);
FIG. 5 shows the synchronization error e without the controller 1 (t) and e 2 A variation trace map of (t);
FIG. 6 shows the state x of the drive system under the action of the synchronous controller 1 (t) and responsive System status y 1 A trace map of (t);
FIG. 7 shows the state x of the drive system under the action of the synchronous controller 2 (t) and responsive System status y 2 A trace map of (t);
FIG. 8 shows the synchronization error e under the action of the synchronization controller 1 (t) and e 2 A variation trace map of (t);
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 fixed time synchronization of a 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 fuzzy neural network, a driving system and a response system are established; the specific contents of the step S1 are as follows:
the establishment of a driving system and a response system based on the fuzzy neural network is respectively as follows:
wherein, the time t is more than or equal to 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, and x i (t) represents the state of the ith neuron of the driving system at time t, y i (t) represents the state of the ith neuron of the response system at time t; a, a i Represents the damping coefficient of the ith neuron, b i Represents the rate at which the ith neuron resets its potential to a quiescent state, a, when the network is disconnected from external inputs i And b i Respectively satisfy a i >0 and b i >0；f j (x j (t)) represents a time-lapse free activation function of the jth neuron of the drive system, f j (x j (t-τ j (t))) represents the jth neuron timing of the drive systemAn activation function of varying discrete time lags, f j (y j (t)) represents a time-lapse free activation function of the jth neuron of the response system, f j (y j (t-τ j (t)) representing an activation function of the j-th neuron of the response system comprising a time-varying discrete time lag, said activation function being a discontinuous activation function and satisfying |f j (.)|≤M j Wherein M is j Is a positive constant; τ j (t) and delta j (t) is time-varying discrete time lag and time-varying distributed time lag respectively, and satisfies 0.ltoreq.τ j (t)≤τ，0≤δ j (t) is less than or equal to delta, wherein tau and delta are positive constants and are setη is an integral variable; z ij Representing a feed-forward element; />And q ij Elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules are represented respectively; h is a ij And ρ ij Elements of the minimum fuzzy feedback and maximum fuzzy feedback modules are respectively represented; m is m j (t) and I i (t) represents the input of the jth neuron and the bias of the ith neuron, respectively; v and V respectively represent fuzzy and fuzzy or operators, and the following conditions are satisfied:
u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x is x i (s)＝φ i (s)，c ij (x i (t))、d ij (x i (t))、w ij (x i (t))、c ij (y i (t))、d ij (y i (t))、w ij (y i (t)) represents memristor connection weights, respectively satisfying:
wherein Γ is 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, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
wherein, kc ij (x i (t))]、K[d ij (x i (t))]、K[w ij (x i (t))]、K[c ij (y i (t))]、K[d ij (y i (t))]、K[w ij (y i (t))]、K[f j (x j (t))]、K[f j (y j (t))]、K[f j (x j (t-τ j (t)))]And K [ f ] j (y j (t-τ j (t)))]The following respectively satisfy:
wherein,
according to the measurable choice theorem, there is And-> Then it is further possible to obtain:
/>
wherein:and->Satisfy-> And->Satisfy-> χ j And iota (iota) j Is a constant;
step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing a synchronous controller;
step S3: based on the response system, under the action of the synchronous controller, the fixed time is synchronous with the driving system, and then the image encryption method is realized.
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:
e i (t)＝y i (t)-x i (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 is t k Starting working time s of the first subinterval controller in the kth period k Indicating the starting working time of the second subinterval controller in the kth period, t k Sum s k The requirements are as follows:omega and->Is constant and meetsε i 、θ i 、∈ i 、λ 1i 、λ 2i 、λ 3i 、λ 4i Controller increment to positiveBenefit is provided; 0<l<1，γ>1；Derivative expressed as synchronization error ∈ ->Is a sign function of (2); e, e i (t-τ i (t)) representing a synchronization error of a state variable of the driving system i-th neuron comprising a time-varying discrete time lag and a state variable of the response system i-th neuron comprising a time-varying discrete time lag, and a controller gain>ε i 、θ i 、∈ i The following inequality is satisfied: />
Wherein,
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 at a fixed time.
In the present embodiment, the upper bound of the fixed timeWherein ψ is a constant and +.>
In this embodiment, step S3: based on the response system, the drive system is synchronized with fixed time under the action of the synchronous controller, and further image encryption and decryption are realized, and the method comprises the following specific implementation steps:
the encryption process comprises the following steps:
step S31: original color image is read, image sizeExtracting red channel component matrix of original color image>Green channel component matrix->And blue channel component matrixWherein- >And->The value ranges are all one value of (0, 1, …, 255);
step S32: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal x of the driving system i (t) selecting three chaotic signal sequencesAnd
step S33: three chaotic signal sequences obtained in the step S32And->After specific transformation, three new signal sequences are obtained +.>And-> Wherein->And->The value ranges are all one value of (0, 1, …, 255); the specific conversion formula used in step S33 is:
step S34: three new signal sequences obtained in step S33And->Three color channel component matrices, each associated with an unencrypted color image> And->Performing exclusive OR operation on the corresponding position elements in the three color channels after replacementChannel component matrix->And
step S35: the three color channel component matrixes after the replacement are subjected to the arold transformation And->Scrambling operation is carried out to obtain a scrambled three-color channel component matrixAnd->The arnold transformation algorithm is:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling; step S36: the three color channel component matrices after the scrambling in step S35 are +. > And->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-> And->The value ranges are all one value of (0, 1, …, 255);
step S38: three color channel component matrices for encrypted images using inverse Arnold transformAnd->Performing inverse scrambling operation and recovering to obtain three color channel component matrixesAnd->The arnold inverse transformation algorithm is as follows:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling;
step S39: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal y of the response system i (t) selecting and in step S32And->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 as follows:
/>
Step S311: three new signal sequences obtained in step S310And->Three color channel component matrices restored in step S38, respectively>And->Exclusive or operation is carried out on the corresponding position elements of the decryption image to obtain three color channel component matrixes of the decryption imageAnd->
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 image encryption system based on fixed time synchronization of a fuzzy neural network, the flow of the image encryption system is shown in figure 2, and the image encryption system comprises:
discrete time sequence chaotic signal acquisition module: the method is used for establishing a driving system and a response system based on a fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjusting synchronous controller so that the driving system and the response system are synchronous at a fixed time; after the driving system and the response system are synchronous, a driving system chaotic signal acquisition module acquires a discrete time sequence chaotic signal x according to the driving system i (t) selecting three chaotic signal sequencesAnd->The response system chaotic signal acquisition module acquires a discrete time sequence chaotic signal y according to the response system i (t) select and->And->Corresponding chaotic signal sequence->And->
The driving system chaotic signal conversion operation module: for sequencing chaotic signalsAndafter specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofAnd->The value ranges are all one value of (0, 1, …, 255);
and the response system chaotic signal conversion operation module: for sequencing chaotic signalsAndafter specific conversion, three new signal sequences are obtained>Wherein the method comprises the steps ofThe value ranges are all one value of (0, 1, …, 255);
original color image component readingAnd the extraction operation module is as follows: used in the encryption process for reading the original color image and extracting the red component matrix of the original color imageGreen component matrix->And blue component matrix
The encrypted image component reading and extracting operation module comprises: in the decryption process, the method is used for reading the encrypted image and extracting three color channel component matrixes of the encrypted image
Signal replacement operation module: for use in encrypting a signal sequenceAndthree color component matrices respectively corresponding to the original color image>And->Performing exclusive OR operation on the corresponding position elements in the table; for inserting the signal sequence during decryption>Andrespectively with the reduced three color channel component matrices +. > And->Performing exclusive OR operation on the corresponding position elements in the table;
signal scrambling operation module: used in encryption process, three color component matrixes after being replaced by arold transformationAnd->Scrambling operation is carried out to obtain a scrambled three-color channel component matrix +.>And->
The signal reverse scrambling operation module is as follows: three color channel component matrices for encrypted images using inverse Arnold transform for decryptionAnd->Performing inverse scrambling operation, and recovering to obtain color channel component matrix +.>And->
An encrypted image component combination operation module: for use in encryption processesThree color channel component matrices for combined encrypted imagesAnd->Generating an encrypted image;
a decrypted image component combining operation module: in the decryption process, three color channel component matrixes for combining decrypted imagesAnd (3) recombining and restoring to a color image.
It is worth noting that, in order to synchronize the response system with the driving system at a fixed time, the invention designs an aperiodic intermittent adjustment synchronous controller, which effectively eliminates the defects and limitations of the periodic intermittent adjustment strategy compared with the periodic intermittent adjustment synchronous controller. And analyzing the synchronous control problem directly by using a non-reduced-order method, so that the obtained synchronous criterion is more in line with the actual situation. Compared with the limited time synchronization control method, the fixed time synchronization control method provided by the invention can effectively obtain the synchronization time of the system, is independent of the initial condition of the system, and is more universal. The image encryption method based on the fuzzy neural network fixed time synchronization 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 fixed time synchronous control method of the fuzzy neural network proposed in the embodiment 1.
Secondly, the method of numerical simulation is directed to whether the driving system and the response system constructed according to the fuzzy neural network in the embodiment 1 achieve fixed time synchronization or not, and whether the 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, e i (t)＝y i (t)-x i (t) the synchronization error system available from the drive system and the response system is as follows:
the quotation that will be adopted in the certification process is given below:
lemma 1: let V (t) be atThe above is a continuous, non-negative function and satisfies the following condition: />
Wherein, t is [0, ++ infinity), t 0 ＝0，k＝0,1,2,…，α>0，β>0，0<l<1，γ>1, if whenV (t) ≡0, where ≡>
And (4) lemma 2: let alpha be 1 ,α 2 ,…,α n Is a normal number and 0<r 1 ≤1，r 2 >1, then
Next, the lyapunov functional is constructed:
The established lyapunov functional is then solved for the dily derivative:
when t is E [ t ] k ,s k ) Time of day
/>
And because of the controller gainε i 、θ i 、∈ i The following four inequalities are satisfied:
/>
then it is further possible to obtain:
wherein the method comprises the steps of，
Then according to lemma 2, since l.epsilon. (0, 1), γ >1 can be obtained
Similarly, when t is E s k ,t k+1 ) Time of day
According to lemma 1, then we can get: when (when)V (t) ≡0.
2. Numerical simulation
In this embodiment, taking a fuzzy neural network containing two neurons as an example, the driving system is determined as:
the response system corresponding to the driving system is as follows:
wherein t is greater than or equal to 0, i=1, 2; f (f) 1 (x 1 (t))＝tanh(x 1 (t))+0.031*sign(x 1 (t))、f 2 (x 2 (t))＝tanh(x 2 (t))+0.031*sign(x 2 (t))、f 1 (x 1 (t-τ 1 (t)))＝tanh(x 1 (t-τ 1 (t)))+0.031*sign(x 1 (t-τ 1 (t)))、f 2 (x 2 (t-τ 2 (t)))＝tanh(x 2 (t-τ 2 (t)))+0.031*sign(x 2 (t-τ 2 (t)))、f 1 (y 1 (t))＝tanh(y 1 (t))+0.031*sign(y 1 (t))、f 2 (y 2 (t))＝tanh(y 2 (t))+0.031*sign(y 2 (t))、f 1 (y 1 (t-τ 1 (t)))＝tanh(y 1 (t-τ 1 (t)))+0.031*sign(y 1 (t-τ 1 (t)))、f 2 (y 2 (t-τ 2 (t)))＝tanh(y 2 (t-τ 2 (t)))+0.031*sign(y 2 (t-τ 2 (t)); constant χ 1 ＝χ 2 ＝1，ι 1 ＝ι 2 ＝0.062，M 1 ＝M 2 ＝1.031；a 1 ＝a 2 ＝0.55，b 1 ＝b 2 ＝2.2；τ=δ=1, then +.>z 11 ＝z 21 ＝-1，z 12 ＝z 22 ＝1，m 1 (t)＝m 2 (t)＝1，/> q 11 ＝q 12 ＝-1，q 21 ＝q 22 ＝1，h 11 ＝h 22 ＝0.1，h 12 ＝h 21 ＝-0.1，ρ 11 ＝ρ 22 ＝0.2，ρ 12 ＝ρ 21 ＝-0.2；I 1 (t)＝I 2 (t) =0; memristor connection weights are selected as: />
According to the above parameter settings, and inequality And-> The parameter value ranges of the non-periodic intermittent adjustment synchronous controller are respectively as follows: /> ε 1 ≧4.2、ε 2 ≧5.2、θ 1 ≧4.8、θ 2 ≧4.2、∈ 1 ≧3.9456、∈ 2 If ∈ 3.9332, the non-periodic intermittent adjustment synchronization controller parameter may take the following values: />ε 1 ＝4.5、ε 2 ＝5.5、θ 1 ＝5、θ 2 ＝4.5、∈ 1 ＝∈ 2 =4; other non-periodic intermittent adjustment synchronous controller parameters take value lambda 11 ＝λ 12 ＝λ 21 ＝λ 22 ＝4，λ 31 ＝λ 32 ＝λ 41 ＝λ 42 =1, l=0.6, γ=1.2, the non-periodic intermittent adjustment control time series is:
and [0,2.55] [2.81,5.5] [5.77,8] [8.2,10.13] [10.3,11.4] [11.5,13.03] [13.2,13.03] [13.2,15.73] [16,18.66] [18.9,19.89], can find 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 is x 1 (s)＝0.2，x 2 (s)＝0.1，y 1 (s)＝-0.25，y 2 (s)＝-0.2，s∈[-1,0]According to the parameter setting, the upper bound T approximately equal to 10.033 of the fixed time can be calculated, and the specific simulation experiment results are as follows: FIG. 3 shows the state x of the drive system without the controller 1 (t) and responsive System status y 1 A trace map of (t); FIG. 4 shows the state x of the drive system without the controller 2 (t) and responsive System status y 2 A trace map of (t); FIG. 5 shows the synchronization error e without the controller 1 (t) and e 2 A variation trace map of (t); FIG. 6 shows the state x of the drive system under the action of the synchronous controller 1 (t) and responsive System status y 1 A trace map of (t); FIG. 7 shows the state x of the drive system under the action of the synchronous controller 2 (t) and responsive System status y 2 A trace map of (t); FIG. 8 shows the synchronization error e under the action of the synchronization controller 1 (t) and e 2 A variation trace map of (t); 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 fixed time under the action of the synchronization controller, verifying synchronization performance.
Based on the fact that the response system in the embodiment is synchronous with the driving system at fixed time under the action of the non-periodic intermittent adjustment synchronous controller, image encryption and decryption are achieved, and the method comprises the following specific implementation steps:
step S31: reading an original color image, as shown in fig. 9 (a), the image size is 256×256×3, and extracting a red channel component matrix of the original color imageGreen channel component matrix->And blue channel component matrixp∈{1,2,…,256}，q∈{1,2, …,256}, where +.> And->The value ranges are all one value of (0, 1, …, 255);
step S32: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal x of the driving system 1 (t)、x 2 (t) and (x) 1 (t)+x 2 (t)) selecting three chaotic signal sequencesAnd->p∈{1,2,…,256}，q∈{1,2,…,256}；
Step S33: three chaotic signal sequences obtained in the step S32And->After specific transformation, three new signal sequences are obtained +.>And->p.epsilon.1, 2, …,256, q.epsilon.1, 2, …,256, where ∈ ->And->The value ranges are all one value of (0, 1, …, 255); the specific conversion formula used in step S33 is:
step S34: three new signal sequences obtained in step S33And->Three color channel component matrices, each associated with an unencrypted color image > And->Performing exclusive OR operation on the corresponding position elements in the color channel matrix to obtain three color channel component matrixes after replacementAnd->p∈{1,2,…,256}，q∈{1,2,…,256}；
Step S35: the three color channel component matrixes after the replacement are subjected to the arold transformation And->Scrambling operation is carried out to obtain a scrambled three-color channel component matrixAnd->p epsilon {1,2, …,256}, q epsilon {1,2, …,256}, the arnold transform algorithm is:
wherein the method comprises the steps ofFor 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 And->As 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 fig. 9 (b);
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 of (0, 1, …, 255);
step S38: three color channel component matrices for encrypted images using inverse Arnold transformAnd->Performing inverse scrambling operation and recovering to obtain three color channel component matrixes And->p epsilon {1,2, …,256}, q epsilon {1,2, …,256}, the arnold inverse transform algorithm is:
wherein the method comprises the steps ofFor the original position of the pixel +.>Is the position of the scrambled pixels;
step S39: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal y of the response system 1 (t)、y 2 (t) and (y) 1 (t)+y 2 (t)) and step S32And->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 as follows:
step S311: three new signal sequences obtained in step S310And->Three color channel component matrices restored in step S38, respectively>And->Exclusive or operation is carried out on the corresponding position elements of the decryption image to obtain three color channel component matrixes of the decryption imageAnd->p∈{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, 11 and 12 are respectively adjacent pixel statistics of the unencrypted color image R, G and the B color channel component and the encrypted color image R, G and the B color channel component in the horizontal, vertical and diagonal directions, fig. 10 (a), 10 (B), 10 (c), 11 (a), 11 (B), 11 (c), 12 (a), 12 (B), 12 (c) are respectively adjacent pixel statistics of the unencrypted color image R, G and the B color channel component in the horizontal, vertical and diagonal directions, and fig. 10 (d), 10 (e), 10 (f), 11 (d), 11 (e), 11 (f), 12 (d), 12 (e), 12 (f) are respectively adjacent pixel statistics of the encrypted color image R, G and the B color channel component in the horizontal, vertical and diagonal directions. 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.
Through an image shannon entropy formulaWhere N represents the total number of pixels, hist i The total number of pixels expressed as i can calculate the image information entropy of the unencrypted image and the information entropy of the encrypted image, and from table 1, it can be seen that the image information entropy of the encrypted image is different from the image information entropy of the unencrypted image, and the image information entropy of the encrypted image is close to 8, while the image information entropy of the completely random image is 8, and it can be seen that the encrypted image is close to the completely random image, thereby embodying the effectiveness of the encryption method provided by the invention.
TABLE 1
| Image processing apparatus | Entropy of image information | R component information entropy | G component information entropy | B component information entropy |
| Unencrypted image | 7.7301 | 7.2353 | 7.5683 | 6.9176 |
| Encrypting an image | 7.9989 | 7.9972 | 7.9974 | 7.9972 |
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 (4)
1. The image encryption method based on the fuzzy neural network fixed time synchronization is characterized by comprising the following steps of:
step S1: based on the fuzzy neural network, a driving system and a response system are established; the specific contents of the step S1 are as follows:
the establishment of a driving system and a response system based on the fuzzy neural network is respectively as follows:
wherein, the time t is more than or equal to 0, i=1, 2, …, n, j=1, 2, …, n; n represents the number of neurons contained in the driving system and the response system, and x i (t) represents the state of the ith neuron of the driving system at time t, y i (t) represents the state of the ith neuron of the response system at time t; a, a i Represents the damping coefficient of the ith neuron, b i Represents the rate at which the ith neuron resets its potential to a quiescent state, a, when the network is disconnected from external inputs i And b i Respectively satisfy a i >0 and b i >0；f j (x j (t)) represents a time-lapse free activation function of the jth neuron of the drive system, f j (x j (t-τ j (t))) an activation function representing a time-varying discrete time lag of a jth neuron of the drive system, f j (y j (t)) represents a time-lapse free activation function of the jth neuron of the response system, f j (y j (t-τ j (t)) representing an activation function of the j-th neuron of the response system comprising a time-varying discrete time lag, said activation function being a discontinuous activation function and satisfying |f j (.)|≤M j Wherein M is j Is a positive constant; τ j (t) and delta j (t) is time-varying discrete time lag and time-varying distributed time lag respectively, and satisfies 0.ltoreq.τ j (t)≤τ，0≤δ j (t) is less than or equal to delta, wherein tau and delta are positive constants and are setη is an integral variable; z ij Representing a feed-forward element; />And q ij Elements of the fuzzy feedforward minimum and fuzzy feedforward maximum modules are represented respectively; h is a ij And ρ ij Elements of the minimum fuzzy feedback and maximum fuzzy feedback modules are respectively represented; m is m j (t) and I i (t) represents the input of the jth neuron and the bias of the ith neuron, respectivelyPlacing; v and V respectively represent fuzzy and fuzzy or operators, and the following conditions are satisfied:
u i (t) is an aperiodic intermittent adjustment synchronous controller; initial values of the driving system and the response system respectively satisfy: x is x i (s)＝φ i (s)，c ij (x i (t))、d ij (x i (t))、w ij (x i (t))、c ij (y i (t))、d ij (y i (t))、w ij (y i (t)) represents memristor connection weights, respectively satisfying:
wherein Γ is 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, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
wherein, kc ij (x i (t))]、K[d ij (x i (t))]、K[w ij (x i (t))]、K[c ij (y i (t))]、K[d ij (y i (t))]、K[w ij (y i (t))]、K[f j (x j (t))]、K[f j (y j (t))]、K[f j (x j (t-τ j (t)))]And K [ f ] j (y j (t-τ j (t))) satisfy respectively:
Wherein,
according to the measurable choice theorem, there is
And-> Then it is further possible to obtain:
wherein:and->Satisfy-> And->Satisfy-> χ j And iota (iota) j Is a constant;
step S2: setting a synchronous error according to the driving system and the response system established in the step S1, and designing a synchronous controller;
step S3: based on the response system, under the action of the synchronous controller, the fixed time is synchronous with the driving system, so that the image encryption and decryption are realized, and the specific implementation steps are as follows:
the encryption process comprises the following steps:
step S31: original color image is read, image sizeExtracting red channel component matrix of original color image>Green channel component matrix->And blue channel component matrixWherein->And->The value ranges are all one value of (0, 1, …, 255);
step S32: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal x of the driving system i (t) selecting three chaotic signal sequencesAnd
step S33: three chaotic signal sequences obtained in the step S32And->After specific transformation, three new signal sequences are obtained +.>And-> Wherein->And->The value ranges are all one value of (0, 1, …, 255); the specific conversion formula used in step S33 is:
Step S34: the step S33 is performedThree new signal sequencesAnd->Three color channel component matrices, each associated with an unencrypted color image> And->Performing exclusive OR operation on the corresponding position elements in the three color channel component matrixes after substitution to obtain +.>Andq∈{1,2,…,/>
step S35: the three color channel component matrixes after the replacement are subjected to the arold transformation Andscrambling operation is carried out to obtain a scrambled three-color channel component matrix +.>And->The arnold transformation algorithm is:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling;
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-> And->The value ranges are all one value of (0, 1, …, 255);
step S38: three color channel component matrices for encrypted images using inverse Arnold transformAnd->Performing inverse scrambling operation and recovering to obtain three color channel component matrixes And->The arnold inverse transformation algorithm is as follows:
wherein the method comprises the steps ofFor the original position of the pixel +.>Alpha and beta are constants for the position after pixel scrambling;
step S39: after the driving system and the response system reach fixed time synchronization, according to the discrete time sequence chaotic signal y of the response system i (t) selecting and in step S32And->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 as follows:
step S311: three new signal sequences obtained in step S310And->Three color channel component matrices restored in step S38, respectively>And->Exclusive or operation is carried out on the corresponding position elements of the (B) and the decryption is carried out to obtain three color channel component matrixes of the decrypted image +.>And->
Step S312: three color channel component matrices of the decrypted image obtained in step S311 are ′ And->And (5) recombining to obtain a decrypted image.
2. The image encryption method based on the fixed time synchronization of the fuzzy neural network according to claim 1, wherein the step S2 specifically comprises the steps of:
Step S21: the synchronization error of the driving system and the response system is set as follows:
e i (t)＝y i (t)-x i (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 is t k Starting working time s of the first subinterval controller in the kth period k Indicating the starting working time of the second subinterval controller in the kth period, t k Sum s k The requirements are as follows:omega and->Is constant and satisfies->ζ i 、ε i 、θ i 、∈ i 、λ 1i 、λ 2i 、λ 3i 、λ 4i A positive controller gain; 0<l<1，γ>1；/>Derivative expressed as synchronization error ∈ ->Is a sign function of (2); e, e i (t-τ i (t)) representing a synchronization error of a state variable of the drive system i-th neuron comprising a time-varying discrete time lag and a state variable of the response system i-th neuron comprising a time-varying discrete time lag, and a controller gain ζ i 、ε i 、θ i 、∈ i The following inequality is satisfied:
ζ i ≧1-a i
wherein,
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 at a fixed time.
3. The image encryption method based on the fixed time synchronization of the fuzzy neural network according to claim 2, wherein the response system is fixed time synchronized with the driving system, and an upper bound T of the fixed time is:
Wherein ψ is a constant and
4. an image encryption system based on fuzzy neural network fixed time synchronization, which is characterized in that the image encryption system comprises:
discrete time sequence chaotic signal acquisition module: the method is used for establishing a driving system and a response system based on a fuzzy neural network, setting a synchronous error, and designing an aperiodic intermittent adjusting synchronous controller so that the driving system and the response system are synchronous at a fixed time; after the driving system and the response system are synchronous, a driving system chaotic signal acquisition module acquires a discrete time sequence chaotic signal x according to the driving system i (t) selecting three chaotic signal sequencesAndthe response system chaotic signal acquisition module acquires a discrete time sequence chaotic signal y according to the response system i (t) select and->And->Corresponding chaotic signal sequence->And->
The driving system chaotic signal conversion operation module: for sequencing chaotic signalsAnd->After specific conversion, three new signal sequences +.>And->Wherein the method comprises the steps ofAnd->The value ranges are all one value of (0, 1, …, 255);
and the response system chaotic signal conversion operation module: for sequencing chaotic signalsAnd->After specific conversion, three new signal sequences are obtained >Wherein the method comprises the steps ofThe value ranges are all one value of (0, 1, …, 255);
the original color image component reading and extracting operation module comprises the following steps: used in the encryption process for reading the original color image and extracting the red component matrix of the original color imageGreen component matrix->And blue component matrix->
The encrypted image component reading and extracting operation module comprises: in the decryption process, the method is used for reading the encrypted image and extracting three color channel component matrixes of the encrypted image
Signal replacement operation module: for use in encrypting a signal sequenceAnd->Three color component matrices respectively corresponding to the original color image>And->Performing exclusive OR operation on the corresponding position elements in the table; for inserting the signal sequence during decryption>And->Respectively with the reduced three color channel component matrices +.> And->Performing exclusive OR operation on the corresponding position elements in the table;
signal scrambling operation module: used in encryption process, three color component matrixes after being replaced by arold transformationAnd->Scrambling operation is carried out to obtain a scrambled three-color channel component matrixAnd->
The signal reverse scrambling operation module is as follows: for use in decryption processes, inverse Arnold transformation pairs are usedThree color channel component matrices for encrypted images And->Performing inverse scrambling operation, and recovering to obtain color channel component matrix +.>And->
An encrypted image component combination operation module: three color channel component matrixes for combining encrypted images in encryption processAnd->Generating an encrypted image;
a decrypted image component combining operation module: in the decryption process, three color channel component matrixes for combining decrypted imagesAnd (3) recombining and restoring to a color image.
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