Heterogeneous underwater wireless sensor network malicious program propagation modeling method and system

Abstract

The invention belongs to the technical field of communication, and particularly relates to a heterogeneous underwater wireless sensor network malicious program propagation modeling method and system.The method comprises the steps that nodes are divided into sensor nodes and autonomous underwater vehicles, and the propagation relation between the states is determined; constructing a heterogeneous underwater wireless sensor network malicious program propagation model; calculating each stable point of which the state change rate is 0 in the constructed heterogeneous underwater wireless sensor network malicious program propagation model; and calculating a basic regeneration number according to the newly added Bayer call rate matrix and the state transition rate matrix of the heterogeneous node at the stable point. According to the method, the dynamic change process of the internal and external states of the heterogeneous nodes with different characteristics is reflected, the stable point representing that the malicious program is finally extinguished or popular is obtained, and the condition for judging the propagation stable state of the malicious program of the heterogeneous underwater wireless sensor network is given; and a theoretical basis is provided for malicious program propagation of the heterogeneous underwater wireless sensor network.

Description

Technical Field

[0001] This application belongs to the field of communication technologies, and particularly relates to a method and system for modeling the propagation of malicious programs in a heterogeneous underwater wireless sensor network. Background Art

[0002] In the field of security for heterogeneous underwater wireless sensor networks, due to limitations in underwater sensing nodes that prevent the deployment of high-intensity defense mechanisms, malicious programs can easily form large-scale propagation through the two-way diffusion effect between heterogeneous nodes. This cross-propagation mode across different types of nodes not only accelerates the spread of malicious code but also triggers more serious security crises, such as stealing marine environment perception data, interfering with underwater acoustic communication links, and damaging node hardware devices, resulting in the failure of network service availability and data confidentiality. Therefore, constructing a malicious program propagation dynamics model with the characteristics of heterogeneous node interaction, revealing the cross-infection threshold and the dynamic characteristics of the propagation path between sensor nodes and autonomous underwater vehicles, has become an important research topic for curbing this threat, and its conclusions have good theoretical value for formulating defense strategies.

[0003] In the field of malicious program propagation modeling, the analysis method based on epidemic dynamics has become an important paradigm for wireless sensor network security research. Early research introduced the susceptible-exposed-infected-recovered model into the wireless sensor network scenario, and its simulation experiments confirmed that the cross-infection mechanism between heterogeneous nodes would significantly affect the basic reproduction number of malicious program propagation. With the in-depth research, it can be found that traditional epidemic models have theoretical limitations such as fixed node state transition probabilities and the lack of underwater acoustic channel characteristics. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a method and system for modeling the propagation of malicious programs in a heterogeneous underwater wireless sensor network, which realizes the modeling of the propagation of malicious programs in a heterogeneous underwater wireless sensor network and reflects the dynamic change process of heterogeneous node states and the cross-propagation process between heterogeneous nodes.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for modeling the propagation of malicious programs in a heterogeneous underwater wireless sensor network includes the following:

[0007] Classify nodes into two types: sensor nodes and autonomous underwater vehicles, divide the categories of heterogeneous node states, and determine the propagation relationships between each state;

[0008] Construct a model for the propagation of malicious programs in a heterogeneous underwater wireless sensor network;

[0009] Calculate the stable points where the change rates of each state in the constructed model for the propagation of malicious programs in a heterogeneous underwater wireless sensor network are 0;

[0010] Calculate the basic reproduction number according to the new change rate matrix and the state transition rate matrix of heterogeneous nodes at the stable point. Preferably, divide the state categories of heterogeneous nodes, including:

[0011] When a heterogeneous node has a system vulnerability but is not infected by a malicious program, this heterogeneous node belongs to state S; when a heterogeneous node has been infected by a malicious program but has not received an attack instruction, this heterogeneous node belongs to state E;

[0012] When a heterogeneous node has been infected by a malicious program and receives an attack instruction, this heterogeneous node belongs to state I; when a heterogeneous node has immunity to the current malicious program after installing a patch program, this heterogeneous node belongs to state R;

[0013] When a heterogeneous node runs out of energy or is physically damaged and loses all its functions, this heterogeneous node belongs to state D.

[0014] Preferably, determine the propagation relationships between each state category, including the following types:

[0015] If a heterogeneous node in state S is infected by a malicious program due to the spread of the malicious program but has not received an attack instruction yet, its state transitions from state S to state E;

[0016] If a heterogeneous node in state E receives an attack instruction and has the ability to infect other nodes, its state transitions from state E to state I;

[0017] If a heterogeneous node in state I clears the malicious program due to installing a security patch and has immunity to the existing malicious program, its state transitions from state I to state R;

[0018] Any heterogeneous node will have its state transitioned to state D due to running out of energy or being physically damaged.

[0019] Preferably, construct a model for the spread of malicious programs in a heterogeneous underwater wireless sensor network, and the formula is as follows:

[0020]

[0021] Among them, Π U 、Π Aare the node update coefficients of the underwater sensor node and the autonomous underwater vehicle respectively. K1 and K2 represent the node infection rates of the underwater sensor node and the autonomous underwater vehicle respectively. K3 and K4 represent the node attack rates of the underwater sensor node and the autonomous underwater vehicle respectively. α1, α2, and α3 represent the exposure rate, immunity rate, and immune prevention rate of the underwater sensor node respectively. β1, β2, and β3 represent the exposure rate, immunity rate, and immune prevention rate of the autonomous underwater vehicle respectively. d1 and d2 represent the damage removal rates of the autonomous underwater vehicle and the underwater sensor node respectively; S U (t), E U (t), I U (t), R U (t) represent the numbers of the underwater sensor node in states S, E, I, and R at time t respectively. S A (t), E A (t), I A (t), R A (t) represent the numbers of the autonomous underwater vehicle in states S, E, I, and R at time t respectively. K 21 is the probability that an infected autonomous underwater vehicle infects susceptible lymph nodes. The transmission coefficient of the infected node that infects the autonomous underwater vehicle is K 12 ; The forward transmission coefficient between any two underwater sensor nodes is K 34 , and the reverse transmission coefficient is K 43 . Preferably, calculate the transmission coefficient of the autonomous underwater vehicle:

[0022] Suppose the autonomous underwater vehicle moves at a speed of v within time t, and its communication radius is r A , and the area it covers is:

[0023] S A = π(vt + r A ) 2 ;

[0024] In the underwater environment of L×L, the density of susceptible nodes is:

[0025]

[0026] Through the above formula, calculate the number of susceptible nodes communicating with the exposed autonomous underwater vehicle as:

[0027]

[0028] The autonomous underwater vehicle will continuously send program data packets to nearby nodes through the communication channel with a probability of ε AU ; Assume the probability of successfully receiving the data packet is σ AU , and the probability of converting from the susceptible state to the exposed state is ξSE , the probability of successful infection is calculated as:

[0029] η SE = ε AU σ AU ξ SE ;

[0030] The number of infected autonomous underwater vehicles that successfully infect susceptible nodes in an underwater wireless sensor network is calculated as follows:

[0031]

[0032] where K 21 is the probability that an infected autonomous underwater vehicle can infect susceptible lymph nodes; K 12 is the transmission coefficient of the infected nodes of the infected autonomous underwater vehicle.

[0033] Preferably, the forward propagation coefficient between any two underwater sensor nodes is K 34 , and the reverse propagation coefficient is K 43 , and the calculation formula is as follows:

[0034]

[0035] Preferably, calculate the basic reproduction number:

[0036] Assume that the infected categories include E A , E U , I A , I U , and represent the infected state variables as:

[0037]

[0038]

[0039] where F(x) represents the individuals newly entering the exposed period, and V(x) represents the process of an individual transferring from one state to another state, or being removed from the infected state;

[0040] F and V can be expressed as:

[0041]

[0042] At the disease-free steady state, the number of susceptibles at the infection-free equilibrium point is:

[0043]

[0044] The Jacobian matrices F and V are expressed under DFE as:

[0045]

[0046] The next-generation matrix can be obtained through matrix multiplication:

[0047]

[0048] By solving its characteristic equation, the basic reproduction number R0 is obtained as:

[0049]

[0050] Preferably, calculate the said new change rate matrix:

[0051]

[0052] Calculate the said state transition rate matrix:

[0053]

[0054] 9. A malicious program propagation system for heterogeneous underwater wireless sensor networks, which is used to implement the method of this application. Compared with the prior art, the beneficial effects of this application are as follows:

[0055] The present invention constructs a dynamic model for the propagation of malicious programs in heterogeneous underwater wireless sensor networks, which completely describes the susceptible-exposed-infected-repaired state transition mechanism of heterogeneous nodes and its cross-type cross-propagation path. By establishing a dynamic equation that includes the characteristics of the underwater acoustic channel and the node movement trajectory, this model not only reveals the phase transition law of the propagation of malicious programs in the two-dimensional underwater space, but also can solve the threshold parameter representing the propagation equilibrium state - when the basic reproduction number is lower than the critical threshold, the system will converge to a stable equilibrium point where the malicious program goes extinct; otherwise, a globally stable state of persistent infection will be formed. This research gives a stability discrimination inequality for the propagation of malicious programs in heterogeneous underwater wireless sensor networks from a dynamic perspective, providing a theoretical basis for the optimization of dynamic defense strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flowchart of the method for modeling the propagation of malicious programs in the heterogeneous underwater wireless sensor network of the present invention

[0057] Figure 2 It is a state transition relationship diagram of heterogeneous nodes of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0059] As Figure 1 shown, in order to solve the technical problems in the prior art, the present invention provides a method for modeling the propagation of malicious programs in a heterogeneous underwater wireless sensor network. After dividing the nodes into two types: sensor nodes and autonomous underwater vehicles, the method includes the following steps:

[0060] (1) Divide the states of heterogeneous nodes;

[0061] When a heterogeneous node has a system vulnerability but has not been infected by a malicious program, the heterogeneous node belongs to state S; when a heterogeneous node has been infected by a malicious program but has not received an attack instruction, the heterogeneous node belongs to state E;

[0062] When a heterogeneous node has been infected by a malicious program and receives an attack instruction, the heterogeneous node belongs to state I; when a heterogeneous node has installed a patch program and has immunity to the current malicious program, the heterogeneous node belongs to state R;

[0063] When a heterogeneous node runs out of energy or is physically damaged, resulting in the loss of all its functions, the heterogeneous node belongs to state D.

[0064] (2) Determine the conversion relationships between the states:

[0065] Figure 2 The conversion relationships of a heterogeneous node caused by different factors are given.

[0066] If a heterogeneous node in state S is infected by a malicious program due to the propagation of the malicious program but has not received an attack instruction, its state changes from state S to state E;

[0067] If a heterogeneous node in state E receives an attack instruction and has the ability to infect other nodes, its state changes from state E to state I;

[0068] If a heterogeneous node in state I clears the malicious program due to installing a security patch and has immunity to the existing malicious program, its state changes from state I to state R;

[0069] Any heterogeneous node will change its state to state D due to running out of energy or being physically damaged.

[0070] (3) Obtain the malicious program propagation model of the heterogeneous underwater wireless sensor network:

[0071] Denote S U (t), E U (t), I U (t), R U (t) represent the numbers of underwater sensor nodes in states S, E, I, and R at time t respectively, SA (t), E A (t), I A (t), R A (t) respectively represent the numbers of autonomous underwater vehicles in states S, E, I, and R at time t.

[0072] Suppose the autonomous underwater vehicle moves at a speed of v within time t, and its communication radius is r A , and the area it covers during this process can be calculated as:

[0073] S A = π(vt + r A ) 2 ;

[0074] The density of susceptible nodes in the underwater environment of L×L is:

[0075]

[0076] Through the above formula, the number of susceptible nodes communicating with the exposed AUV can be calculated as:

[0077]

[0078] The autonomous underwater vehicle will continuously send program data packets to nearby nodes through the communication channel with a probability of ε AU . However, due to factors such as communication channel congestion or power exhaustion, the data packets may not be accepted. We assume that the probability of successfully receiving the data packet is σ AU , and the probability of transitioning from the susceptible state to the exposed state is ξ SE . Therefore, the probability of successful infection can be given as:

[0079] η SE = ε AU σ AU ξ SE ;

[0080] In summary, the number of infected autonomous underwater vehicles that successfully infect susceptible nodes in the underwater wireless sensor network is calculated as follows:

[0081]

[0082] where K 21 is the probability that an infected autonomous underwater vehicle can infect susceptible lymph nodes. Therefore, we can obtain:

[0083]

[0084] In an underwater wireless sensor network, the communication range of sensor nodes is much smaller than that of autonomous underwater vehicles. Assume the transmission coefficients of infected nodes that infect autonomous underwater vehicles are as follows:

[0085]

[0086] According to the above derivation, the forward transmission coefficient K of any two underwater sensor nodes can be obtained 34 , and the reverse transmission coefficient K 43 :

[0087]

[0088] Construct a model for the spread of malicious programs in a heterogeneous underwater wireless sensor network according to the following formula:

[0089]

[0090] where Π U , Π A are the node update coefficients of underwater sensor nodes and autonomous underwater vehicles respectively, K1 and K2 represent the node infection rates of underwater sensor nodes and autonomous underwater vehicles respectively, K3 and K4 represent the node attack rates of underwater sensor nodes and autonomous underwater vehicles respectively, α1, α2, α3 represent the exposure rate, immunity rate and immune prevention rate of underwater sensor nodes respectively, β1, β2, β3 represent the exposure rate, immunity rate and immune prevention rate of autonomous underwater vehicles respectively, and d1, d2 represent the damage removal rates of autonomous underwater vehicles and underwater sensor nodes respectively.

[0091] (4) Calculate the stable points and basic reproduction numbers of the model:

[0092] In the given model, the infected categories include E A , E U , I A , I U . Therefore, the infected state variables can be expressed as:

[0093]

[0094] The equations of the model can be transformed into the following form:

[0095]

[0096] where F(x) represents the individuals newly entering the exposed period, and V(x) represents the process of individuals transferring from one state to another or being removed from the infected state.

[0097] According to the given model, F and V can be expressed as:

[0098]

[0099] Under the disease - free steady state, according to the above - mentioned model, the number of susceptible individuals at the infection - free equilibrium point can be obtained as follows:

[0100]

[0101] The Jacobian matrices F and V can be expressed under the DFE as:

[0102]

[0103] The next - generation matrix can be obtained through matrix multiplication:

[0104]

[0105] By solving its characteristic equation, the basic reproduction number R0 can be obtained as:

[0106]

[0107] Calculate the said new change - rate matrix according to the following formula:

[0108]

[0109] Optionally, calculate the said state - transition rate matrix according to the following formula:

[0110]

[0111] The method embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. One can select some or all of the modules according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative labor.

[0112] The system is constructed to run the method of this application. Through the description of the above - mentioned implementation manners, those skilled in the art can clearly understand that each implementation manner can be realized by means of software plus a necessary general - purpose hardware platform, and of course, it can also be realized by hardware. Based on such an understanding, the essence of the above - mentioned technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer - readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0113] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for modeling malicious program propagation in heterogeneous underwater wireless sensor networks, characterized in that: Includes the following: The nodes are divided into two types: sensor nodes and autonomous underwater vehicles, the heterogeneous node states are classified, and the propagation relationship between each state is determined; Construct a model for the propagation of malicious programs in heterogeneous underwater wireless sensor networks; Calculate the stable points where the state change rate is 0 in the malicious program propagation model of heterogeneous underwater wireless sensor networks. The basic reproduction number is calculated based on the newly added change rate matrix and state transition rate matrix of heterogeneous nodes at stable points.

2. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 1 is characterized in that: Classify heterogeneous node status categories, including: When a heterogeneous node has a system vulnerability but is not infected by a malicious program, the heterogeneous node is in state S; when a heterogeneous node is infected by a malicious program but has not been attacked, the heterogeneous node is in state E; When a heterogeneous node has been infected by a malicious program and receives an attack instruction, the heterogeneous node is in state I; when a heterogeneous node is immune to the current malicious program after installing a patch program, the heterogeneous node is in state R; When a heterogeneous node loses all functions due to energy exhaustion or physical damage, the heterogeneous node is in state D.

3. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 1 is characterized in that: Determine the propagation relationship between each status category, including the following types: If the heterogeneous node in state S is infected by a malicious program due to the spread of the malicious program but has not received an attack instruction, its state changes from state S to state E; If a heterogeneous node in state E receives an attack instruction and has the ability to infect other nodes, its state changes from state E to state I; If the heterogeneous node in state I clears the malicious program and becomes immune to the existing malicious program due to the installation of security patches, its state is transformed from state I to state R; Any heterogeneous node will transform its state to state D due to energy exhaustion or physical damage.

4. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 1 is characterized in that: A model for the propagation of malicious programs in heterogeneous underwater wireless sensor networks is constructed, and the formula is as follows: Among them, U , Π A are the node update coefficients of underwater sensor nodes and autonomous underwater vehicles, respectively; K1 and K2 represent the node infection rates of underwater sensor nodes and autonomous underwater vehicles, respectively; K3 and K4 represent the node attack rates of underwater sensor nodes and autonomous underwater vehicles, respectively; α1, α2, α3 represent the exposure rate, immunity rate and immune prevention rate of underwater sensor nodes, respectively; β1, β2, β3 represent the exposure rate, immunity rate and immune prevention rate of autonomous underwater vehicles, respectively; d1 and d2 represent the damage removal rates of autonomous underwater vehicles and underwater sensor nodes, respectively; S U (t), E U (t), I U (t), R U (t) represents the number of underwater sensor nodes in state S, E, I, and R at time t, respectively. A (t), E A (t), I A (t), R A (t) respectively represent the number of autonomous underwater vehicles in state S, E, I, and R at time t, and K 21 is the probability that an infected AUV infects a susceptible lymph node, and the propagation coefficient of an infected node that infects an AUV is K 12 ; The forward propagation coefficient of any two underwater sensor nodes is K 34 , the reverse propagation coefficient is K 43 .

5. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 4 is characterized in that: Calculate the autonomous underwater vehicle propagation coefficient: Assume that the autonomous underwater vehicle moves at a speed of v in time t and its communication radius is r A , the area it covers is: S A =π(vt+r A ) 2 ; The density of susceptible nodes in an L×L underwater environment is: Through the above formula, the number of susceptible nodes communicating with the exposed autonomous underwater vehicle is calculated as: The autonomous underwater vehicle will communicate via the communication channel AU The probability of successfully receiving a data packet is σ AU , the probability of changing from susceptible state to exposed state is ξ SE , the probability of successful infection is calculated as: or SE =e AU s AU x SE ; The number of infected AUVs that successfully infected susceptible nodes in an underwater wireless sensor network is calculated as follows: Where K 21 is the probability that an infected AUV can infect a susceptible lymph node; K 12 is the propagation coefficient of the infected node that infects the autonomous underwater vehicle.

6. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 4 is characterized in that: The forward propagation coefficient between any two underwater sensor nodes is K 34 , the reverse propagation coefficient is K 43 , the calculation formula is as follows:

7. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 1, characterized in that: Calculate the basic reproduction number: Assume that the infected categories include E A ,E U ,I A ,I U , the infected state variable is expressed as: Where F(x) represents an individual newly entering the exposure period, and V(x) represents the process of an individual transferring from one state to another, or removing from an infected state; F and V are expressed as: In the disease-free steady state, the number of susceptible people at the infection-free equilibrium point is: The Jacobian matrices F and V are expressed under DFE as: The next generation matrix can be obtained by matrix multiplication: By solving its characteristic equation, The basic reproduction number R0 is obtained as:

8. The method for modeling the propagation of malicious programs in heterogeneous underwater wireless sensor networks according to claim 1 is characterized in that: Calculate the newly added change rate matrix: Calculate the state transition rate matrix:

9. A malicious program propagation system for heterogeneous underwater wireless sensor networks, characterized in that: A method for modeling the propagation of malicious programs in a heterogeneous underwater wireless sensor network used to implement any one of claims 1-8.

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