Moran process-based honey array graph evolution method

Abstract

The Moran process-based honey array diagram evolution method provided by the invention comprises the following steps: on the basis of an evolutionary game theory, constructing a Moran process-based honey array diagram evolution model for simulating an attack and defense strategy evolution condition; calculating an attack and defense income matrix according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model; setting selection strength coefficients of attackers and defenders according to the historical game decision data; and according to the attack and defense income matrix and the selection strength coefficient, constructing a dynamic evolution equation of the network attack and honey array diagram decision based on the Moran process, and solving the dynamic evolution equation to obtain stable and balanced attack and defense strategy evolution, thereby obtaining an optimal honey array diagram strategy set. By applying the method, the honey array diagram evolution model which adapts to a dynamic network environment and can represent an evolution power mechanism of a honey array diagram strategy can be constructed, and the expandability of the model is ensured by introducing a selection strength coefficient to describe the rational degree of the honey array diagram.

Description

Technical Field

[0001] The present invention relates to the field of network security technology, and in particular to a honeycomb graph evolution method based on Moran process. Background Art

[0002] Current network attacks are showing trends of intelligence, combination, and concealment. The "Four Honeys" system represented by Honey Points, Honey Courtyards, Honey Caves, and Honey Arrays has proposed a new paradigm of network defense in the guard mode for the first time. As the central subsystem of the "Four Honeys" system, Honey Arrays play an irreplaceable role in deception resource scheduling and decision-making. Under the condition of limited rationality, Honey Arrays can learn and adapt to the environment through trial and error, accumulate experience and adjust strategies in continuous attempts to find the optimal Honey Array solution.

[0003] The existing honey array graph evolution model mainly obtains the optimal array graph strategy by replicating the dynamic strategy update mechanism. However, since the replication of dynamic driven strategy adjustment is only a simple imitation and diffusion of the dominant array graph strategy, it often ignores the individual differences of the attack and defense groups as well as the strategy adaptability and dependence, which is not highly consistent with the network attack and defense process, greatly reducing its practical application value. The network environment is complex and changeable, and the existing honey array graph scheduling method lacks the ability to dynamically adjust the strategy. When faced with dynamic changes in the network environment, such as when new attack methods or vulnerabilities appear, the existing dominant array graph strategy may not be able to respond in time or become invalid.

[0004] Therefore, it is necessary to provide a honeybee graph evolution method that can accurately describe the dynamic changes of strategies and fit the actual network attack and defense scenarios. Summary of the invention

[0005] The purpose of the present invention is to provide a honey array graph evolution method based on the moran process, so as to solve the problem that the existing array graph evolution method has low compatibility with the actual network attack and defense process.

[0006] In the first aspect, the honey array graph evolution method based on the Moran process provided by the present invention includes: based on the evolutionary game theory, constructing a honey array graph evolution model based on the Moran process to simulate the evolution of attack and defense strategies; calculating the attack and defense benefit matrix according to the attack and defense strategy combinations in the evolution process of the honey array graph evolution model; setting the selection intensity coefficient of the attack and defense parties according to the historical game decision data; constructing a dynamic evolution equation of network attack and honey array graph decision based on the Moran process according to the attack and defense benefit matrix and the selection intensity coefficient, solving the dynamic evolution equation to obtain a stable equilibrium of the attack and defense strategy evolution, thereby obtaining an optimal honey array graph strategy set.

[0007] The beneficial effect of the method provided by the present invention is that the proposed honey array graph evolution model is based on evolutionary game theory, and from the perspective of limited rationality, the honey array graph evolution model based on the Moran process is constructed by combining the characteristics of randomness of individual selection in the attacking and defending groups and a limited number of individuals. It can adapt to the dynamic network environment and characterize the evolutionary dynamic mechanism of the honey array graph strategy. The rationality of the honey array graph is characterized by introducing the selection intensity coefficient to ensure the scalability of the model. The optimal array graph strategy is obtained by solving the network attack and defense dynamic evolution equation, and its evolution trajectory is characterized, which has a good application prospect.

[0008] In a possible embodiment, the honeycomb graph evolution model based on the moran process includes a quintuple (E, S, P, θ, U); wherein E represents the set of network attack and defense participants, S represents the state set of network attack and defense, P represents the strategy space of network attack and defense, θ represents the network attack and defense belief set, and U represents the profit function in the network attack and defense process.

[0009] In another possible embodiment, the attack and defense benefit matrix is ​​calculated according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model, including: in the evolution process of the honey array graph evolution model, the honey array adjusts the array graph strategy to obtain the attack strategy set AS and the honey array graph strategy set DS, where i and j represent the number of strategies, 1≤i≤m, And m ≥ 2, 1 ≤ j ≤ n, And n≥2; Set the attack and defense profit matrix to be composed of the profit under different strategy combinations The attack and defense benefit matrix satisfies the following formula: , where X represents the attack and defense profit matrix, represents the payoff matrix of the network attacker, represents the payoff matrix of the honey array graph, , , It represents the profit function of the network attacker in the process of network attack and defense, It represents the profit function of the honeycomb graph during the network attack and defense process.

[0010] In other possible embodiments, a dynamic evolution equation of network attack and honey array diagram decision based on Moran process is constructed according to the attack and defense benefit matrix and the selection intensity coefficient, including: calculating the expected benefit of the attack strategy and the expected benefit of the honey array diagram strategy according to the attack and defense benefit matrix, introducing the selection intensity coefficient to calculate the individual fitness of the attack strategy and the individual fitness of the honey array diagram strategy; constructing a dynamic evolution equation of network attack and honey array diagram decision based on Moran process according to the individual fitness of the attack strategy and the individual fitness of the honey array diagram strategy.

[0011] The expected benefits of the attack strategy and the expected benefits of the honey array map strategy are calculated according to the attack and defense benefit matrix, and the selection intensity coefficient is introduced to calculate the individual fitness of the attack strategy and the individual fitness of the honey array map strategy, including: the expected benefits of the attack strategy and the expected benefits of the honey array map strategy are calculated according to the attack and defense benefit matrix to meet the following formula: , ,in, represents the expected return of the attack strategy, represents the expected return of the honey-array graph strategy, , represents the i-th attack strategy, N represents the total number of attack strategies, represents the jth honey-array graph strategy, M represents the total number of honey-array graph strategies, Representation strategy The following income, Representation strategy The benefits under this condition; the selection intensity coefficient is introduced to calculate the individual fitness of the attack strategy and the individual fitness of the honey array strategy to meet the following formula: ,in, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, represents the selection intensity coefficient of the network attacker, Represents the selection intensity coefficient of the honey array diagram.

[0012] According to the individual fitness of the attack strategy and the individual fitness of the honey array map strategy, a dynamic evolution equation of network attack and honey array map decision-making based on the moran process is constructed, including: calculating the transfer probability of the number of individuals who choose the attack strategy and the transfer probability of the number of individuals who choose the honey array map strategy during the evolution of the honey array map evolution model according to the individual fitness of the attack strategy and the individual fitness of the honey array map; the rate of change of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the honey array map strategy in the moran process over time is approximately expressed by a stochastic differential equation. When , the following formula is satisfied: ,in, , represents the rate of change of the proportion of individuals who choose the attack strategy over time, represents the rate of change of the proportion of individuals who choose the honey-array strategy over time, Indicates the choice of attack strategy The proportion of individuals in the attack group, Indicates the selection of honey array graph strategy The proportion of individuals in the defense group, represents the drift term of the stochastic differential equation, represents the diffusion term of the stochastic differential equation, represents the time variation, represents the random change in an infinitesimal time interval, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, represents the transition probability that the number of individuals choosing the attack strategy remains unchanged, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, represents the transition probability when the number of individuals who choose the honey array graph strategy remains unchanged, M represents the total number of honey array graph strategies, and N represents the total number of attack strategies. Substituting the drift term and diffusion term of the stochastic differential equation into the stochastic differential equation, the network attack and honey array graph decision-making dynamic evolution equation based on the moran process satisfies the following formula: ,in, and m≥2, and n≥2, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, Indicates The probability of selecting an attack strategy is Indicates The expected return of an attack strategy is Indicates The probability of selecting a honey array strategy, Indicates The expected return of a honey array strategy.

[0013] Solve the dynamic evolution equation to obtain the stable equilibrium of attack and defense strategy evolution, and then obtain the optimal honey array strategy set, including: It is used to calculate the evolutionary stable equilibrium point of the dynamic evolution equation; the dynamic evolution equation is solved to obtain the network attack and honey array graph equilibrium strategy, thereby obtaining the optimal honey array graph strategy set.

[0014] In a second aspect, the present invention further provides a honeybee graph evolution device based on the moran process, the device comprising: The model building unit is used to build a honey array graph evolution model based on the Moran process based on evolutionary game theory to simulate the evolution of attack and defense strategies; The benefit calculation unit is used to calculate the attack and defense benefit matrix according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model; A coefficient selection unit, used to set the selection intensity coefficients of the attacking and defending parties according to historical game decision data; The evolutionary solution unit is used to construct a dynamic evolution equation of network attack and honey array diagram decision based on the Moran process according to the attack and defense benefit matrix and the selection intensity coefficient, and solve the dynamic evolution equation to obtain a stable equilibrium of the attack and defense strategy evolution, thereby obtaining an optimal honey array diagram strategy set.

[0015] In a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the above-mentioned honeybee graph evolution method based on the Moran process is implemented.

[0016] In a fourth aspect, the present invention also provides an electronic device, comprising: a processor and a memory; the memory is used to store a computer program; the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above-mentioned honey array graph evolution method based on the Moran process.

[0017] For the beneficial effects of the second to fourth aspects, reference may be made to the description of the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A schematic diagram of a flow chart of a honeybee graph evolution method based on a moran process provided by an embodiment of the present invention; Figure 2 A schematic diagram of a honeybee graph evolution device based on a moran process provided by an embodiment of the present invention; Figure 3 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with general skills in the field to which the present invention belongs. "Including" and similar words used in this article mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0020] In view of the problems existing in the prior art, an embodiment of the present invention provides a honeybee graph evolution method based on the Moran process.

[0021] This embodiment provides a method for evolving a honeybee graph based on the Moran process. Figure 1 , the method comprising: S101: Based on evolutionary game theory, a honeybee graph evolution model based on the moran process is constructed to simulate the evolution of attack and defense strategies.

[0022] In the process of network attack and defense, honey array scheduling often shows the characteristics of limited rationality under the influence of various factors (such as information asymmetry, computing resource constraints, decision-making time pressure, etc.), that is, it is not completely rational to choose the optimal array. This limited rationality makes honey array scheduling a dynamic and complex system. By constructing a suitable honey array evolution game model, the dynamic changes and adaptation rules of array strategies can be revealed.

[0023] In a possible embodiment, the present invention defines a honeycomb graph evolution model based on the moran process, including a five-tuple (E, S, P, θ, U). Among them, E represents the set of network attack and defense participants, S represents the state set of network attack and defense, P represents the strategy space of network attack and defense, θ represents the network attack and defense belief set, and U represents the profit function in the process of network attack and defense.

[0024] In a specific embodiment, represents the set of network attack and defense participants, where Indicates a network attack. It represents a picture of honey waves. Represents a set of states of network attack and defense, where each state is regarded as the network attack surface at a certain stage. Represents the strategy space of network attack and defense, where represents the attack strategy set, and , represents the honey array graph strategy set, and . represents the network attack and defense belief set, where represents the probability distribution of the attack strategy set AS, Indicates the choice of attack strategy The probability of , represents the DS probability distribution of the honey array strategy set, Indicates the selection of honey array graph strategy The probability of . It represents the profit function in the process of network attack and defense. The profit function is determined by both the attacker and the defender. That is, the network attack and the honey array are combined through different strategies. The respective profits obtained.

[0025] The honey array graph evolution model provided by the present invention takes into account that in actual attack and defense confrontation scenarios, there are usually multiple attackers and defenders. The present invention divides these participants into different groups, simulates the trial and error, learning and adjustment process of the attacker and defender strategies, and focuses on the evolution process of the honey array graph strategy. It can dynamically characterize the evolution trajectory of the array graph decision and improve the accuracy and effectiveness of the array graph decision results.

[0026] S102: Calculate the attack and defense benefit matrix according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model.

[0027] In the network attack and defense confrontation, driven by the learning mechanism, the honey arrays at different stages will continuously adjust and optimize their array strategies over time. Setting the attack and defense benefit matrix X is based on different strategy combinations. The benefits of attack and defense are Then, we can derive the specific attack and defense benefit matrix expression.

[0028] In a possible embodiment, the attack and defense benefit matrix is ​​calculated according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model, including: in the evolution process of the honey array graph evolution model, the honey array adjusts the array graph strategy to obtain the attack strategy set AS and the honey array graph strategy set DS, where i and j represent the number of strategies, 1≤i≤m, And m ≥ 2, 1 ≤ j ≤ n, And n≥2.

[0029] Set the attack and defense profit matrix in different strategy combinations The following is the income The attack and defense benefit matrix satisfies the following formula: , where X represents the attack and defense profit matrix, represents the payoff matrix of the network attacker, represents the payoff matrix of the honey array graph, , , It represents the profit function of the network attacker in the process of network attack and defense, It represents the profit function of the honeycomb graph during the network attack and defense process.

[0030] S103: Setting the selection intensity coefficients of the attacking and defending parties according to the historical game decision data.

[0031] In the Moran process, selection intensity is an important parameter that determines the evolutionary dynamics of different strategies or individuals in the population. Characterizes the preference of the attacker and defender for different strategies, that is, the degree of limited rationality. Indicates the strength of network attack selection. Indicates the selection strength of the honey array graph, Among them, when It indicates neutral choice when indicates weak selection; When , it indicates strong choice. At this time, the attack and defense confrontation is a completely rational game, that is, both the attacker and the defender have complete control over the profit information of their respective strategies, which is inconsistent with the actual attack and defense game process. and When it approaches 0, the rationality of both the attacker and the defender gradually decreases.

[0032] According to the historical game decision data, the appropriate selection intensity coefficient of the attacker and defender can be determined for subsequent evolutionary calculations.

[0033] S104: constructing a dynamic evolution equation of network attack and honeycomb diagram decision based on Moran process according to the attack and defense benefit matrix and the selection intensity coefficient, solving the dynamic evolution equation to obtain a stable equilibrium of attack and defense strategy evolution, thereby obtaining an optimal honeycomb diagram strategy set.

[0034] In a possible embodiment, a dynamic evolution equation of network attack and honey array diagram decision based on Moran process is constructed according to the attack and defense benefit matrix and the selection intensity coefficient, including: calculating the expected benefit of the attack strategy and the expected benefit of the honey array diagram strategy according to the attack and defense benefit matrix, introducing the selection intensity coefficient to calculate the individual fitness of the attack strategy and the individual fitness of the honey array diagram strategy; constructing the dynamic evolution equation of network attack and honey array diagram decision based on Moran process according to the individual fitness of the attack strategy and the individual fitness of the honey array diagram strategy.

[0035] In a specific embodiment, the expected benefits of the attack strategy and the expected benefits of the honey array map strategy are calculated according to the attack and defense benefit matrix, and the individual fitness of the attack strategy and the individual fitness of the honey array map strategy are calculated by introducing the selection intensity coefficient, including: the expected benefits of the attack strategy and the expected benefits of the honey array map strategy are calculated according to the attack and defense benefit matrix to satisfy the following formula: , ,in, represents the expected return of the attack strategy, represents the expected return of the honey-array graph strategy, , represents the i-th attack strategy, N represents the total number of attack strategies, represents the jth honey-array graph strategy, M represents the total number of honey-array graph strategies, Representation strategy The following income, Representation strategy The benefits under the above-mentioned selection intensity coefficient are introduced to calculate the individual fitness of the attack strategy and the individual fitness of the honey array map strategy to satisfy the following formula: ,in, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, represents the selection intensity coefficient of the network attacker, Represents the selection intensity coefficient of the honey array diagram.

[0036] According to the individual fitness of the attack strategy and the individual fitness of the honey array map strategy, a dynamic evolution equation of network attack and honey array map decision-making based on the moran process is constructed, including: calculating the transfer probability of the number of individuals who choose the attack strategy and the transfer probability of the number of individuals who choose the honey array map strategy during the evolution of the honey array map evolution model according to the individual fitness of the attack strategy and the individual fitness of the honey array map; the rate of change of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the individual proportion of the honey array map strategy in the moran process over time is approximately expressed by a stochastic differential equation. When , the following formula is satisfied: ,in, , represents the rate of change of the proportion of individuals who choose the attack strategy over time, represents the rate of change of the proportion of individuals who choose the honey-array strategy over time, Indicates the choice of attack strategy The proportion of individuals in the attack group, Indicates the selection of honey array graph strategy The proportion of individuals in the defense group, represents the drift term of the stochastic differential equation, represents the diffusion term of the stochastic differential equation, represents the time variation, represents the random change in an infinitesimal time interval, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, represents the transition probability that the number of individuals choosing the attack strategy remains unchanged, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, represents the transition probability that the number of individuals who choose the honey-array graph strategy remains unchanged, M represents the total number of honey-array graph strategies, and N represents the total number of attack strategies. Substituting the drift term and diffusion term of the stochastic differential equation into the stochastic differential equation, the network attack and honey-array graph decision-making dynamic evolution equation based on the moran process satisfies the following formula: ,in, and m≥2, and n≥2, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, Indicates The probability of selecting an attack strategy is Indicates The expected return of an attack strategy is Indicates The probability of selecting a honey array strategy, Indicates The expected return of a honey array strategy.

[0037] In a specific embodiment, the calculation of the probability of individuals selecting the attack strategy during the evolution of the honeycomb graph evolution model satisfies the following formula: , .

[0038] During the evolution of the honey array graph evolution model, the probability of individual number transfer that chooses the honey array graph strategy satisfies the following formula: , .

[0039] Solve the dynamic evolution equation to obtain the stable equilibrium of attack and defense strategy evolution, and then obtain the optimal honey array strategy set, including: It is used to calculate the evolutionary stable equilibrium point of the dynamic evolution equation; the dynamic evolution equation is solved to obtain the network attack and honey array graph equilibrium strategy, thereby obtaining the optimal honey array graph strategy set.

[0040] In a possible embodiment, the honey array graph evolution method based on the moran process designed by the present invention can be implemented by an algorithm. The process executed by the algorithm according to the honey array graph evolution method based on the moran process includes: input: honey array graph evolution model, output: optimal honey array graph strategy .

[0041] start

[0042] 1) Initialization

[0043] / * Initialize the honey array graph evolution model * /

[0044] {

[0045] 1.1) Build ,

[0046] / *Analyze the characteristics of network attack behavior and initialize the attack behavior strategy set * /

[0047] 1.2) Build

[0048] / * Collect defense strategies and summarize and classify them, initialize the honey array strategy set * /

[0049] 1.3) Build

[0050] / *The attacker has a probability Choose an attack strategy * /

[0051] 1.4) Build

[0052] / *Defender with probability Choose a formation strategy * /

[0053] }

[0054] 2) For

[0055] For

[0056] {

[0057] calculate

[0058] }

[0059] / * Calculate different strategy combinations The attack and defense benefit matrix* /

[0060] 3) Settings

[0061] / *Set the strength coefficient for both attack and defense * /

[0062] 4) For

[0063] For

[0064] {

[0065] calculate

[0066] calculate

[0067] Build

[0068] }

[0069] / *Construct the network attack and honey array graph decision dynamic evolution equation based on Moran process* /

[0070] 5) Calculation

[0071] / *Calculate the evolutionary stable equilibrium point* /

[0072] 6) Output

[0073] / *Output the optimal honey array strategy set* /

[0074] Finish

[0075] The honey array graph evolution method based on the Moran process of the present invention is based on evolutionary game theory. Starting from the perspective of limited rationality, combined with the characteristics of randomness of individual selection and limited number of individuals in the attacking and defending groups, a honey array graph evolution model based on the Moran process is constructed. The proposed honey array graph evolution model can adapt to the dynamic network environment and can characterize the evolutionary dynamic mechanism of the honey array graph strategy. The rationality of the honey array graph is characterized by introducing the selection intensity coefficient to ensure the scalability of the model. The optimal array graph strategy is obtained by solving the network attack and defense dynamic evolution equation, and its evolution trajectory is characterized, which has a good application prospect.

[0076] See the instruction manual Figure 2 This embodiment also provides a honeybee graph evolution device based on the Moran process, which is used to implement the above method embodiment. The device includes: The model building unit 201 is used to build a honeycomb graph evolution model based on the Moran process based on the evolutionary game theory to simulate the evolution of attack and defense strategies.

[0077] The benefit calculation unit 202 is used to calculate the attack and defense benefit matrix according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model.

[0078] The coefficient selection unit 203 is used to set the selection intensity coefficients of the attacking and defending parties according to the historical game decision data.

[0079] The evolutionary solution unit 204 is used to construct a dynamic evolution equation of network attack and honeycomb diagram decision based on the Moran process according to the attack and defense benefit matrix and the selection intensity coefficient, and solve the dynamic evolution equation to obtain a stable equilibrium of the attack and defense strategy evolution, thereby obtaining an optimal honeycomb diagram strategy set.

[0080] All relevant contents of each step involved in the above method embodiment can be referred to the functional description of the corresponding functional module, and will not be repeated here.

[0081] In other embodiments of the present application, the present application discloses an electronic device, such as Figure 3 As shown, the electronic device 300 may include: one or more processors 301; a memory 302; a display 303; one or more applications (not shown); and one or more computer programs 304. The above components may be connected via one or more communication buses 305. The one or more computer programs 304 are stored in the above memory and configured to be executed by the one or more processors 301. The one or more computer programs 304 include instructions. The above instructions may be used to execute the following: Figure 1 , Figure 2 And each step in the corresponding embodiment.

[0082] Through the description of the above implementation methods, technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. The specific working process of the system, device and unit described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0083] Each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of software functional units.

[0084] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as flash memory, mobile hard disk, read-only memory, random access memory, disk or optical disk.

[0085] The above is only a specific implementation of the embodiment of the present application, but the protection scope of the embodiment of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed in the embodiment of the present application should be included in the protection scope of the embodiment of the present application. Therefore, the protection scope of the embodiment of the present application should be based on the protection scope of the claims.

Claims

1. A honeycomb graph evolution method based on Moran process, characterized in that: include: Based on evolutionary game theory, a honeybee graph evolution model based on the moran process is constructed to simulate the evolution of attack and defense strategies; The attack and defense benefit matrix is ​​calculated based on the attack and defense strategy combinations during the evolution of the honey array graph evolution model; Set the selection intensity coefficients for both the attacker and the defender based on historical game decision data; According to the attack and defense benefit matrix and the selection intensity coefficient, a dynamic evolution equation of network attack and honey array diagram decision based on Moran process is constructed, and the dynamic evolution equation is solved to obtain the stable equilibrium of attack and defense strategy evolution, thereby obtaining the optimal honey array diagram strategy set.

2. The method according to claim 1, characterized in that The honey burst graph evolution model based on the moran process includes five tuples (E, S, P, θ, U); Among them, E represents the set of network attack and defense participants, S represents the state set of network attack and defense, P represents the strategy space of network attack and defense, θ represents the network attack and defense belief set, and U represents the profit function in the process of network attack and defense.

3. The method according to claim 1, characterized in that The attack and defense benefit matrix is ​​calculated based on the attack and defense strategy combination in the evolution process of the honey array graph evolution model, including: In the evolution process of the honey array graph evolution model, the honey array adjusts the array graph strategy to obtain the attack strategy set AS and the honey array graph strategy set DS, where i and j represent the number of strategies, 1≤i≤m, And m≥2, 1≤j≤n, and n≥2; Set the attack and defense profit matrix in different strategy combinations The following is the income The attack and defense benefit matrix satisfies the following formula: , where X represents the attack and defense profit matrix, represents the payoff matrix of the network attacker, represents the payoff matrix of the honey array graph, , , It represents the profit function of the network attacker in the process of network attack and defense, It represents the profit function of the honeycomb graph during the network attack and defense process.

4. The method according to claim 1, characterized in that According to the attack and defense benefit matrix and the selection intensity coefficient, a dynamic evolution equation of network attack and honeycomb diagram decision based on Moran process is constructed, including: Calculating the expected benefits of the attack strategy and the expected benefits of the honey array map strategy according to the attack and defense benefit matrix, and introducing the selection intensity coefficient to calculate the individual fitness of the attack strategy and the individual fitness of the honey array map strategy; According to the individual fitness of the attack strategy and the individual fitness of the honey array graph strategy, a network attack and honey array graph decision-making dynamic evolution equation based on the moran process is constructed.

5. The method according to claim 4, characterized in that The expected benefits of the attack strategy and the expected benefits of the honey array map strategy are calculated according to the attack and defense benefit matrix, and the individual fitness of the attack strategy and the individual fitness of the honey array map strategy are calculated by introducing the selection intensity coefficient, including: The expected return of the attack strategy and the expected return of the honey array strategy calculated according to the attack and defense return matrix satisfy the following formula: , ,in, represents the expected return of the attack strategy, represents the expected return of the honey-array graph strategy, , represents the i-th attack strategy, N represents the total number of attack strategies, represents the jth honey-array graph strategy, M represents the total number of honey-array graph strategies, Representation strategy The following income, Representation strategy The following income; The selection intensity coefficient is introduced to calculate the individual fitness of the attack strategy and the individual fitness of the honey array map strategy to meet the following formula: ,in, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, represents the selection intensity coefficient of the network attacker, Represents the selection intensity coefficient of the honey array diagram.

6. The method according to claim 4, characterized in that According to the individual fitness of the attack strategy and the individual fitness of the honey array graph strategy, a dynamic evolution equation of network attack and honey array graph decision based on the moran process is constructed, including: According to the individual fitness of the attack strategy and the individual fitness of the honey array diagram, the probability of individual number transition of selecting the attack strategy and the probability of individual number transition of selecting the honey array diagram strategy in the evolution process of the honey array diagram evolution model are calculated; The rate of change of the proportion of individuals who choose the attack strategy and the proportion of individuals who choose the honey-array strategy in the Moran process over time is approximately expressed by a stochastic differential equation. When , the following formula is satisfied: ,in, , represents the rate of change of the proportion of individuals who choose the attack strategy over time, represents the rate of change of the proportion of individuals who choose the honey-array strategy over time, Indicates the choice of attack strategy The proportion of individuals in the attack group, Indicates the selection of honey array graph strategy The proportion of individuals in the defense group, represents the drift term of the stochastic differential equation, represents the diffusion term of the stochastic differential equation, represents the time variation, represents the random change in an infinitesimal time interval, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, Indicates the number of individuals who choose the attack strategy from Changes to The transition probability, represents the transition probability that the number of individuals choosing the attack strategy remains unchanged, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, Indicates the number of individuals who choose the honey-array strategy from Changes to The transition probability, represents the transition probability when the number of individuals choosing the honey array strategy remains unchanged, M represents the total number of honey array strategies, and N represents the total number of attack strategies; Substituting the drift term and diffusion term of the stochastic differential equation into the stochastic differential equation, the network attack and honeycomb graph decision dynamic evolution equation based on the Moran process satisfies the following formula: ,in, and m≥2, and n≥2, represents the individual fitness of the attack strategy, represents the individual fitness of the honey-array graph strategy, Indicates The probability of selecting an attack strategy is Indicates The expected return of an attack strategy is Indicates The probability of selecting a honey array strategy, Indicates The expected return of a honey array strategy.

7. The method according to claim 6, characterized in that Solving the dynamic evolution equations, we can obtain the stable equilibrium of the attack and defense strategy evolution, and thus obtain the optimal honey array strategy set, including: make Used to calculate the evolutionary stable equilibrium point of the dynamic evolution equation; The dynamic evolution equation is solved to obtain the equilibrium strategy of network attack and honey array graph, thus obtaining the optimal honey array graph strategy set.

8. A honey-array graph evolution device based on the Moran process, characterized in that: include: The model building unit is used to build a honey array graph evolution model based on the Moran process based on evolutionary game theory to simulate the evolution of attack and defense strategies; The benefit calculation unit is used to calculate the attack and defense benefit matrix according to the attack and defense strategy combination in the evolution process of the honey array graph evolution model; A coefficient selection unit, used to set the selection intensity coefficients of the attacking and defending parties according to historical game decision data; The evolutionary solution unit is used to construct a dynamic evolution equation of network attack and honey array diagram decision based on the Moran process according to the attack and defense benefit matrix and the selection intensity coefficient, and solve the dynamic evolution equation to obtain a stable equilibrium of the attack and defense strategy evolution, thereby obtaining an optimal honey array diagram strategy set.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for evolving a honeybee graph based on a Moran process according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: include: Processor and memory; The memory is used to store computer programs; The processor is used to execute the computer program stored in the memory so that the electronic device executes the honeybee graph evolution method based on the Moran process as described in any one of claims 1 to 7.

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