CN115169539B - Secret communication method based on inertial complex value memristor neural network - Google Patents
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Abstract
The invention discloses a secret communication method based on an inertial complex value memristor neural network. The method is based on an inertial complex value memristor neural network, a driving system and a response system are constructed, a self-adaptive anti-synchronous controller is designed, a signal generated by a driving system of a transmitting end is superposed with a ciphertext signal to generate a superposed signal, the superposed signal is transmitted to a receiving end through a channel, and the signal generated by the response system of the receiving end is superposed with the received superposed signal to restore the ciphertext signal, so that secret communication is realized. The invention solves the problem that the inertial complex-valued memristor neural network with infinite distribution time lag is difficult to realize anti-synchronization, and improves the information transmission efficiency of the secret communication scheme and is more difficult to crack.
Description
Technical Field
The invention relates to the field of memristor neural networks and secret communication, in particular to a secret communication method based on an inertial complex value memristor neural network.
Background
Memristors have the advantages of small volume, high density, good expandability and the like. Unlike resistors, memristors can remember the last charge value passed when the circuit is open. This characteristic is similar to the memory characteristics of biological neuron synapses, so memristors are often used to simulate synapses in artificial neural networks. Such a neural network with memristors is referred to as a memristive neural network. With respect to current research, many researchers in different fields have studied the dynamic behavior of memristive neural networks with significant results. Analysis of the dynamic behavior of memristive neural networks plays an important role in practical applications. These fields include machine learning, signal processing, image processing, and the like.
In addition, most of the research results achieved at present are achieved in the field of real values, but the results have a plurality of limitations. The complex-valued neural network can solve some problems which cannot be solved by the real-valued neural network, such as unilateral detection and exclusive or. Complex valued neural networks contain complex states, connection weights, and activation functions, with more complex properties. In practical applications, the system generates an inertia term due to the influence of inductance. Therefore, in order to make the research on the neural network closer to the actual situation, the invention also introduces an inertia term in the memristive neural network.
Desynchronization is a fundamental dynamic behavior of nonlinear systems and has been a hotspot in neural network research. At present, asymptotic anti-synchronization and exponential anti-synchronization researches based on neural networks are most widely conducted. Anti-synchronous control is a very important control method of a nonlinear system in many fields of chemistry, biology, associative memory, combinatorial optimization and the like. Therefore, the desynchronization of inertial complex-valued memristive neural networks remains a problem worthy of further investigation.
The anti-synchronization of the inertial complex-valued memristor neural network is realized, the complexity and the safety of secret communication are improved, and meanwhile, the information transmission efficiency can be improved.
Disclosure of Invention
The invention aims to solve the problem of anti-synchronization of an inertial complex value memristor neural network and provides a secret communication method based on the inertial complex value memristor neural network, so that the security of secret communication and the information transmission efficiency are improved.
The invention is realized by adopting the following scheme: a secret communication method based on an inertial complex value memristor neural network comprises the following steps:
step S1: based on the inertia complex-valued memristor neural network, a driving system and a response system are constructed; the step S1 specifically comprises the following steps:
step S11: establishing a driving system of an inertial complex value memristor neural network;
the state equation for establishing the inertial complex value memristor neural network with infinite distribution time lag is as follows:
wherein r is p (t) is the state of the p-th neuron, n is the number of neurons, ε p And d p Is a system parameter, f q (. Cndot.) is an activation function, sigma q (t) represents discrete time lag, K pq (t) is an infinite distribution time-lag kernel real value function, and the memristor weight value a pq (r p (t))，b pq (r p (t))，c pq (r p (t)) satisfy respectively:
wherein, the switching threshold T i >0；
And performing variable substitution order reduction processing on a state equation of the inertia complex value memristor neural network with infinite distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein, 
α p is a constant, beta p ＝d p -α p ，γ p ＝β p α p -ε p Let->
Step S12: constructing a corresponding response system according to the driving system;
establishing a response system according to the driving system, wherein the state equation of the response system is as follows:
wherein, 
u p (t) is a controller;
step S2: designing an anti-synchronization controller according to the anti-synchronization error of the driving system and the response system;
step S3: and realizing secret communication according to an anti-synchronization control method of the inertial complex-value memristor neural network.
Further, the step S2 specifically includes the following steps:
step S21: defining an anti-synchronization error of a driving system and a response system;
the anti-synchronization error of the driving system and the response system is set as
Step S22: designing a self-adaptive anti-synchronization controller;
the self-adaptive anti-synchronization controller is designed as follows:
wherein->
And
for real part error->
And->
For imaginary part error->
And->
For adaptive update rate, λ is a constant greater than 1.
Further, the step S3 specifically includes the following steps:
step S31: the transmitting end driving system generates a signal r (t), superimposes the r (t) and a ciphertext signal z (t) to obtain a superimposed signal h (t), wherein h (t) =r (t) +z (t), and then transmits the superimposed signal to the receiving end through a channel;
step S32: the receiving end receives the superposition signal h (t), the response system generates an anti-synchronization signal r (t), the r (t) is in anti-synchronization with the r (t), and the received superposition signal h (t) and the r (t) are superposed again to obtain a ciphertext signal z '(t), and z' (t) =h (t) +r (t).
The invention provides a secret communication method based on an inertial complex value memristor neural network, which has the following advantages compared with the prior art:
(1) According to the invention, on the selection of the inertial complex-valued memristor neural network model, a more complex network model is particularly introduced according to the characteristics of a memristor circuit, and the complexity and the cracking difficulty of a secret communication scheme are obviously improved.
(2) The invention can separate the real part and the imaginary part of the inertial complex value memristive neural network system, the real part and the imaginary part can generate different signals, and the different signals are respectively overlapped with different ciphertext signals to generate overlapped signals, and the overlapped signals are transmitted, so that the information transmission efficiency is improved.
(3) The invention provides an inertial complex-value memristor neural network anti-synchronization control method which adopts a self-adaptive anti-synchronization controller. Compared with a common controller, the adaptive controller has wider application range, so that the driving system and the response system are more convenient to achieve anti-synchronization.
Drawings
FIG. 1 is a flow chart of a secret communication method based on an inertial complex-valued memristor neural network of the present invention;
FIG. 2 is a schematic diagram of network transmission according to the present invention;
FIG. 3 is a variation curve of an anti-synchronization error in a two-dimensional inertial complex-valued memristor neural network system in embodiment 2 of the present disclosure;
FIG. 4 is a trace map of real part states of the driving system and the response system in embodiment 2 of the present invention;
FIG. 5 is a trace map of the imaginary states of the driving system and the response system in embodiment 2 of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Example 1:
as shown in fig. 1, the present embodiment provides a secret communication method based on an inertial complex-valued memristor neural network. The secret communication method comprises the following steps:
step S1: based on the inertia complex-valued memristor neural network, a driving system and a response system are constructed; the step S1 specifically comprises the following steps:
step S11: establishing a driving system of an inertial complex value memristor neural network;
the state equation for establishing the inertial complex value memristor neural network with infinite distribution time lag is as follows:
wherein r is p (t) is the state of the p-th neuron, n is the number of neurons, ε p And d p Is a system parameter, f q (. Cndot.) is an activation function, sigma q (t) represents discrete time lag, K pq (t) is an infinite distribution time-lag kernel real value function, and the memristor weight value a pq (r p (t))，b pq (r p (t))，c pq (r p (t)) satisfy respectively:
wherein, the switching threshold T i >0；
And performing variable substitution order reduction processing on a state equation of the inertia complex value memristor neural network with infinite distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein, 
α p is a constant, beta p ＝d p -α p ，γ p ＝β p α p -ε p Let->
Step S12: constructing a corresponding response system according to the driving system;
establishing a response system according to the driving system, wherein the state equation of the response system is as follows:
wherein, 
u p (t) is a controller;
step S2: designing an anti-synchronization controller according to the anti-synchronization error of the driving system and the response system;
step S3: and realizing secret communication according to an anti-synchronization control method of the inertial complex-value memristor neural network.
In this embodiment, the step S2 specifically includes the following steps:
step S21: defining an anti-synchronization error of a driving system and a response system;
the anti-synchronization error of the driving system and the response system is set as
Step S22: designing a self-adaptive anti-synchronization controller;
the self-adaptive anti-synchronization controller is designed as follows:
wherein->
And
for real part error->
And->
For imaginary part error->
And->
For adaptive update rate, λ is a constant greater than 1.
In this embodiment, the step S3 specifically includes the following steps:
step S31: as shown in fig. 2, the transmitting-end driving system generates a signal r (t), superimposes r (t) with a ciphertext signal z (t) to obtain a superimposed signal h (t), where h (t) =r (t) +z (t), and then transmits the superimposed signal to the receiving end through a channel;
step S32: as shown in fig. 2, the receiving end receives the superimposed signal h (t), the response system generates an anti-synchronization signal r (t), r (t) is anti-synchronized with r (t), the received superimposed signals h (t) and r (t) are superimposed again to obtain a ciphertext signal z '(t), and z' (t) =h (t) +r (t).
It is worth to say that, in the selection of the inertial complex-valued memristor neural network model, a more complex network model is particularly introduced according to the characteristics of the memristor circuit, and the complexity and the cracking difficulty of a secret communication scheme are obviously improved. The invention can separate the real part and the imaginary part of the inertial complex value memristive neural network system, the real part and the imaginary part can generate different signals, and the different signals are respectively overlapped with different ciphertext signals to generate overlapped signals, and the overlapped signals are transmitted, so that the information transmission efficiency is improved. The invention provides an inertial complex-value memristor neural network anti-synchronization control method which adopts a self-adaptive anti-synchronization controller. Compared with a common controller, the adaptive controller has wider application range, so that the driving system and the response system are more convenient to achieve anti-synchronization.
Example 2:
the embodiment mainly comprises two parts of contents:
the effectiveness of the designed desynchronized controller in the desynchronized control method of the inertial complex-valued memristor neural network provided in the embodiment 1 is theoretically proved.
Secondly, aiming at the driving system and the response system which are constructed based on the inertial complex value memristor neural network in the embodiment 1 by a numerical simulation method, whether the driving system and the response system reach desynchronization or not is judged.
(neither theoretical demonstration nor simulation experiment is intended to limit the invention, in other embodiments, simulation experiments may be omitted, or other experimental schemes may be used to verify the performance of the neural network system.)
1. Proof of theory
1. In order to analyze and prove that the process is simpler, more convenient and clearer, the complex value system is split into two equivalent real value systems for analysis. An anti-synchronous error system is established by combining an anti-synchronous controller, a driving system and a response system, and the real part and the imaginary part of the error system are separated to obtain:
compared with an inertial complex value memristor neural network model before separation of a real part and an imaginary part: in the separated model, all the quantities with the superscript R are real parts of corresponding quantities in the inertial complex-valued memristor neural network model before separation; all the quantities with the superscript I are the imaginary part of the corresponding quantities in the inertial complex-valued memristor neural network model before separation.
For the drive system and the response system, if desynchronization needs to be achieved by the designed adaptive feedback controller, three assumptions first need to be satisfied:
suppose 1: activation function f q (. Cndot.) is Lipohsz continuous, i.e. there is a constant μ q >0, such that
|f q (r q (t))-f q (s q (t))|≤μ q |r q (t)-s q (t)|
Wherein all r q (t)，
Suppose 2: time lag sigma q (t) (q=1, 2, …, n) satisfies
0≤σ q (t)≤σ 1 ，
Wherein sigma 1 Sum sigma 2 Is a positive constant.
Suppose 3: there is a positive constant k pq (p, q=1, 2,) n is such that the following formula holds
Under the assumption that 1-3 holds, if a constant l exists pq >0，m pq >0，δ pq >0，η pq >0 and lambda.gtoreq.1, so that the following inequality holds true
So that the drive system and the response system can be asymptotically de-synchronized under the influence of the controller. Wherein, 
2. solving and proving: the lyapunov function was constructed as:
wherein,
The constructed lyapunov function is derived by assuming 1-3 and Young inequality:
will be
And->
The method comprises the following steps:
can be obtained according to the condition hypothesis
Thereby, an anti-synchronization error can be obtainedGradually tending toward 0, i.e., the drive system and the response system reach anti-synchronization.
2. Numerical simulation
In this embodiment, taking the two-dimensional inertial complex value memristor neural network system with unbounded distribution time lag as an example, the model is determined as follows:
wherein the activation function is f q (r q (·))＝tanh(x(·))+itanh(y(·))，K pq (θ)＝e -θ ，α 1 ＝α 2 ＝1,ε 1 ＝0.3，ε 2 ＝0.7，d 1 ＝0.8，d 2 ＝1.2，κ pq ＝1，
Memristance weight is selected to be +>
Adaptive feedback controller adaptive update rate is set to +.>
Calculated to obtain
FIG. 3 shows a variation curve of the anti-synchronization error in a two-dimensional inertial complex-valued memristive neural network system. Whereas fig. 4 and 5 show a trace map of the real states of the drive system and the response system, and a trace map of the imaginary states of the drive system and the response system, respectively.
Claims (2)
1. The secret communication method based on the inertial complex value memristor neural network is characterized by comprising the following steps of:
step S1: based on the inertia complex-valued memristor neural network, a driving system and a response system are constructed; the step S1 specifically comprises the following steps:
step S11: establishing a driving system of an inertial complex value memristor neural network;
the state equation for establishing the inertial complex value memristor neural network with infinite distribution time lag is as follows:
wherein r is p (t) is the state of the p-th neuron, n is the number of neurons, ε p And d p Is a system parameter, f q (. Cndot.) is an activation function, sigma q (t) represents discrete time lag, K pq (t) is an infinite distribution time-lag kernel real value function, and the memristor weight value a pq (r p (t))，b pq (r p (t))，c pq (r p (t)) satisfy respectively:
wherein, the switching threshold T i >0；
And performing variable substitution order reduction processing on a state equation of the inertia complex value memristor neural network with infinite distribution time lag to obtain a state equation of a driving system, wherein the state equation is as follows:
wherein, 
α p is a constant, beta p ＝d p -α p ，γ p ＝β p α p -ε p Let->
Step S12: constructing a corresponding response system according to the driving system;
establishing a response system according to the driving system, wherein the state equation of the response system is as follows:
wherein, 
u p (t) is a controller;
step S2: designing an anti-synchronization controller according to the anti-synchronization error of the driving system and the response system;
step S3: according to the anti-synchronization control method of the inertial complex-valued memristor neural network, secret communication is realized; the step S3 specifically comprises the following steps:
step S31: the transmitting end driving system generates a signal r (t), superimposes the r (t) and a ciphertext signal z (t) to obtain a superimposed signal h (t), wherein h (t) =r (t) +z (t), and then transmits the superimposed signal to the receiving end through a channel;
step S32: the receiving end receives the superposition signal h (t), the response system generates an anti-synchronization signal r (t), the r (t) is in anti-synchronization with the r (t), and the received superposition signal h (t) and the r (t) are superposed again to obtain a ciphertext signal z '(t), and z' (t) =h (t) +r (t).
2. The secret communication method based on the inertial complex-valued memristor neural network according to claim 1, wherein the step S2 specifically comprises the following steps:
step S21: defining an anti-synchronization error of a driving system and a response system;
the anti-synchronization error of the driving system and the response system is set as
Step S22: designing a self-adaptive anti-synchronization controller;
the self-adaptive anti-synchronization controller is designed as follows:
wherein->
And->
For real part error->
And->
For imaginary part error->
And
for adaptive update rate, λ is a constant greater than 1. />
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