Secure communication method based on multi-modal inertial neural network under deception attack

Abstract

The application discloses a secure communication method based on a multi-modal inertial neural network under a deception attack, comprising the following steps: a multi-modal inertial neural network system with random disturbance and mixed time delay is established; a target system is established according to the multi-modal inertial neural network system; a synchronization error is set and a synchronization error system is constructed according to the multi-modal inertial neural network system and the target system; an attack-resistant controller is designed by fully considering the deception attack in the communication network; the multi-modal inertial neural network system is exponentially synchronized with the target system under the action of the attack-resistant controller, so that the encryption and decryption of the plaintext signal are successfully completed, and the secure communication method is further realized; a multi-modal inertial neural network model is built, and the exponential synchronization effect and the effectiveness of the model in secure communication are verified through numerical simulation. The application not only can achieve the secure communication effect, but also can resist the communication network attack, has low control cost and high safety.

Description

Technical Field

[0001] This invention relates to the field of next-generation information technology, specifically to a secure communication method based on a multimodal inertial neural network under deception attacks. Background Technology

[0002] With the rapid development of communication technology, more and more information exchange relies on network transmission, such as confidential documents and digital images. Therefore, ensuring secure communication has become a critical issue. Research has found that the synchronization performance of inertial neural networks significantly improves the security of data communication. Synchronization of inertial neural networks refers to multiple inertial neural networks reaching a common trajectory, such as a common equilibrium, limit cycle, or chaotic trajectory. On the other hand, the structure and parameters of many real-world systems often face unpredictable changes. In this context, Markov hopping systems demonstrate excellent ability to describe these systems. A Markov hopping system is a multimodal hybrid system where transitions between different modes follow the principles of Markov chains. This multimodal system can effectively simulate various emergency situations that may be encountered in real-life systems, such as sudden changes in system parameters, component failures, or maintenance. Therefore, the synchronization performance of multimodal inertial neural network systems following Markov chains has broad application prospects in the field of communication security, especially in secure communication.

[0003] In secure communications, communication networks typically face various threats from adversaries. In particular, due to technological limitations or constraints of physical components, data transmission between sensors, controllers, and other devices is vulnerable to malicious attacks. For example, spoofing attacks, a common type of network attack, maliciously tamper with transmitted data, thereby compromising the integrity of control signals. Therefore, researching the application of multimodal inertial neural network synchronization performance under spoofing attacks in secure communications is of great significance. Summary of the Invention

[0004] The purpose of this invention is to provide a secure communication method based on a multimodal inertial neural network under deception attacks, so as to solve the synchronization problem of multimodal inertial neural networks with random perturbations and mixed time delays under deception attacks, and to apply it to the field of information security, thereby achieving the function of secure communication.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a secure communication method based on a multimodal inertial neural network under deception attacks, comprising the following steps:

[0006] Step S1: Establish a multimodal inertial neural network system with random perturbations and mixed time delays, whose dynamic equations are:

[0007]

[0008] in, N represents the number of nodes in the neural network system; f(x) represents the state variable of the p-th node at time t. p (t))=[f1(x p1 (t)),…,f n (x pn (t))] T f(x) p (t-δ(t))=[f1(x p1 (t-δ(t))),…,f n (x pn (t-δ(t)))] T and f(x) p (s))=[f1(x p1 (s)),…,f n (x pn (s))] T Let f be the activation function of a neuron and satisfy |f p (y)-f p (x)|≤l p |yx|, where l p The given value is a positive constant and y ≠ x is a known parameter; Let represent the inertia term; δ(t) and τ(t) represent the discrete time delay and distributed time delay, respectively, and satisfy 0 < δ(t) ≤ δ and 0 < τ(t) ≤ τ. Indicates the external input of the system; and Represents a positive definite diagonal matrix; Represents n-dimensional Euclidean space. Represents an n×n real matrix; and Represents the connection weight matrix; φ p (s) and ψ p (s) is a continuous bounded function; r(t) is a right-continuous Markov process with a value of And the following mode transition probabilities are given:

[0009]

[0010] Where χ>0 and satisfies π ij ≥0 (i≠j) represents the transition probability from the i-th mode to the j-th mode. c represents the coupling strength. G represents the internal coupling positive definite matrix, G = (G pq (r(t))) N×NLet G represent the coupling weight configuration matrix; if the q-th node is connected to the p-th node (p≠q), then G... pq (r(t))>0, otherwise G pq (r(t)) = 0, and the diagonal elements of G are defined as ρ(t,x p (t),r(t)): Represents the intensity of random disturbances experienced by the system and satisfies |ρ(t,x)| p (t),r(t))| 2 ≤Ξ p (i)|x p (t)| 2 , among which Ξ p (i) are positive constants; W(t) represents the expression defined in the full probability space. Brownian motion on Ω, where Ω is the sample space. For a subset of the sample space, For probability; u p (t) represents the anti-attack controller;

[0011] The multimodal inertial neural network with random perturbations and mixed time delays is subjected to variable substitution to reduce its order. The substitution variables are set as follows: The system is then rewritten as follows:

[0012]

[0013] Where, C(r(t))=C(r(t))+I n -D(r(t)), I n φ represents an n-order identity matrix; p (s), ψ p (s) and Δ p (s) is a continuous bounded function;

[0014] Step S2: Based on the multimodal inertial neural network system, establish the target system as follows:

[0015]

[0016] in, φ represents the state variables of the target system. * (ω) and ψ * (ω) is a continuous bounded function; the other performance indicators of the target system are the same as those of the multimodal inertial neural network with random perturbations and mixed time delays described in step S1;

[0017] The target system is subjected to variable substitution to reduce its order, with the substitution variable set as follows: The system is then rewritten as follows:

[0018]

[0019] Where, C(r(t))=C(r(t))+I n -D(r(t)), φ * (ω), ψ * (ω) and Δ * (ω) is a continuous bounded function;

[0020] Step S3: Based on the multimodal inertial neural network system and the target system, set the synchronization error and construct the synchronization error system, specifically including the following steps:

[0021] Step S3-1: Set the synchronization error between the multimodal inertial neural network system and the target system as: e p (t)=x p (t)-S(t);

[0022] Step S3-2: Based on the aforementioned synchronization error, construct the synchronization error system as follows:

[0023]

[0024] The error system is subjected to variable substitution to reduce its order, with the substitution variable set as follows: The system is then rewritten as follows:

[0025]

[0026] Among them, g(e p (t))=f(x p (t))-f(S(t)), g(e p (t-δ(t)))=f(x p (t-δ(t)))-f(S(t-δ(t))), g(e p (s))=f(x p (s))-f(S(s));

[0027] Step S4: Taking full account of spoofing attacks in the communication network, and based on the synchronization error system constructed in Step S3, design an anti-attack controller u under spoofing attacks. p (t), so that the multimodal inertial neural network system is in the anti-attack controller u p Under the action of (t), the exponent is synchronized with the target system, thereby successfully completing the encryption and decryption of plaintext signals and further realizing secure communication.

[0028] Step S5: Build a multimodal inertial neural network model and verify its exponential synchronization effect under deception attacks and its effectiveness in secure communication through numerical simulation.

[0029] Furthermore, step S4 specifically includes the following steps:

[0030] Step S4-1: Design an anti-attack controller for deception attacks. p (t) is:

[0031]

[0032] Where θ1, θ2, and θ3 are positive constants; [t 2k ,t 2k+1 ) and [t 2k+1 ,t 2k+2 ) represent the control time interval and rest time interval of the anti-attack controller, respectively; α(t) is the spoofing attack signal and follows a Bernoulli distribution, defined as: The probability is Let be the expected value of random variable a; h(·) is a nonlinear function satisfying |h(·)|≤h1, where h1 is a positive constant; R p (t) represents the anti-attack term, specifically:

[0033] R p (t)=-η p (t)q(z p (t))-msign(q(z p (t)))

[0034] Where, q(·): For quantizer, m is a positive integer Represents the set of real numbers. These are the initial quantization parameters. To quantize the density, the specific quantization function is defined as follows:

[0035]

[0036] in, q(m * ) is a quantified value. It is the precise parameter of the quantizer; η p (t) is the adaptive exponential update rate against the attack and satisfies the equation:

[0037]

[0038] Where, βp α and ε p The values ​​are positive constants and satisfy the inequality m(1+αθ1)≥αθ2h1; the relevant parameters in the anti-attack controller satisfy the following inequalities:

[0039]

[0040] Where, η p and For positive integers,

[0041]

[0042] Step S4-2: Apply the anti-attack controller to the multimodal inertial neural network system, so that the multimodal inertial neural network system can also be exponentially synchronized with the target system under deception attacks;

[0043] Step S4-3: After the multimodal inertial neural network system is exponentially synchronized with the target system, the transmitting end acquires the chaotic signal y generated by the multimodal inertial neural network system. p (t) is used as the encryption signal, and the receiving end obtains the chaotic signal v(t) generated by the target system as the key signal;

[0044] Step S4-4: The sending end encrypts the signal y p (t) and plaintext signal Z p (t) performs encryption operations to obtain the ciphertext signal H. p (t)=y p (t)+Z p (t);

[0045] Step S4-5: The transmitting end transmits the encrypted signal H p (t) is transmitted to the receiving end via the transmission channel, and the receiving end receives the ciphertext signal H via the transmission channel. p (t);

[0046] Step S4-6: The receiving end transmits the received ciphertext signal H p (t) and key signal v p (t) is used to perform decryption operations to obtain the decrypted plaintext signal Z′. p (t)=H p (t)-v p (t).

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. Taking into account factors such as communication delay and random interference faced by the system, this invention specifically introduces random perturbation and hybrid time delay to form a more general multimodal inertial neural network, thereby making this invention have a wider range of application prospects.

[0049] 2. In order to resist spoofing attacks that modify transmitted data with a certain probability, this invention designs an adaptive anti-attack controller for multimodal inertial neural networks. This controller has the ability to automatically adjust its own parameters according to external attacks.

[0050] 3. Considering that the signal transmission of real-time systems is often constrained by communication capacity and bandwidth limitations, the present invention performs quantification processing on the anti-attack controller. This processing method helps to reduce control costs and effectively alleviate problems caused by communication resource limitations. Attached Figure Description

[0051] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0052] In the attached diagram:

[0053] Figure 1 This is a flowchart of a first specific embodiment of the secure communication method based on a multimodal inertial neural network under deception attack according to the present invention;

[0054] Figure 2 The system state y in the numerical simulation of this invention without the action of an anti-attack controller. p The state trajectories of v(t) and v(t) are given, where (a) represents the system state y under the action of the unattack-resistant controller. p1 (a) is the state trajectory of v1(t) and v1(t); (b) is the system state y under the action of the unattack-resistant controller. p2 The state trajectories of v1(t) and v2(t);

[0055] Figure 3 The system state y under the action of the anti-attack controller in the numerical simulation of this invention. p The state trajectories of v(t) and v(t) are given, where (a) represents the system state y under the action of the anti-attack controller. p1 (a) is the state trajectory of v1(t) and v1(t); (b) is the system state y under the action of the anti-attack controller. p2 The state trajectories of v1(t) and v2(t);

[0056] Figure 4 This is the state trajectory of the synchronization error system without a controller in the numerical simulation of this invention, where (a) is the state trajectory of the synchronization error system z without an anti-attack controller. p1(t) is the state trajectory; (b) is the synchronization error system z under the action of an anti-attack controller. p2 The state trajectory of (t);

[0057] Figure 5 This is the state trajectory of the synchronization error system under the action of the anti-attack controller in the numerical simulation of this invention, where (a) is the state trajectory of the synchronization error system z under the action of the anti-attack controller. p1 (t) is the state trajectory; (b) is the synchronization error system z under the action of the anti-attack controller. p2 The state trajectory of (t);

[0058] Figure 6 This is a graph of the Markov process r(t) in the numerical simulation of this invention.

[0059] Figure 7 This is a graph of the deception attack signal α(t) in the numerical simulation of this invention;

[0060] Figure 8 This is a schematic diagram of signal transmission during secure communication provided in an embodiment of the present invention;

[0061] Figure 9 The figure shows the numerical simulation results of the secure communication method provided in the embodiment of the present invention, wherein (a) is the encrypted signal y. p (t) is the state trajectory; (b) is the plaintext signal Z. p (t) represents the state trajectory; (c) represents the ciphertext signal H. p (d) is the state trajectory of the key signal v(t); (e) is the state trajectory of the decrypted signal Z′. p (t) represents the state trajectory; (f) represents the plaintext signal Z. p (t) and the decrypted signal Z' p (t) The state trajectory of the error. Detailed Implementation

[0062] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0063] Example 1

[0064] like Figure 1 As shown, this embodiment provides a secure communication method based on a multimodal inertial neural network under deception attacks. The secure communication method includes the following steps:

[0065] Step S1: Establish a multimodal inertial neural network system with random perturbations and mixed time delays, whose dynamic equations are:

[0066]

[0067] in, N represents the number of nodes in the neural network system; f(x) represents the state variable of the p-th node at time t. p (t))=[f1(x p1 (t)),…,f n (x pn (t))] T f(x) p (t-δ(t))=[f1(x p1 (t-δ(t))),…,f n (x pn (t-δ(t)))] T and f(x) p (s))=[f1(x p1 (s)),…,f n (x pn (s))] T Let f be the activation function of a neuron and satisfy |f p (y)-f p (x)|≤l p |yx|, where l p The given value is a positive constant and y ≠ x is a known parameter; Let represent the inertia term; δ(t) and τ(t) represent the discrete time delay and distributed time delay, respectively, and satisfy 0 < δ(t) ≤ δ and τ(t). Indicates the external input of the system; and Represents a positive definite diagonal matrix; Represents n-dimensional Euclidean space. Represents an n×n real matrix; and Represents the connection weight matrix; φ p (s) and ψ p (s) is a continuous bounded function; r(t) is a right-continuous Markov process with a value of And the following mode transition probabilities are given:

[0068]

[0069] Where χ>0 and satisfies π ij ≥0 (i≠j) represents the transition probability from the i-th mode to the j-th mode. c represents the coupling strength. G represents the internal coupling positive definite matrix, G = (G pq(r(t))) N×N Let G represent the coupling weight configuration matrix; if the q-th node is connected to the p-th node (p≠q), then G... pq (r(t))>0, otherwise G pq (r(t)) = 0, and the diagonal elements of G are defined as Represents the intensity of random disturbances experienced by the system and satisfies |ρ(t,x)| p (t),r(t))| 2 ≤Ξ p (i)|x p (t)| 2 , among which Ξ p (i) are positive constants; W(t) represents the expression defined in the full probability space. Brownian motion on Ω, where Ω is the sample space. For a subset of the sample space, For probability; u p (t) represents the anti-attack controller;

[0070] The multimodal inertial neural network with random perturbations and mixed time delays is subjected to variable substitution to reduce its order. The substitution variables are set as follows: The system is then rewritten as follows:

[0071]

[0072] Where, C(r(t))=C(r(t))+I n -D(r(t)), I n φ represents an n-order identity matrix; p (s), ψ p (s) and Δ p (s) is a continuous bounded function;

[0073] Step S2: Based on the multimodal inertial neural network system, establish the target system as follows:

[0074]

[0075] in, φ represents the state variables of the target system. * (ω) and ψ * (ω) is a continuous bounded function; the other performance indicators of the target system are the same as those of the multimodal inertial neural network with random perturbations and mixed time delays described in step S1;

[0076] The target system is subjected to variable substitution to reduce its order, with the substitution variable set as follows: The system is then rewritten as follows:

[0077]

[0078] Where, C(r(t))=C(r(t))+I n -D(r(t)), φ * (ω), ψ * (ω) and Δ * (ω) is a continuous bounded function;

[0079] Step S3: Based on the multimodal inertial neural network system and the target system, set the synchronization error and construct the synchronization error system, specifically including the following steps:

[0080] Step S3-1: Set the synchronization error between the multimodal inertial neural network system and the target system as: e p (t)=x p (t)-S(t);

[0081] Step S3-2: Based on the aforementioned synchronization error, construct the synchronization error system as follows:

[0082]

[0083] The error system is subjected to variable substitution to reduce its order, with the substitution variable set as follows: The system is then rewritten as follows:

[0084]

[0085] Among them, g(e p (t))=f(x p (t))-f(S(t)), g(e p (t-δ(t)))=f(x p (t-δ(t)))-f(S(t-δ(t))), g(e p (s))=f(x p (s))-f(S(s));

[0086] Step S4: Taking full account of spoofing attacks in the communication network, and based on the synchronization error system constructed in Step S3, design an anti-attack controller u under spoofing attacks. p (t), so that the multimodal inertial neural network system is in the anti-attack controller u p Under the action of (t), the exponent is synchronized with the target system, thereby successfully completing the encryption and decryption of plaintext signals and further realizing secure communication.

[0087] Step S5: Build a multimodal inertial neural network model and verify its exponential synchronization effect under deception attacks and its effectiveness in secure communication through numerical simulation.

[0088] In this embodiment, step S4 specifically includes the following steps:

[0089] Step S4-1: Design an anti-attack controller for deception attacks. p (t) is:

[0090]

[0091] Where θ1, θ2, and θ3 are positive constants; [t 2k ,t 2k+1 ) and [t 2k+1 ,t 2k+2 ) represent the control time interval and rest time interval of the anti-attack controller, respectively; α(t) is the spoofing attack signal and follows a Bernoulli distribution, defined as: The probability is Let be the expected value of random variable a; h(·) is a nonlinear function satisfying |h(·)|≤h1, where h1 is a positive constant; R p (t) represents the anti-attack term, specifically:

[0092] R p (t)=-η p (t)q(z p (t))-msign(q(z p (t)))

[0093] in, For quantizer, m is a positive integer Represents the set of real numbers. These are the initial quantization parameters. To quantize the density, the specific quantization function is defined as follows:

[0094]

[0095] in, q(m * ) is a quantified value. It is the precise parameter of the quantizer; η p (t) is the adaptive exponential update rate against the attack and satisfies the equation:

[0096]

[0097] Where, β p α and εp The values ​​are positive constants and satisfy the inequality m(1+αθ1)≥αθ2h1; the relevant parameters in the anti-attack controller satisfy the following inequalities:

[0098]

[0099] Where, η p and For positive integers,

[0100] Step S4-2: Apply the anti-attack controller to the multimodal inertial neural network system, so that the multimodal inertial neural network system can also be exponentially synchronized with the target system under deception attacks;

[0101] Step S4-3: After the multimodal inertial neural network system is exponentially synchronized with the target system, the transmitting end acquires the chaotic signal y generated by the multimodal inertial neural network system. p (t) is used as the encryption signal, and the receiving end obtains the chaotic signal v(t) generated by the target system as the key signal;

[0102] Step S4-4: The sending end encrypts the signal y p (t) and plaintext signal Z p (t) performs encryption operations to obtain the ciphertext signal H. p (t)=y p (t)+Z p (t);

[0103] Step S4-5: The transmitting end transmits the encrypted signal H p (t) is transmitted to the receiving end via the transmission channel, and the receiving end receives the ciphertext signal H via the transmission channel. p (t);

[0104] Step S4-6: The receiving end transmits the received ciphertext signal H p (t) and key signal v p (t) is used to perform decryption operations to obtain the decrypted plaintext signal Z′. p (t)=H p (t)-v p (t).

[0105] It is worth noting that, considering factors such as communication delays and random interference faced by the system, this invention specifically introduces random disturbances and hybrid time delays to form a more general multimodal inertial neural network, thus giving the invention a wider range of application prospects. To resist spoofing attacks that modify transmitted data with a certain probability, an adaptive anti-attack controller is designed for the multimodal inertial neural network. This controller has the ability to automatically adjust its own parameters according to external attacks. Considering that the signal transmission of real-time systems is often constrained by communication capacity and bandwidth limitations, the anti-attack controller is subjected to quantization processing. This processing method helps to reduce control costs and effectively alleviate problems caused by communication resource limitations.

[0106] Example 2

[0107] This embodiment mainly includes two parts:

[0108] One is to provide a theoretical proof of the effectiveness of the anti-attack controller in Example 1 in achieving synchronization between a multimodal inertial neural network system with random disturbances and mixed time delays and a target system.

[0109] Secondly, numerical simulations were used to verify the exponential synchronization effect of the multimodal inertial neural network system with random perturbations and mixed time delays and the target system in Example 1, as well as its effectiveness in secure communication.

[0110] (Theoretical proofs and simulation experiments are not intended to limit the present invention. In other embodiments, simulation experiments may not be performed, or other experimental schemes may be used to verify the performance of the neural network system.)

[0111] I. Theoretical Proof

[0112] The definition of synchronization and the lemma to be used are given below.

[0113] Definition 1: If the system error state satisfies Where W>0,

[0114] This indicates that a multimodal inertial neural network system with random perturbations and mixed time delays is exponentially synchronized with the target system under the action of an anti-attack controller.

[0115] Lemma 1: Define a random function V p (t,e p The infinitesimal operator for (t),i) is:

[0116]

[0117] in,

[0118] Lemma 2: Suppose V(t,e(t),r(t)) is A non-negative continuous function on the interval [0, 1], satisfying the following conditions:

[0119]

[0120] Where ε1, ε2, v, and μ are positive constants. If ε1+ε2>0, ε1>v+μδ, So there are

[0121]

[0122] Where t≥t0, ρ>0 are equations The root,

[0123] Next, we will establish some coefficient-based criteria to ensure that the multimodal inertial neural network system with random perturbations and mixed time delays and the target system are exponentially synchronized;

[0124] Construct the Lyapunov function as follows:

[0125]

[0126] When t∈[t 2k ,t 2k+1 When ), according to Lemma 1, calculate have to:

[0127]

[0128] Where trace(A) is the trace of matrix A.

[0129] According to 0 < δ(t) ≤ δ, 0 < τ(t) ≤ τ and |f p (y)-f p (x)|≤l p Given |yx|, we can obtain the following inequality:

[0130]

[0131]

[0132] Therefore, we further obtain:

[0133]

[0134] Among them, for Expanding, we get:

[0135]

[0136] The quantization function satisfies the following inequality:

[0137]

[0138] Therefore, we can obtain:

[0139]

[0140] Similarly, when t∈[t 2k+1 ,t 2k+2 When ), we can obtain:

[0141]

[0142] in,

[0143] Therefore, when t∈[t 2k ,t 2k+1 When ), based on the above derivation, we can obtain:

[0144]

[0145] in,

[0146] From Itoh's formula and the above equation, we can obtain:

[0147]

[0148] When t∈[t 2k+1 ,t 2k+2 When ), we can obtain:

[0149]

[0150] in,

[0151] Therefore, according to Lemma 2, we can obtain:

[0152]

[0153] For any Does a positive constant w exist? p (i) Makes the inequality true: V p (t,e p (t),i)≥w p (i)|e p (t)| 2 ;

[0154] Therefore, we can obtain:

[0155]

[0156] in,

[0157] Therefore, we can obtain:

[0158]

[0159] in, Therefore, according to Definition 1, a multimodal inertial neural network system with random perturbations and mixed time delays is exponentially synchronized with the target system under the action of an anti-attack controller.

[0160] II. Numerical Simulation

[0161] In this embodiment, consider the following multimodal inertial neural network system with 4 nodes:

[0162]

[0163] Where p = 1, 2, 3, 4, r(t) is a Markov chain with values ​​of 1, 2, 3, 4. x p (t)=(x p1 (t),x p2 (t)) T f(x) p (t))=(tanh(x p1 (t)),tanh(x p2 (t))) T ;ρ(t,x p (t),1)=(0.15sin(x p1 (t)),0.15sin(x p2 (t))) T ,ρ(t,x p (t),2)=(0.2x p1 (t), 0.2x p2 (t)) T ;I(1)=(1.2,1.8) T ,I(2)=(1.6,2.2) T , where (1) is the value for mode 1, and (2) is the value for mode 2; the mixed time-varying delay δ(t) = 0.2|cost|, τ(t) = 0.15sin 2 t; can be used to calculate l p =1, δ=0.2, τ=0.15.

[0164] By substituting variables into the above system, we obtain:

[0165]

[0166] The corresponding target system description is as follows:

[0167]

[0168] in, Coupling strength c = 1, G 1,1 (1) = G 1,1 (2) = -1, G 1,2 (1) = G 1,2 (2) = 1, G 1,3 (1) = G 1,3 (2) = 0, G 1,4 (1) = G 1,4 (2) = 0, G 2,1 (1) = G 2,1 (2) = 1, G 2,2 (1) = G 2,2 (2) = -2, G 2,3 (1) = G 2,3 (2) = 1, G 2,4 (1) = G 2,4 (2) = 0, G 3,1 (1) = G 3,1 (2) = 0, G 3,2 (1) = G 3,2 (2) = 1.5, G 3,3 (1) = G 3,3 (2) = -2, G 3,4 (1) = G 3,4 (2) = 0.1, G 4,1 (1) = G 4,1 (2) = 0.5, G 4,2 (1) = G 4,2 (2) = 0, G 4,3 (1) = G 4,3 (2) = 0, G 4,4 (1) = G 4,4 (2) = -1;

[0169] Select parameter γ p (1)=1,γ p (2) = 1.1; we can calculate v = 0.0968, μ = 0.0231, Θ p1 =-1.118, Θ p =1.217; Adaptive exponential update rate:

[0170]

[0171] Where, β p =0.2, ε p =0.6, quantization density θ1 = 0.05, θ2 = 0.5, θ3 = 0.5, m = 0.5, nonlinear function h(·) = tanh(·), deception attack probability α = 0.5, control interval interval set to Calculations show that the inequality satisfies: -Θ p1 -ε p >0, Therefore, ε1 = 0.6, ε2 = 1.25, satisfying ε1 > v + μδ, equation The root ρ = 0.49 satisfies

[0172] The simulation results of the multimodal inertial neural network system with random perturbations and mixed time delays and the target system under the parameters set above are as follows: Figure 2 The system state y under the action of the non-anti-attack controller p The state trajectories of v(t) and v(t) are given, where (a) represents the system state y under the action of the unattack-resistant controller. p1 (a) is the state trajectory of v1(t) and v1(t); (b) is the system state y under the action of the unattack-resistant controller. p2 The state trajectories of v1(t) and v2(t); Figure 3 The system state y under the action of the anti-attack controller p The state trajectories of v(t) and v(t) are given, where (a) represents the system state y under the action of the anti-attack controller. p1 (a) is the state trajectory of v1(t) and v1(t); (b) is the system state y under the action of the anti-attack controller. p2 The state trajectories of v1(t) and v2(t); Figure 4 Let z be the state trajectory of the synchronization error system without a controller, where (a) is the state trajectory of the synchronization error system z without an anti-attack controller. p1 (t) is the state trajectory; (b) is the synchronization error system z under the action of an anti-attack controller. p2 The state trajectory of (t); Figure 5 Let z be the state trajectory of the synchronization error system under the action of the anti-attack controller, where (a) is the state trajectory of the synchronization error system z under the action of the anti-attack controller. p1 (t) is the state trajectory; (b) is the synchronization error system z under the action of the anti-attack controller. p2 The state trajectory of (t); by Figure 4 and Figure 5 It can be seen that without an anti-attack controller, the state trajectory of the synchronization error system continues to oscillate. After the anti-attack controller is added, the state trajectory of the synchronization error system gradually converges to 0. Figure 6 The graph of the Markov process r(t); Figure 7 The graph shows the deception attack signal α(t). Figures 2-5This demonstrates that a multimodal inertial neural network system with random perturbations and mixed time delays can exponentially synchronize with the target system under the action of an anti-attack controller, thus verifying the exponential synchronization performance. Figure 8 This is a schematic diagram of signal transmission during secure communication in this embodiment; Figure 9 The figure shows the numerical simulation results of the secure communication method in this embodiment, where (a) is the encrypted signal y. p (t) is the state trajectory; (b) is the plaintext signal Z. p (t) represents the state trajectory; (c) represents the ciphertext signal H. p (d) is the state trajectory of the key signal v(t); (e) is the state trajectory of the decrypted signal Z′. p (t) represents the state trajectory; (f) represents the plaintext signal Z. p (t) and the decrypted signal Z′ p (t) The state trajectory of the error; from Figure 9 It can be seen that the ciphertext signal effectively guarantees the security of the plaintext signal; the error between the decrypted signal and the initial plaintext signal is 0, successfully achieving the decryption function. In summary, when the multimodal inertial neural network system and the target system are synchronized, secure communication can be achieved.

[0173] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1.A secure communication method based on multi-modal inertial neural network under deception attack, characterized in that, The method comprises the following steps: Step S1: a multi-modal inertial neural network system with random disturbance and mixed time delay is established, and the dynamic equation is: wherein, N denotes the number of nodes of the neural network system; x p (t) = denotes the state variable of the pth node at time t; f(x p (t)) = [f1(x p1 (t)), …, f n (x pn (t))] T , f(x p (t - δ(t)) = [f1(x p1 (t - δ(t))), …, f n (x pn (t - δ(t)))] T and f(x p (s)) = [f1(x p1 (s)), …, f n (x pn (s))] T denotes the activation function of the neuron and satisfies |f p (y) - f p (x)| ≤ l p |y - x|, where l p is a positive constant and y ≠ x is a known parameter; denotes the inertia term; δ(t) and τ(t) denote the discrete and distributed time delays, respectively, and satisfy 0 < δ(t) ≤ δ and 0 < τ(t) ≤ τ, denotes the external input of the system; and denotes a positive definite diagonal matrix; represents an n-dimensional Euclidean space, denotes an n x n real matrix; and denotes a connection weight matrix; φ p (s) and ψ p (s) are continuous bounded functions; r(t) is a right-continuous Markov process with values and has the following mode transition probabilities: where χ > 0 and satisfies π ij ≥ 0 (i≠j) represents the transition probability from the ith modality to the jth modality, c represents the coupling strength, represents an internal coupling positive definite matrix, G = (G pq (r(t)) N×N represents a coupling weight configuration matrix; if the qth node has a connection with the pth (p≠q) node, G pq (r(t)) > 0, otherwise G pq (r(t)) = 0, and the diagonal elements of G are defined as represents the random disturbance strength suffered by the system and satisfies |ρ(t, x p (t), r(t))| 2 ≤ Ξ p (i) |x p (t)| 2 , where Ξ p (i) is a normal number; W(t) represents a Brown motion defined on a complete probability space , where Ω is a sample space, is a sample space subset, is a probability; u p (t) is an attack-resistant controller; The multi-modal inertial neural network with random disturbance and mixed time delay is subjected to variable substitution and reduction, and a substitution variable is set as Further, the system is rewritten in the following form: where C(r(t)) = C(r(t)) + I n - D(r(t)), I n denotes the n x n identity matrix; φ p (s), ψ p (s) and Δ p (s) are continuous bounded functions; Step S2: according to the multi-modal inertial neural network system, the target system is established as: wherein, denotes a state variable of the target system; φ * (ω) and ψ * (ω) are continuous bounded functions; other performance indices in the target system and in the multi-modal inertial neural network with stochastic perturbation and hybrid time-delay in step S1 are the same; The target system is subjected to variable substitution and reduction processing, and a replacement variable is set as The system is further rewritten in the following form: where C(r(t)) = C(r(t)) + I n - D(r(t)), φ * (ω), ψ * (ω), and Δ * (ω) are continuous bounded functions; Step S3: according to the multi-modal inertial neural network system and the target system, the synchronization error is set, and the synchronization error system is constructed, which comprises the following steps: Step S3-1: Set the synchronization error of the multi-modal inertial neural network system and the target system as: e p (t) = x p (t) - S(t); Step S3-2: according to the synchronization error, the synchronization error system is constructed as: The error system is subjected to variable substitution and order reduction processing, and the substitution variable is set as Further, the system is rewritten in the following form: where, g(e p (t)) = f(x p (t)) - f(S(t)), g(e p (t - δ(t))) = f(x p (t - δ(t))) - f(S(t - δ(t))), g(e p (s)) = f(x p (s)) - f(S(s)); Step S4: Considering the spoofing attack in the communication network, an anti-attack controller u is designed under the spoofing attack according to the synchronization error system constructed in step S3 p (t) such that the multi-modal inertial neural network system is exponentially synchronized with the target system under the action of the anti-attack controller u p (t), thereby successfully completing the encryption and decryption of the plaintext signal and further realizing secure communication. Step S5: a multi-modal inertial neural network model is built, and the exponential synchronization effect under the deception attack and the effectiveness in secure communication are verified through numerical simulation; Step S4 comprises the following steps: Step S4-1: Designing attack-resistant controller u under spoofing attack p (t) is: where θ1, θ2, and θ3 are constants;[t 2k ,t 2k+1 ) and [t 2k+1 ,t 2k+2 ) represent the control time interval and the rest time interval of the anti-attack controller, respectively; α(t) is a deceptive attack signal and satisfies a Bernoulli distribution, defined as: The probability is is the mathematical expectation of the random variable a; h(·) is a nonlinear function and satisfies |h(·)|≤h1, where h1 is a constant; R p (t) is an anti-attack term, specifically: wherein is a quantizer, m is a positive integer, represents the set of real numbers, is an initial quantization parameter, is a quantization density, and the specific quantization function is defined as follows: wherein, q(m * ) is the quantized value, is the precision parameter of the quantizer; η p (t) is the adaptive exponential update rate for the attack and satisfies the equation: where β p , a and ε p are normal numbers and satisfy the inequality m(1+ a θ1)≥ a θ2h1; the relevant parameters in the anti-attack controller satisfy the following inequality: - Θ p1 - ε p > 0, wherein η p and are positive constants, γ p (i) > 0, Step S4-2: the anti-attack controller is applied to the multi-modal inertial neural network system, so that the multi-modal inertial neural network system can also be exponentially synchronized with the target system under the deception attack. Step S4-3: After the multi-modal inertial neural network system is synchronized with the target system, the sending end acquires the chaotic signal y generated by the multi-modal inertial neural network system p (t) As an encrypted signal, the receiving end acquires the chaotic signal v(t) generated by the target system as a key signal; Step S4-4: the sending end performs encryption operation on the encrypted signal y p (t) and the plaintext signal Z p (t) to obtain the ciphertext signal H p (t) = y p (t) + Z p (t); Step S4-5: The sending end sends the ciphertext signal H p (t) to the receiving end through the transmission channel, and the receiving end receives the ciphertext signal H p (t) through the transmission channel. Step S4-6: The receiving end performs a decryption operation on the received ciphertext signal H p (t) and the key signal v p (t) to obtain a decrypted plaintext signal Z' p (t) = H p (t) - v p (t).

Images