Internet of vehicles virus propagation defense strategy optimization method based on differential game

Abstract

The invention provides an Internet of Vehicles virus propagation defense strategy optimization method based on differential game, and belongs to the field of computer information security. The method comprises the following steps of: 1, establishing a node-level dynamic model according to a network topology structure of the Internet of Vehicles; 2, establishing a differential equation model for describing virus transmission according to states (a low-susceptibility state, a high-susceptibility state, an infection state and a recovery state) of nodes; 3, based on the game theory, analyzing the income and loss of attackers and defenders, and constructing a differential game model; and 4, solving an optimal strategy (Nash equilibrium) of the attack and defense parties by utilizing a Hamiltonian function and combining a Pontryagin optimal value principle. And 5, through experiments, comparing the proposed method with a uniform strategy and an uncertain attack strategy, and verifying the effectiveness and superiority of the model in an actual Internet of Vehicles environment.

Description

[0001] Methodology Area

[0002] The present invention belongs to the field of computer information security and relates to a method for optimizing a virus propagation defense strategy for Internet of Vehicles based on differential games, which is an active defense method against network threats.

[0003] Background Methods

[0004] The concept of the Internet of Things (IoT) provides a structural framework for the integration of various systems, and with the support of ubiquitous computing, it enables the unique identification of connected smart devices. The IoT has made unprecedented progress in today's society, giving rise to innovative concepts such as Social IoT, Industrial IoT, and healthcare integration. The fusion of vehicle networks and the IoT has given birth to the Internet of Vehicles, a paradigm that combines the capabilities of the IoT with vehicle interaction. This fusion of digital connectivity and the relationship between vehicles creates a dynamic ecosystem that enhances the interaction of vehicles, objects, and virtual environments.

[0005] A computer virus is a set of instructions compiled into a program that damages computers and data, or interferes with computing processes, and has the ability to replicate. Computer network viruses are usually confined to a network or have a propagation function, which can spread while damaging. Malware infiltrates networks to gain unfair advantage and poses a serious threat to network security. Networks are constantly threatened by fast-spreading viruses that are difficult to eradicate. Email and system vulnerabilities are the main infection vectors, and hackers use ransomware to attack users by encrypting data and manipulating device settings, occupying users' assets and restricting network access.

[0006] Currently, the number of connected cars is increasing day by day, and their communication needs are also expanding. In this context, computer viruses hidden in the Internet of Vehicles environment pose a major threat to personal privacy protection, system security and data integrity. Especially in the scenario of communication between cars and cloud platforms, problems such as insufficient network isolation measures, security vulnerabilities in communication protocols, and access control without strict authentication are particularly prominent. In view of these challenges, a series of research works are focusing on in-depth exploration and effective suppression of virus propagation pathways in the Internet of Vehicles. Summary of the invention

[0007] The present invention aims to solve the problems in the above existing methods and proposes a method for optimizing the virus propagation defense strategy of Internet of Vehicles based on differential game.

[0008] In order to achieve the above object, the method scheme of the present invention is as follows:

[0009] A method for optimizing a virus propagation defense strategy for Internet of Vehicles based on differential games includes the following steps:

[0010] Step 1: Construct the network topology of the Internet of Vehicles, give the parameters related to the state transfer of network nodes, and establish a node-level dynamic model;

[0011] Step 2: Establish the profit function and loss function according to the attack strategy of the Internet of Vehicles network attacker and the defense strategy of the network defender;

[0012] Step 3: Summarize the strategy pairs of the attacker and the defender and the related parameter probabilities into an overall differential game problem and establish a differential game model;

[0013] Step 4: Construct a numerical solution process to solve the attack-defense differential game problem;

[0014] Step 5: Design an iterative algorithm to generate Nash equilibrium, which is used to find the optimal strategy combination of attackers and defenders in the attack and defense game of the Internet of Vehicles. Compare it with the uniform strategy and the uncertain attack strategy to prove the effectiveness of the Nash equilibrium strategy.

[0015] Furthermore, the specific process of step one includes:

[0016] Using graph theory, the network topology in the Internet of Vehicles is represented as an undirected graph G = (V, E), where V represents a set of nodes, including vehicles, roadside units (RSUs), infrastructure, etc., and E represents the communication links between these nodes. The adjacency matrix A = (a ij ) is used to represent the node V i and V j Is there a communication link between them? ij =1, indicating that there is a connection, otherwise a ij = 0. Each node (such as a vehicle or infrastructure) can be in one of the following four states at any time t: low susceptibility state (L): the node device in the Internet of Vehicles is not infected with the virus, and the user is not aware of the virus threat; high susceptibility state (H): the node device in the Internet of Vehicles is not infected with the virus, but the user knows that there is a virus threat; recovery state (R): the node device in the Internet of Vehicles has recovered from the virus infection; infection state (I): the node device in the Internet of Vehicles has been infected by the virus.

[0017] At any time t, use X i (t) represents the node V i Status, possible status include: X i (t) = 0 means the node is in a low susceptibility state (L), X i (t) = 1 means the node is in a highly susceptible state (H), X i (t) = 2 means the node is in recovery state (R), X i (t) = 3 means the node is in the infected state (I). The state of each node is represented by the corresponding probability, Li (t), H i (t), R i (t), I i (t) represent the probability of the node being in these four states at time t, and the sum of these probabilities is 1: L i (t)+H i (t)+R i (t)+I i (t) = 1, which can be further expressed as:

[0018] L i (t) = Pr{X i (t)=0},H i (t) = Pr{X i (t)=1},R i (t) = Pr{X i (t)=2},I i (t) = Pr{X i (t) = 3}

[0019] The probability of a node transitioning between different states depends on the way the virus spreads and the system's ability to repair itself. The specific state transition parameters are defined in the following table:

[0020]

[0021]

[0022] According to L i (t)+H i (t)+R i (t)+I i (t) = 1, the node-level evolution dynamic model can be expressed by the Kolmogorov forward equation (used for Markov chains) as follows:

[0023]

[0024] Furthermore, the specific process of step 2 includes:

[0025] Define the gains in attack and the losses in defense. Assume t∈[0,T], let A and D be piecewise continuous functions, describing the malicious communication infection rate θ respectively. i (t),φ i (t) and virus invasion rate β i (t),σ i (t), the attacker’s attack plan, and the virus repair rate γ i (t),α i (t) is the defender’s defense strategy, as described in the following equation:

[0026] A(t)=(θ1(t),...,θ N (t),φ1(t),...,φ N (t),β1(t),...,β N (t),σ1(t),...,σ N (t))

[0027] D(t)=(γ1,...,γ N ,α1,...,α N )

[0028] make Represents θ i (t),φ i (t),β i (t),σ i (t),γ i (t),α i (t) is the maximum value. Therefore, Respectively represent the maximum limits of A(t) and D(t):

[0029]

[0030] The sets A and D can be expressed according to the following formula:

[0031]

[0032] Attack strategy A∈A S With the defense strategy D∈D S Related, attack gains and defense losses can be calculated in a specified time period [0, T] by G A (A,D) and L D (A,D) represents.

[0033] The attacker’s profit is calculated as the total income minus the total expenditure, let represents the attacker’s attack profit at time t. At any time t, the attacker’s profit from infecting highly susceptible nodes and low susceptible nodes is expressed as and It means that the attacker gains by operating the infected node to infect the high / low susceptible nodes respectively. and express.

[0034] So, attacker B A The total revenue of (A,D) in the time period [0,T] can be expressed by the following formula for the infected node:

[0035]

[0036] The total payment B for the attacker to directly infect high / low susceptible nodesC (A,D) is represented as follows:

[0037]

[0038] The total payment B of the attacker to infect high / low susceptible nodes through infected nodes U (A,D) is represented as follows:

[0039]

[0040] The profit of the attack is expressed by the function as follows:

[0041]

[0042] Defense losses include repair costs and losses caused by infection, called infection losses. represents the loss of the defender at time t. At any time t, the cost of the defender to repair the infected node to a highly susceptible node and restore the node is L A (A,D), the formula is as follows:

[0043]

[0044] Defender Repair I i (t) to H i (t) and R i The cost of (t) is expressed as follows:

[0045]

[0046] Let the function L D (A,D) represents defense loss:

[0047]

[0048] Further, the specific process of step three includes:

[0049] In the vehicle-to-everything (V2X) environment, a differential game model is established through game theory to find the optimal strategies of the attacker and the defender. Assume that the time interval is t∈[0,T], where T is the total time of the game, and the attack strategy A∈A S , defense strategy D∈D S , the differential game system for dealing with attack and defense can be expressed as follows:

[0050]

[0051] Dependency system 1 initial state:

[0052] L i (0),H i(0),I i (0)∈[0,1],t∈[0,T]

[0053] To satisfy the above formula, the attacker’s goal is to find a pair of strategies (A * ,D * )∈(A S ,D S ), thus reaching Nash equilibrium. The attack and defense differential game problems in the formula can be calculated using the following tuples:

[0054]

[0055] When attacker A executes its optimal attack A * , while defender D maintains its best defense D * To reduce the risk of attack and avoid heavy losses, a strategy pair (A * ,D * ) is a Nash equilibrium. In this case, the defender reduces losses through defense, and the attacker ensures benefits by maximizing his plan, so it is necessary to determine the Nash equilibrium.

[0056] Furthermore, the specific process of step 4 includes:

[0057] In order to solve the attack-defense differential game problem, it is necessary to construct a process for solving the Nash equilibrium.

[0058] In order to reduce the volatility of Nash equilibrium in attack-defense game problems, several basic conditions for achieving Nash equilibrium must be determined. First, we propose two Hamiltonians for differential game problems involving attack and defense.

[0059] The attacker's Hamiltonian H A It is expressed as:

[0060]

[0061] The defender's Hamiltonian H D It is expressed as:

[0062]

[0063] Among them, L(t), H(t), I(t) represent the node states of low susceptibility, high susceptibility and infection respectively; λ A (t), λ B (t), λ c (t), μ A (t), μ B (t), μ C(t) is the adjoint function. In the attack-defense differential game scenario, the Nash equilibrium point will be expressed through specific conditions. Assume that there is a Nash equilibrium (A, D) in the framework of the differential game problem, and consider the solution L of system (1) i ,

[0064] H i , I i , the following significant results can be observed:

[0065] Existence A ,λ B ,λ C , μ A , μ B , μ C The following system is satisfied, here called System 3:

[0066]

[0067] The above are the relevant equations of System 3, and at time T, λ is satisfied A (T) = λ B (T) = λ C (T) = 0, μ A (T) = μ B (T) = μ C (T) = 0. For 1≤i≤N, 0≤t≤T, the following equation can be established:

[0068]

[0069] in

[0070]

[0071] For 1≤i,j≤N,0≤t≤T, the following equation can be determined:

[0072]

[0073] in

[0074]

[0075] For 1≤i≤N,0≤t≤T, the following equation can be established:

[0076]

[0077] in

[0078]

[0079] According to the Pontryagin extreme value principle, for 1≤i≤N,0≤t≤T, there exists an accompanying variable λ A,λ B ,λ C , μ A , μ B , μ C Satisfies the following equation:

[0080]

[0081] Likewise, for the defender:

[0082]

[0083]

[0084] From this, system (2) can be derived by direct calculation. Since the final state is free and the terminal cost is unknown, Using Pontryagin's maximum / minimum principle, we can get the following equation:

[0085]

[0086] Thus, the system (2) is proven.

[0087] According to differential game theory, L i (0), H i (0),I i (0), = 0 and the system equations (1), (3), (4), (5), (6) form a requirement system (2) of the attack-defense differential game problem. By solving this necessary system, the Nash equilibrium in the attack-defense strategy can be found.

[0088] Further, the specific process of step 5 includes:

[0089] Design an algorithm to generate Nash equilibria that solves the necessary systems in the above steps and identifies the Nash equilibria (A * ,D * ). When dealing with the differential game problem of attack and defense, A * is considered an attack strategy, while D * is considered a defensive strategy. The algorithm in the following table is an iterative process. In each cycle, we obtain a new adjoint function in the backward direction through system (3), perform device evolution in the forward direction through system (1), and use systems (4), (5) and (6) to generate a new strategy combination in the forward direction. The process terminates when two consecutive strategy choices are very close, or when the number of iterations reaches a certain point. The algorithm is shown in the following table:

[0090]

[0091] The above algorithm is used to obtain Nash equilibrium, which can then be compared with the uniform strategy and random attack strategy through designed experiments to verify the effectiveness of the Nash equilibrium strategy.

[0092] The beneficial effects of the present invention are as follows: The present invention proposes a method for optimizing the virus propagation defense strategy of the Internet of Vehicles based on differential games, including: 1) establishing the network topology structure of the Internet of Vehicles and establishing a node-level dynamic model; 2) establishing the process of attack and defense as a differential game problem, and establishing two Hamiltonians functions to analyze the differential game model. The two Hamiltonians functions correspond to the gains and losses of the attacker and the defender, respectively. Solve the equation to find the optimal strategy of both parties in the attack and defense game, that is, the Nash equilibrium. 3) Design an algorithm to generate Nash equilibrium, through which the attacker and the defender can find the optimal attack and defense strategy to achieve Nash equilibrium. Compare the Nash equilibrium strategy with other strategies to prove its effectiveness.

[0093] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and research, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] In order to make the purpose, method, scheme and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, in which:

[0095] Figure 1 The differential game process for dealing with the threat of virus transmission in the Internet of Vehicles;

[0096] Figure 2 This is the node state evolution diagram of the differential game against the threat of virus transmission in the Internet of Vehicles; DETAILED DESCRIPTION

[0097] The following is an explanation of the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied by other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the features in the following embodiments and embodiments can be combined with each other without conflict.

[0098] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0099] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as a limitation on the present invention. For ordinary method personnel in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0100] like Figure 1 As shown in the figure, the present invention proposes a method for optimizing the virus propagation defense strategy of the Internet of Vehicles based on differential game. The application scenario of this method is that when a node in the Internet of Vehicles (such as a vehicle, roadside unit or cloud server) is attacked maliciously, the system uses a dynamic game method to analyze the behavior strategies of the attacker and the defender, and then formulates the optimal defense plan. The specific implementation steps are as follows:

[0101] Step 1: Establish a node-level dynamic model based on the topological structure of the Internet of Vehicles. Each node initializes relevant parameters according to its current state (such as low / high susceptibility, infection, recovery). In order to obtain a state evolution dynamic model, we assume that the node state evolves over time t, and its state transition is controlled by the following probability parameters:

[0102] (1) The probability of a node infecting a low / high susceptibility node through IoV communication is θ,

[0103] (2) The probability of infecting low / high susceptible nodes through infected nodes is β and σ respectively;

[0104] (3) The probability that a node in the low susceptibility state changes to the high susceptibility state is δ;

[0105] (4) The probability of low / high susceptible state recovering to safe state is ∈1, ∈2 respectively;

[0106] (5) The probability that a node in the infected state changes to a highly susceptible state is γ;

[0107] (6) The probability that a node in the recovered state is infected again to a highly susceptible state is η;

[0108] (7) The probability of recovery of an infected node is α;

[0109] The changes in the states of these nodes can be described using the following differential equations:

[0110]

[0111] Step 2: In the attack and defense process of the Internet of Vehicles, define the attacker strategy A(t) and the defender strategy D(t), as shown in the following formula:

[0112]

[0113] D(t)=(γ1(t),...,γ N (t),α1(t),...,α N (t))

[0114] Set the attacker's profit function G A (A, D) and the defender’s loss function L D (A, D), and based on the profit function, build a game model:

[0115]

[0116] Step 3: By maximizing G A and minimize L D , we can find the optimal strategy for both the attacker and the defender, that is, the Nash equilibrium point, so as to provide theoretical guidance for the security protection of the Internet of Vehicles. The Nash equilibrium point is obtained according to the designed iterative algorithm.

[0117] Step 4: Based on the obtained Nash equilibrium defense strategy D * , and implement corresponding security measures in the Internet of Vehicles. To prove the effectiveness of the proposed Nash equilibrium strategy, it is compared with the uniform strategy and the uncertain attack strategy, and tests are carried out under different Internet of Vehicles topologies and communication modes to verify the effectiveness of the strategy.

[0118] After completing the above steps, when the Internet of Vehicles is threatened by virus transmission, the defender can take corresponding optimal defense measures based on the optimal defense strategy and the status of different nodes in the Internet of Vehicles.

[0119] Figure 2 This is a node state evolution diagram of the present invention, which is described below in conjunction with the accompanying drawings:

[0120] Through the analysis of the existing Internet of Vehicles security mechanism and combined with the characteristics of inter-node communication, we found that the existing model has limitations in dealing with large-scale virus propagation. To this end, we proposed a new node state evolution model, such as Figure 2, where X i (t) = 0, X i (t) = 1, X i (t) = 2, X i (t) = 3 represents low susceptibility state, high susceptibility state, recovery state and infection state respectively.

[0121] Each node in the IoV can be an onboard device, a roadside device, or other device that interacts with a cloud server. When a node in the IoV is infected by a virus, the node state evolves over time due to the influence of attackers and defenders, so we make the following assumptions at time t:

[0122] 1) When a node device is in an uninfected state and the user is defenseless, if the user is aware of the potential virus threat through security warnings, information notifications, or network security monitoring systems, the device will change from a low susceptibility state to a high susceptibility state. This process is represented by the parameter δ(t);

[0123] 2) When the node is in a susceptible state, the device can be infected by the virus through the Internet of Vehicles infrastructure (such as roadside units) or communication between vehicles. The probability of infection through vehicle-road or vehicle-to-vehicle is θ i (t) and φ i (t), the probability of low susceptibility and high susceptibility states being infected through infected nodes are β i (t) and σ i (t).

[0124] 3) The infected node can be restored to a safe state through security patches, antivirus software updates or system reinstallation. This process is determined by the parameter α i (t) indicates that the node recovers from the infected state to the virus-free state.

[0125] 4) After recovery, the node device may be exposed to virus threats again, especially when the antivirus software fails or the security measures fail to operate effectively, the node device may enter a highly susceptible state again. This process is represented by the parameter η.

[0126] 5) Before the infected node is completely restored to a virus-free state, it can return to a highly susceptible state to maintain anti-virus vigilance. This process is determined by the parameter γ i (t) indicates that the node device directly changes from the infected state to the highly susceptible state without fully recovering.

[0127] According to the above assumptions, we have the following Figure 2 Node state evolution model.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the method scheme of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary method personnel in the field should understand that the method scheme of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the method scheme, which should be included in the scope of the claims of the present invention.

Claims

1. The virus propagation defense strategy for Internet of Vehicles based on differential game is characterized by: The nodes in the Internet of Vehicles are modeled according to the characteristics of virus propagation and their state changes are described by differential equations. Game theory is used to analyze the attack and defense strategies, and the optimal strategy is solved by combining Hamiltonians function and Pontryagin maximum principle. The specific steps include: Step 1: Establish a node-level dynamic model based on the network topology of the Internet of Vehicles and give the state transition parameters of the nodes that change over time; Step 2: Construct the attacker's profit function and the defender's loss function based on the attack strategy and defense strategy. Step 3: Construct an overall tuple to characterize the differential game problem between attack and defense, and build a differential game model based on it; Step 4: Introduce Hamiltonians function and combine with Pontryagin optimal value principle to establish a numerical solution to deal with differential game problems; Step 5: Design an iterative algorithm to generate Nash equilibrium solutions for the differential game problems of attackers and defenders. At the same time, compare the Nash equilibrium strategy used with other strategies (uniform strategy and uncertain attack strategy) to verify the effectiveness of the Nash equilibrium strategy.

2. The differential game-based Internet of Vehicles virus propagation defense strategy according to claim 1 is characterized in that The communication model representation process of the Internet of Vehicles described in step 1 is as follows: the network topology structure in the Internet of Vehicles can be represented as an undirected graph G = (V, E), where V represents a node set, including vehicles, roadside equipment (RSU), infrastructure, etc., and E represents the link relationship between nodes. Using the adjacency matrix A = (a ij ) indicates vehicle V i and other vehicles V j or whether there is a communication link between devices. ij =1, indicating that there is a connection, otherwise a ij = 0. Each node can be in one of the following four states: low susceptibility state (L), high susceptibility state (H), recovery state (R), infection state (I). At any time t, use X i (t) represents the node V i Status, specifically: X i (t) = 0 indicates low susceptibility (L), X i (t) = 1 indicates a highly susceptible state (H), X i (t) = 2 indicates the recovery state (R), X i (t) = 3 indicates the infected state (I). The probabilities corresponding to the four states are L i (t), H i (t), R i (t), I i (t), and satisfy L i (t)+H i (t)+R i (t)+I i (t) = 1. In the Internet of Vehicles, changes in node status are affected by multiple factors such as virus transmission, system vulnerabilities, and owner behavior. Once a vehicle or device is aware of a virus threat, the low susceptibility state (L) will irreversibly transform into a high susceptibility state (H). This process means that after learning of the virus threat, the owner will maintain a high level of vigilance and will no longer return to an unaware state.

3. The differential game-based Internet of Vehicles virus propagation defense strategy according to claim 1 is characterized by: The construction of the attacker's profit function and the defender's loss function in step 2 includes: let the function G A (A,D) represents the attacker’s profit function, B A (A, D) represents the total income in the entire time interval [0, T], B C (A,D) and B U (A, D) represents the total cost paid by the attacker to directly infect low / high susceptible nodes and the total cost paid to indirectly infect nodes; let function L D (A,D) represents defense loss, L A (A, D) represents the cost of restoring a node repaired by the defender from an infected state to a highly susceptible node, L R (A,D) represents the cost for the defender to repair the infected node to a restored node. Then the following formula can be obtained: G A (A,D)=B A (A,D)-B C (A,D)-B U (A,D) L D (A,D)=L A (A,D)+L R (A,D) 4. The differential game-based Internet of Vehicles virus propagation defense strategy according to claim 1 is characterized by: Step 3: Construct an overall tuple to characterize the differential game problem between attack and defense. Assuming that the game takes place in the time interval t∈[0,T], both the attacker and the defender can formulate corresponding strategies. The attacker's strategy can be expressed as A(t), including plans to spread the virus through vehicle-to-vehicle communication, V2V or V2I; the defender's strategy D(t) includes defense measures such as system repair, software update, and vehicle terminal restart. The attacker's goal is to gain benefits by infecting as many vehicles as possible, and the defender's goal is to minimize the losses caused by vehicle infection by repairing infected vehicles. The defender's loss function L D (A, D) includes the loss caused by vehicle infection and the cost of repairing the vehicle. So the game model can be defined by the following mathematical expression: And use the following tuple to represent the entire differential game problem between attack and defense:

5. The differential game-based Internet of Vehicles virus propagation defense strategy according to claim 1 is characterized by: Step 4: Construct two Hamiltonians to represent the attacker’s and defender’s objective functions respectively. The attacker’s Hamiltonian H A Describes the benefits obtained by the attacker through infecting vehicles (nodes) and the cost of virus propagation. The Hamiltonian H of the defender D Describe the defense costs and reduced losses incurred by defenders through operations such as repairing infected vehicles and installing protective software. According to differential game theory, the condition for Nash equilibrium is that the attacker's strategy A * and the defender's strategy D * Requirements: In order to find the solution to the differential game, we first need to construct Lagrange multipliers to represent the rate of change of the state variables. Then, we optimize the strategies of the attacker and defender respectively through the Pontryagin maximum principle.

6. The differential game-based Internet of Vehicles virus propagation defense strategy according to claim 1 is characterized by: Step 5: An iterative algorithm for generating Nash equilibrium solutions, based on iteratively solving the attacker's optimal strategy A * and the defender’s optimal strategy D * .

Images