CN109951269A - A kind of secret communication method of Parameter uncertainties time-lag chaos neural network - Google Patents
A kind of secret communication method of Parameter uncertainties time-lag chaos neural network Download PDFInfo
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Abstract
The invention discloses a kind of secret communication methods of Parameter uncertainties time-lag chaos neural network, belong to private communication technology field.A kind of secret communication method of Parameter uncertainties time-lag chaos neural network of the invention, initially sets up drive system, constructs response system further according to drive system, then constructs anti-isochronous controller according to drive system and response system；When transmitting ciphertext signal, drive system generates chaotic signal, and obtains superposed signal according to chaotic signal and ciphertext Signal averaging, then superposed signal is passed through transmission to response system；Response system generates anti-synchronous chaos signal by anti-isochronous controller, and response system obtains the ciphertext signal of decryption further according to superposed signal and anti-synchronous chaos signal.The present invention overcomes the weak deficiencies of existing chaotic neural network secure communication technology anti-interference ability, provide a kind of secret communication method of the time-lag chaos neural network of Parameter uncertainties, improve the anti-interference ability of secret communication.
Description
Technical field
The present invention relates to private communication technology fields, more specifically to a kind of Parameter uncertainties time-lag chaos nerve
The secret communication method of network.
Background technique
Nineteen ninety, Pecora and Carroll propose the synchronism of chaos system, chaos letter using drive response concept
Number due to having the characteristics that class is random, aperiodic and unpredictable, the carrier of cipher-text information can be used as, chaos is logical in secrecy
The research hotspot being applied to for information security field in letter.Since neural network is nonlinearity dynamic system, and
Chaos has above-mentioned characteristic again, therefore neural network and chaos are closely related, chaotic neural network usually have structure it is simple,
The features such as dynamic property is complicated is highly suitable as the generator of chaotic signal, therefore, chaotic neural network encryption communication technology
It has broad application prospects.
How to realize the secret communication of chaotic neural network, also gives some solutions in the prior art, such as send out
Bright creation title are as follows: it is a kind of based on time lag memristor chaotic neural network secret communication method (application number:
201510256103.9；The applying date: on May 18th, 2015), the program discloses a kind of based on time lag memristor chaotic neural network
Secret communication method, this method using a two-dimensional time lag memristor chaotic neural network establish drive system and response be
System, devises simple isochronous controller, makes clear text signal to be encrypted in the transmission and can achieve secret communication effect.The party
Case overcomes the disadvantages of traditional chaotic neural network weight is fixed, network energy consumption is more, mentions for the secret communication transmission of signal
A solution is supplied.
In addition, there are also invention and created name are as follows: a kind of chaotic neural network encryption communication method under signal quantization situation
(application number: 201510256103.9；The applying date: on May 18th, 2015), the program discloses under a kind of signal quantization situation
Chaotic neural network encryption communication method, contains following steps: (one) establishes Mechanics in Chaotic Neural Networks and Quantization Model；
(2) structural regime feedback controller obtains error dynamics system；(3) controller gain matrix K is solved, is substituted into actual
In controller, obtain isochronous controller: (four) drive system load ciphertext signal obtains superposed signal, passes through transmission of network to sound
Answer system；(5) under isochronous controller effect, keep drive system synchronous with response system；(6) by superposed signal with it is synchronous
The ciphertext signal that signal is restored.The program considers the uniform quantization phenomenon in network environment, proposes a kind of synchronously control
Device keeps drive system synchronous with response system under the action of isochronous controller, by the superposed signal and synchronization signal after quantifying
The ciphertext signal being restored can effectively eliminate the influence of uniform quantization bring.But the problem of above-mentioned two scheme, exists
In: the Parameter uncertainties factor and the interference of random noise of system are not fully considered, and anti-interference ability is caused to have certain deficiency.
How Parameter uncertainties and random noise factor are successfully managed in chaotic neural network encryption communication, be that the prior art needs to solve
Certainly the problem of.
Summary of the invention
1. to solve the problems, such as
It is an object of the invention to overcome in the prior art, the secret communication anti-interference ability based on chaotic neural network is not
Strong deficiency provides a kind of secret communication method of the time-lag chaos neural network of Parameter uncertainties, improves secret communication
Anti-interference ability, further improve transmission information accuracy.
2. technical solution
To solve the above-mentioned problems, the technical solution adopted in the present invention is as follows:
The secret communication method of a kind of Parameter uncertainties time-lag chaos neural network of the invention, it is characterised in that: first
Drive system is established, constructs response system further according to drive system, it is then anti-synchronous with response system building according to drive system
Controller；
When transmitting ciphertext signal, drive system generates chaotic signal, and is obtained according to chaotic signal and ciphertext Signal averaging
Superposed signal is obtained, then superposed signal is passed through into transmission to response system；Response system is generated anti-by anti-isochronous controller
Synchronous chaos signal, response system obtain the ciphertext signal of decryption further according to superposed signal and anti-synchronous chaos signal.
Preferably, drive system, drive system model are established are as follows:
Wherein, x (t)=[x1(t),x2(t),...,xn(t)]TWith x (t- τ)=[x1(t-τ),x2(t-τ),...x,n(t-
τ)]TIt is the state vector of t moment chaotic neural network, x1(t),x2(t),...,xn(t) neuron 1,2 is respectively indicated ..., n
State, the transposition of T representing matrix, τ indicate time lag,WithIt is activation primitive vector；Φk(x(t)),Ψl(x (t- τ)) is all
Nonlinear function matrix, φk,ψlIt is all unknown constant parameter vector, coefficient matrices A is the connection matrix of x (t)；AτFor x (t-
Connection matrix τ)；B is the connection matrix of f (x (t))；BτFor the connection matrix of g (x (t- τ)).
Preferably, response system, response system model are established according to drive system are as follows:
Wherein,WithIt is in response to system
State vector,
All indicate that the activation primitive vector of response system, w (t) are in response to the random perturbation vector in system, u (t) is anti-synchronously control
Device, coefficient matrices A areConnection matrix；AτForConnection matrix；B isConnection matrix；BτForConnection matrix；H is the connection matrix of w (t).
Preferably, anti-isochronous controller, specific steps are constructed according to drive system and response system are as follows:
The synchronous error of drive system and response system isThe anti-isochronous controller expression formula of construction
Are as follows:
Wherein, K is control gain matrix,WithFor unknown constant parameter vector.
Preferably, the error system of drive system and response system are as follows:
Preferably, anti-isochronous controller is obtained according to following steps:
Construct following linear matrix LMI:
Wherein,γ > 0 is unknown
Positive real number, M is known constant matrices, and M=PK is the matrix of required solution, and P and R are unknown matrix, and P > 0, R > 0, Q1
And Q2For diagonal matrix, and Q1>0,Q2> 0, LfAnd LgFor activation primitive；
Solution formula Ξ obtains matrix P；Gain matrix K:K=P is acquired according to the following formula-1M, wherein P-1Represent matrix P
It is inverse；Following equation is recycled to solveWith
Wherein Γ and Υ are arbitrary symmetric positive definite matrix,WithIndicate beWithDerivative, p
0 positive integer is greater than with q；The gain matrix K that solution is obtained,WithIt substitutes into anti-isochronous controller expression formula,
Obtain anti-isochronous controller u (t).
Preferably, the tool box the LMI solution formula Ξ in MATLAB is utilized.
Preferably, drive system generates n dimension chaotic signal x (t), and drive system is folded by signal x (t) and ciphertext signal z (t)
Add, obtains superposed signal s (t), s (t)=x (t)+z (t), then superposed signal is transmitted to response by channel by drive system
System；
Response system receives superposed signal s (t), and response system generates anti-synchronous chaos signal by anti-isochronous controllerIt is anti-synchronous with x (t)；The then superposed signal s (t) and anti-synchronous chaos signal by receivingIt is decrypted
Ciphertext signal z ' (t),
Preferably, f (x (t)) and g (x (t- τ)) meets Lipschitz condition, and f (x (t)) and g (x (t- τ)) is respectively
For odd function.
Preferably, A is self feed back matrix, AτTo postpone self feed back matrix, B is connection weight matrix, BτTo postpone connection weight square
Battle array.
3. beneficial effect
Compared with the prior art, the invention has the benefit that
(1) a kind of secret communication method based on Parameter uncertainties time-lag chaos neural network of the invention, according to driving
System and response system construct anti-isochronous controller；To improve the anti-interference ability of secret signalling, and solves ginseng
Number uncertain problem, may further make error system converge to a stable value, to improve the anti-of secret communication
Interference performance；
(2) a kind of secret communication method based on Parameter uncertainties time-lag chaos neural network of the invention is rung in building
Random factors are considered when answering system, is suitable for complicated secret signalling in the prior art, further improves biography
The accuracy of defeated information；
(3) a kind of secret communication method based on Parameter uncertainties time-lag chaos neural network of the invention, passes through building
Anti- isochronous controller, so that secret signalling remains to reality in the case where having Parameter uncertainties factor and random noise disturbance
Existing response system is anti-synchronous with drive system, to improve the anti-interference ability of secret communication, further improves transmission letter
The accuracy of breath.
Detailed description of the invention
Fig. 1 is a kind of process of secret communication method based on Parameter uncertainties time-lag chaos neural network of the invention
Figure；
Fig. 2 is that a kind of structure of secret communication method based on Parameter uncertainties time-lag chaos neural network of the invention is shown
It is intended to；
Fig. 3 is that drive system of the invention is transmitted to the signal chaos state figure in channel；
Fig. 4 a is state trajectory figure of the drive system under no anti-isochronous controller effect in the present invention；
Fig. 4 b is state trajectory figure of the response system under no anti-isochronous controller effect in the present invention；
Fig. 5 a is that drive system realizes anti-synchronous state trajectory figure in the case where there is anti-isochronous controller to act in the present invention；
Fig. 5 b is that response system realizes anti-synchronous state trajectory figure in the case where there is anti-isochronous controller to act in the present invention；
Fig. 6 is the synchronous error figure of drive system and response system in the case where there is anti-isochronous controller to act in the present invention；
Fig. 7 is the ciphertext signal time-domain diagram of the drive system of embodiment 2；
Fig. 8 is the coded signal time-domain diagram in the network transmission channels of embodiment 2；
Fig. 9 is the Error Graph of the original cipher text signal z (t) of embodiment 2 and the ciphertext signal z ' (t) of decryption.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments；Moreover, be not between each embodiment it is relatively independent, according to
It needs can be combined with each other, to reach more preferably effect.Therefore, below to the embodiment of the present invention provided in the accompanying drawings
Detailed description is not intended to limit the range of claimed invention, but is merely representative of selected embodiment of the invention.Base
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts it is all its
His embodiment, shall fall within the protection scope of the present invention.
To further appreciate that the contents of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments.
Embodiment 1
In conjunction with shown in Fig. 1~6, a kind of secret communication method of Parameter uncertainties time-lag chaos neural network of the invention,
Drive system is first established, response system is constructed according to drive system；It is worth noting that drive system of the invention is based on ginseng
Number unknown time-delay chaotic neural network is established, and response system is to allow the response system of random noise disturbance.The present invention
The secret communication method of Parameter uncertainties time-lag chaos neural network a kind of to consider parameter when constructing response system not true
Fixed and random factors are suitable for complicated secret signalling in the prior art, further improve the standard of transmission information
True property.
Further, anti-isochronous controller is constructed further according to drive system and response system；It is worth noting that the present invention
Anti- isochronous controller be made of STATE FEEDBACK CONTROL and self adaptive control two parts, secrecy is improved by STATE FEEDBACK CONTROL
The anti-interference ability of communication system, and solve the problems, such as Parameter uncertainties by self adaptive control.
When transmitting ciphertext signal, drive system generates chaotic signal according to ciphertext signal, and drive system is by chaotic signal
Superposed signal is generated with ciphertext Signal averaging, then superposed signal is passed through into transmission to response system；Response system is according to folded
Plus signal generates chaotic signal, and the ciphertext signal decrypted by anti-isochronous controller.
Specific step is as follows for a kind of secret communication method of Parameter uncertainties time-lag chaos neural network of the invention:
Step 1: drive system, drive system model are established are as follows:
Wherein, x (t)=[x1(t),x2(t),...,xn(t)]TWith x (t- τ)=[x1(t-τ),x2(t-τ),...,xn(t-
τ)]TIt is the state vector of t moment chaotic neural network, x1(t),x2(t),...,xn(t) neuron 1,2 is respectively indicated ..., n
State, the transposition of T representing matrix, τ indicate time lag,WithIt is activation primitive vector；Φk(x(t)),Ψl(x (t- τ)) is all
Nonlinear function matrix, φk,ψlIt is all unknown constant parameter vector, coefficient matrices A is the connection matrix of x (t)；AτFor x (t-
Connection matrix τ)；B is the connection matrix of f (x (t))；BτFor the connection matrix of g (x (t- τ)).It is worth noting that this implementation
The f (x (t)) and g (x (t- τ)) of example meet Lipschitz condition, and f (x (t)) and g (x (t- τ)) are respectively odd function；Into
One step, A is self feed back matrix, AτTo postpone self feed back matrix, B is connection weight matrix, BτTo postpone connection weight matrix.
Step 2: response system is established
Response system is established according to drive system, specifically, response system model are as follows:
Wherein,WithIt is in response to system
State vector,
All indicate the activation primitive vector of response system, u (t) is anti-isochronous controller, w (t) be in response to the random perturbation in system to
Amount, coefficient matrices A areConnection matrix；AτForConnection matrix；B isConnection matrix；BτForConnection matrix, A, Aτ, B and BτWith A, A in step 1τ, B and BτIt is identical；H is the connection matrix of w (t).It is worth
Illustrate, the response system of the present embodiment is that uncertain factor is eliminated on the basis of drive system, that is, is considered random
The factor of noise further improves the accuracy of transmission information.
Step 3: constructing anti-isochronous controller according to drive system and response system,
Specific step is as follows:
The synchronous error of drive system and response system isThe anti-isochronous controller expression formula of construction
Are as follows:
Wherein, K is control gain matrixWithFor unknown constant parameter vector；
Solution controller gain matrix K,WithBy K,WithValue substitute into the expression of anti-isochronous controller
In formula, anti-isochronous controller u (t) is obtained.Further, error system, the error system of drive system and response system are obtained
Are as follows:
By establishing error system, drive system can be made to realize with response system anti-synchronous, and finally to miss
Poor system tends to 0, to improve the accuracy of signal transmission.
It is worth noting that " Ke (t) " indicates STATE FEEDBACK CONTROL in the anti-isochronous controller expression formula of the present embodiment,Self adaptive control is indicated, to improve the anti-of secret signalling
Interference performance, and solve the problems, such as Parameter uncertainties, and error system can be made to converge to a stable value, to mention
The high anti-interference ability of secret communication.
Step 4: anti-isochronous controller is obtained
Specific step is as follows:
Following linear matrix LMI is constructed first:
Wherein,γ > 0 is unknown
Positive real number, M are known constant matrices, and M=PK is the matrix of required solution, and P and R are unknown matrix, and P > 0, R > 0, Q1And Q2
For diagonal matrix, and Q1>0,Q2> 0, LfAnd LgFor activation primitive；
Solution formula Ξ obtains matrix P；It is worth noting that the present embodiment solves public affairs using the tool box LMI in MATLAB
Formula Ξ.
Gain matrix K is then acquired according to the following formula:
K=P-1M,
Wherein, P-1Represent the inverse of matrix P；
Following equation is recycled to solveWith
Wherein Γ and Υ are arbitrary symmetric positive definite matrix,WithIndicate beWithDerivative, p
0 positive integer is greater than with q；
The gain matrix K that solution is obtained,WithIt substitutes into anti-isochronous controller expression formula, solves and obtain instead
Isochronous controller u (t).
Step 5: transmission ciphertext signal
When transmitting ciphertext signal, enabling drive system is transmitting terminal, and response system is input terminal (as shown in Figure 2)；Specifically
Ground,
Transmitting terminal: drive system believes chaotic signal x (t) and ciphertext according to n dimension chaotic signal x (t), drive system is generated
Number z (t) superposition, obtains superposed signal s (t), i.e. s (t)=x (t)+z (t), then superposed signal is passed through channel by drive system
It is transmitted to response system；As shown in connection with fig. 3, the signal in transmission channel is chaos state, so as to guarantee communication process
Confidentiality.
Receiving end: response system receives superposed signal s (t), and response system is generated anti-synchronous by anti-isochronous controller
Chaotic signalAnti- synchronous with x (t), i.e., response system generates anti-same with x (t) under the action of anti-isochronous controller
The anti-synchronous chaos signal of stepThe then superposed signal s (t) and anti-synchronous chaos signal by receivingIt is solved
Close ciphertext signal z ' (t),It is worth noting that effect of the response system in anti-isochronous controller
It is lower to generate the anti-synchronous chaos signal anti-synchronous with x (t)Reach anti-synchronous effect required for secret signalling, from
And the anti-interference ability of secret communication is improved, further improve the accuracy of transmission information.
It is worth noting that under the action of anti-isochronous controller, so that secret signalling is having random noise disturbance
In the case where, still it is able to achieve that response system is anti-synchronous with drive system, so that the anti-interference ability of secret communication is improved, into one
Step improves the accuracy of transmission information.Specifically, in conjunction with shown in Fig. 4 a, 4b, 5a and 5b, without anti-isochronous controller the case where
Under, it is anti-synchronous with response system to cannot achieve drive system；And under the action of anti-isochronous controller, drive can be realized well
Dynamic system is anti-synchronous with response system, is finally completed the normal secure communication of the neural network in the case where there is random disturbances.
Embodiment 2
In conjunction with shown in Fig. 7~9, the present embodiment and 1 content of embodiment are essentially identical, and the present embodiment uses the one of embodiment 1
The secret communication method of kind of parameter unknown time-delay chaotic neural network, pass through transmission ciphertext signal z (t): z (t)=
2sin(0.5t+4)。
The parameter that the present embodiment uses are as follows:
Time lag: τ=1；Sampling period: T=100；Step-length: dt=0.005；
Drive system initial value are as follows:
Response system initial value are as follows:
Activation primitive:
Γ=50, Y=200；
Constant matrices:
Gain matrix:
Coded signal time-domain diagram of the ciphertext signal time-domain diagram of transmitting terminal drive system referring to Fig. 7, in network transmission channels
Referring to Fig. 8, the Error Graph of the ciphertext signal z ' (t) of original cipher text signal z (t) and the decryption of receiving end response system is referring to Fig. 9.By
Fig. 7 to Fig. 9, the superposed signal of network transmission and original ciphertext signal difference are very big, have very strong confidentiality.In addition,
Under the action of anti-isochronous controller, receiving end response system can be decrypted ciphertext signal, and the ciphertext signal obtained
Z ' (t) and original ciphertext signal z (t) error very little.
The present invention is described in detail above in conjunction with specific exemplary embodiment.It is understood, however, that can not take off
It is carry out various modifications in the case where from the scope of the present invention being defined by the following claims and modification.Detailed description and drawings
Should be to be considered only as it is illustrative and not restrictive, if there is any such modifications and variations, then they all will
It falls into the scope of the present invention described herein.In addition, Development Status and meaning that background technique is intended in order to illustrate this technology,
It is not intended to limit the present invention or the application and application field of the invention.
Claims (10)
1. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network, it is characterised in that: initially set up driving system
System constructs response system further according to drive system, then constructs anti-isochronous controller according to drive system and response system；
When transmitting ciphertext signal, drive system generates chaotic signal, and is folded according to chaotic signal and ciphertext Signal averaging
Plus signal, then superposed signal is passed through into transmission to response system；Response system is generated anti-synchronous by anti-isochronous controller
Chaotic signal, response system obtain the ciphertext signal of decryption further according to superposed signal and anti-synchronous chaos signal.
2. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 1, feature
It is: establishes drive system, drive system model are as follows:
Wherein, x (t)=[x1(t),x2(t),...,xn(t)]TWith x (t- τ)=[x1(t-τ),x2(t-τ),...x,n(t-τ)]T
It is the state vector of t moment chaotic neural network, x1(t),x2(t),...,xn(t) neuron 1,2 is respectively indicated ..., the shape of n
State, the transposition of T representing matrix, τ indicate time lag,WithIt is activation primitive vector；Φk(x(t)),Ψl(x (t- τ)) all right and wrong
Linear function matrix, φk,ψlIt is all unknown constant parameter vector, coefficient matrices A is the connection matrix of x (t)；AτFor x (t- τ)
Connection matrix；B is the connection matrix of f (x (t))；BτFor the connection matrix of g (x (t- τ)).
3. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 2, feature
It is: response system, response system model is established according to drive system are as follows:
Wherein,WithIt is in response to system mode
Vector,
All indicate that the activation primitive vector of response system, w (t) are in response to the random perturbation vector in system, u (t) is anti-synchronously control
Device, coefficient matrices A areConnection matrix；AτForConnection matrix；B isConnection matrix；BτForConnection matrix；H is the connection matrix of w (t).
4. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 3, feature
It is: anti-isochronous controller, specific steps is constructed according to drive system and response system are as follows:
The synchronous error of drive system and response system isThe anti-isochronous controller expression formula of construction are as follows:
Wherein, K is control gain matrix,WithFor unknown constant parameter vector.
5. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 4, feature
It is: the error system of drive system and response system are as follows:
6. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 4, feature
It is: obtains anti-isochronous controller according to following steps:
Construct following linear matrix LMI:
Wherein,γ > 0 is unknown positive reality
Number, M are known constant matrices, and M=PK is the matrix of required solution, and P and R are unknown matrix, and P > 0, R > 0, Q1And Q2It is right
Angular moment battle array, and Q1>0,Q2> 0, LfAnd LgFor activation primitive；
Solution formula Ξ obtains matrix P；
Gain matrix K is acquired according to the following formula:
K=P-1M,
Wherein, P-1Represent the inverse of matrix P；
Following equation is recycled to solveWith
Wherein Γ and Υ are arbitrary symmetric positive definite matrix,WithIndicate beWithDerivative, p and q are
Positive integer greater than 0；
The gain matrix K that solution is obtained,WithIt substitutes into anti-isochronous controller expression formula, obtains anti-isochronous controller
u(t)。
7. a kind of secret communication method of Parameter uncertainties time-lag chaos neural network according to claim 6, feature
It is: utilizes the tool box the LMI solution formula Ξ in MATLAB.
8. the secret communication side of described in any item a kind of Parameter uncertainties time-lag chaos neural networks according to claim 1~7
Method, it is characterised in that:
Drive system generates n dimension chaotic signal x (t), and signal x (t) is superimposed with ciphertext signal z (t), is superimposed by drive system
Signal s (t), s (t)=x (t)+z (t), then superposed signal is transmitted to response system by channel by drive system；
Response system receives superposed signal s (t), and response system generates anti-synchronous chaos signal by anti-isochronous controllerIt is anti-synchronous with x (t)；The then superposed signal s (t) and anti-synchronous chaos signal by receivingIt is decrypted
Ciphertext signal z ' (t),
9. according to a kind of described in any item secret communication sides of Parameter uncertainties time-lag chaos neural network of claim 2~7
Method, it is characterised in that: f (x (t)) and g (x (t- τ)) meets Lipschitz condition, and f (x (t)) and g (x (t- τ)) is respectively
For odd function.
10. according to a kind of described in any item secret communication sides of Parameter uncertainties time-lag chaos neural network of claim 2~7
Method, it is characterised in that: A is self feed back matrix, AτTo postpone self feed back matrix, B is connection weight matrix, BτTo postpone connection weight square
Battle array.
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