CN112822682B - WSN attack and defense game method based on non-cooperative game - Google Patents

WSN attack and defense game method based on non-cooperative game Download PDF

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CN112822682B
CN112822682B CN202011633353.7A CN202011633353A CN112822682B CN 112822682 B CN112822682 B CN 112822682B CN 202011633353 A CN202011633353 A CN 202011633353A CN 112822682 B CN112822682 B CN 112822682B
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CN112822682A (en
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刘贵云
罗朝龙
孟繁星
冯凯力
彭智敏
李君强
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Guangzhou University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention discloses a WSN attack and defense game method based on a non-cooperative game, which comprises the following steps: s1, constructing a malicious program propagation model of the WSN; judging the participants of the malicious program propagation model; s2, listing a function income table according to the functional relation among the participants of the malicious program propagation model; s3, constructing a revenue function of each participant under the model according to the function revenue table; and carrying out mixed Nash equilibrium strategy solution on the revenue function to obtain a mixed Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model. The invention solves the mixed Nash equilibrium strategy solution of the WSN attack and defense game model, particularly the mixed Nash equilibrium strategy solution of the SIR three-party attack and defense game, and solves the defect of single individual game analysis.

Description

WSN attack and defense game method based on non-cooperative game
Technical Field
The invention relates to the technical field of wireless sensor network security, in particular to a WSN (wireless sensor network) attack and defense game method based on a non-cooperative game.
Background
Malicious program propagation is a class of important security issues faced by Wireless Sensor Networks (WSNs). Most of the current researches on malicious program propagation only comprise researches on two aspects of intrusion detection and malicious program propagation, the researches on the two aspects are independent and separate researches, the internal relations of the two aspects are not connected, and an immune repair process is also lacked. Although game theory analysis is also adopted in the research process, more is double random game analysis, and the processes of intrusion detection and malicious program propagation are carried out with the event occurrence probability of 1, so that certain loss costs, such as energy costs, of the intrusion detection and the malicious program propagation are ignored.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a WSN (wireless sensor network) attack-defense game method based on a non-cooperative game, which can obtain a mixed Nash equilibrium strategy solution.
The purpose of the invention is realized by the following technical scheme:
a WSN attack and defense game method based on a non-cooperative game comprises the following steps:
s1, constructing a malicious program propagation model of the WSN; judging the participants of the malicious program propagation model;
s2, listing a function profit table according to the functional relation between the participants of the malicious program propagation model;
s3, constructing a profit function of each participant under the model according to the function profit table; and carrying out mixed Nash equilibrium strategy solution on the revenue function to obtain a mixed Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model.
Preferably, the participating parties are SIR three parties, SI two parties, SR two parties and IR two parties, and S is a susceptible node; i is a malicious node; r is an immune node.
Preferably, if the participants of the malware propagation model are SIR triplets, the revenue function is:
E uS(SIR) ＝x*(y*z*(a-e S )+y*(1-z)*(a-e S )+(1-y)*z*(-c-e S )+(1-y)*(1-z)*(-e S ))+(1-x)*y*(1-z)*(-b)
E uI(SIR) ＝y*(x*z*(-a-c-e I )+x*(1-z)*(-a-e I )+(1-x)*z*(-e I )+(1-x)*(1-z)*(b-e I ))+(1-y)*(x*z*(-c-e I )+x*(1-z)*(-e I )+(1-x)*z*(-c-e I )+(1-x)*(1-z)*(-e I ))
E uR(SIR) ＝z*(x*y*(2*c-e R )+x*(1-y)*(2*c-e R )+(1-x)*y*(c-e R )+(1-x)*(1-y)*(c-e R ))
in SIR three-party attack and defense game, the final result E of the three-party attack and defense game is easy to know uR(SIR) Is maximum, i.e. when z =1, E uR(SIR) To the maximum, there are:
E uS(SIR) ＝x*(y*(a-e S )+(c+e S )*(y-1))
E uI(SIR) ＝c*y-e I -c-a*x*y-c*x*y
E uR(SIR) ＝c-e R +c*x；
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure BDA0002875548170000031
Comprises the following steps:
Figure BDA0002875548170000032
Figure BDA0002875548170000033
Figure BDA0002875548170000034
there is a system of equations:
Figure BDA0002875548170000035
the solution to the system of equations is:
Figure BDA0002875548170000036
(where c > e) S ) Namely, the hybrid Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model is obtained;
wherein E is uS (SIR)、E uI(SIR) 、E uR(SIR) Respectively as the revenue functions of susceptible nodes, malicious nodes and immune nodes; a is the profit of the susceptible node detecting the malicious program and the loss of the malicious node attacking the identified susceptible node, b is the profit of the malicious node attacking the susceptible node successfully and the loss of the susceptible node infected by the malicious program; c, the yield of the immune node for converting the malicious node into the susceptible node is obtained, and the malicious node is converted into the loss of the susceptible node by the immune node and is prevented from being usedThe epidemic nodes convert the susceptible nodes into the gains of the immune nodes, and the susceptible nodes are converted into the losses of the immune nodes by the immune nodes; e.g. of a cylinder s Detecting energy costs of malicious programs for susceptible nodes, e I Energy cost of sending general information or malicious programs for malicious nodes, e R The method comprises the steps of sending common information or energy cost of an immune recovery program for an immune node, wherein x is the probability of detecting a malicious program by a susceptible node, y is the probability of attacking by a malicious node, z is the probability of converting the malicious node into the susceptible node by the immune node, and the probability of converting the susceptible node into the immune node by the immune node.
Preferably, if the participants of the malware propagation model are SI parties, the revenue function is:
E uS(SI) ＝x*(y*(a-e S )+(1-y)(-e S ))+(1-x)*y*(-b)
E uI(SI) ＝y*(x*(-a-e I )+(1-x)*(b-e I ))+(1-y)*(x*(-e I )+(1-x)*(-e I ))
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure BDA0002875548170000041
Comprises the following steps:
Figure BDA0002875548170000042
Figure BDA0002875548170000043
there is a system of equations:
Figure BDA0002875548170000044
the solution to the system of equations is:
Figure BDA0002875548170000045
hybrid Nash equilibrium strategy of attack and defense game, namely malicious program propagation modelAnd (5) solving.
Preferably, if the participants of the malware propagation model are both SR parties, the revenue function is:
E uS(SR) ＝x*(z*(-c-e S )+(1-z)*(-e S ))
E uR(SR) ＝z*(x*(c-e R )+(1-x)*(-e R ))
when both SR parties attack and defense game, according to the function income table and the income function thereof, the income of the susceptible node is always negative, E uS(SR) To achieve maximum, i.e. when z =0, E uS(SR) The maximum is reached, and for the benefit of the immune node, there are:
order to
Figure BDA0002875548170000051
Comprises the following steps:
Figure BDA0002875548170000052
get it solved
Figure BDA0002875548170000053
Preferably, if the participants of the malware propagation model are IR parties, the revenue function is:
E uI(IR) ＝y*(z*(-c-e I )+(1-z)*(-e I ))+(1-y)*(z*(-c-e I )+(1-z)*(-e I ))
E uR(IR) ＝z*(y*(c-e R )+(1-y)*(c-e R ))
when the two parties of the IR attack and defense game are in the attack and defense game, the income of the malicious node is known to be negative forever according to the function income table and the income function thereof, and E ul(IR) To achieve maximum, i.e. when z =0, E uI(IR) The maximum is reached, for the benefit of the immune node, the function benefit table and the benefit function thereof can show that the value of y (y is more than or equal to 0 and less than or equal to 1) does not influence the benefit of the immune node, and the benefit of the immune node is always positive.
Preferably, when the susceptible node is in the detection state, the immune node converts the susceptible node into the immune node.
Preferably, when the susceptible node is in the detection state, the immune node converts the susceptible node into the immune node.
Compared with the prior art, the invention has the following advantages:
the method not only researches the internal connection association of two aspects of intrusion detection and malicious program transmission, but also adds a new state process as an immune repair process, namely when the susceptible node is in a detection state, the immune node can convert the susceptible node into the immune node, thereby better conforming to the current research on malicious program transmission.
The invention solves the mixed Nash equilibrium strategy solution of the WSN attack and defense game model, particularly the mixed Nash equilibrium strategy solution of the SIR three-party attack and defense game, and solves the defect of single individual game analysis.
In the random game analysis process, the invention considers certain loss costs of the random game analysis process, such as energy costs, besides the intrusion detection and malicious program propagation process.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic flow diagram of a WSN attack and defense gaming method based on a non-cooperative game in the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
Referring to fig. 1, a WSN attack and defense game method based on a non-cooperative game includes:
s1, constructing a malicious program propagation model of the WSN; judging the participants of the malicious program propagation model; the participating parties are SIR three parties, SI two parties, SR two parties and IR two parties, and S is a susceptible node; i is a malicious node; r is an immune node.
The WSN attacking and defending game model is composed of an S (susceptible node) I (malicious node) R (immune node) and can respectively form four sub-models of SIR, SI, SR and IR.
The three parties communicate with each other by sending and receiving information.
The purpose of the malicious node is to attack the susceptible node, namely, the malicious program information is sent, the attack process is embodied as spreading the malicious program to the susceptible node, and the susceptible node is converted into the malicious node after the attack is successful; the attack of the malicious node is ineffective to the immune node.
The susceptible node has the function of detecting the attack of the malicious node, namely, the received information is detected, and when the attack of the malicious node is successfully detected, the attack of the malicious node is ineffective to the susceptible node; when the susceptible node is in a detection state, immune recovery program information sent by immune node detection can be received, and the susceptible node is converted into an immune node.
The immune node can detect the susceptible node and convert the susceptible node into the immune node, namely, the immune recovery program information is injected to the susceptible node by sending the immune recovery program information, and the susceptible node is converted into the immune node when being in a detection state; the attack of the malicious node is ineffective to the immune node, and the immune node can detect the malicious node and convert the malicious node into the susceptible node, namely, the immune recovery program information is injected into the malicious node by sending the immune recovery program information, and the malicious node is converted into the susceptible node. All nodes have normal communication information exchange capacity, and malicious nodes can pretend to be susceptible nodes by sending normal information.
S2, listing a function income table according to the functional relation among the participants of the malicious program propagation model; the functional gain is as follows:
and (3) a yield table when the SIR three parties simultaneously serve as neighbors:
Figure BDA0002875548170000071
description of the drawings: when the susceptible node is in a detection state (whether the susceptible node is attacking the susceptible node is detected), and the malicious node attacks the susceptible nodeAnd the immune node detects (the immune node detects whether the susceptible node is in a detection state), the benefit of the susceptible node is a-c-e s 。
Figure BDA0002875548170000081
Figure BDA0002875548170000082
The income table when the SI, SR and IR are simultaneously used as neighbors:
Figure BDA0002875548170000083
Figure BDA0002875548170000084
Figure BDA0002875548170000091
the symbols are defined as follows:
Figure BDA0002875548170000092
note:
①a＞e S ＞0；b＞e R ＞0；c＞e R ＞0；
(2) when the susceptible node is in a detection state, the immune node can convert the susceptible node into the immune node;
(3) the malicious nodes are converted into susceptible nodes through the immune nodes, the susceptible nodes are converted into immune nodes through the immune nodes, and the two processes belong to independent processes;
(4) s: a susceptible node; i: a malicious node; r: an immune node;
s3, constructing a revenue function of each participant under the model according to the function revenue table; and carrying out mixed Nash equilibrium strategy solution on the revenue function to obtain a mixed Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model. The method comprises the steps of analyzing attack and defense game behaviors among three parties or two parties among a susceptible node, a malicious node and an immune node from the perspective of a game theory, and further researching and discussing a WSN malicious program propagation process driven by a game strategy to obtain a mixed Nash equilibrium strategy solution of the attack and defense game of each model. The method comprises the following specific steps:
if the participants of the malicious program propagation model are SIR three parties, the gain function is as follows:
E uS(SIR) ＝x*(y*z*(a-e S )+y*(1-z)*(a-e S )+(1-y)*z*(-c-e S )+(1-y)*(1-z)*(-e S ))+(1-x)*y*(1-z)*(-b)
E uI(SIR) ＝y*(x*z*(-a-c-e I )+x*(1-z)*(-a-e I )+(1-x)*z*(-e I )+(1-x)*(1-z)*(b-e I ))+(1-y)*(x*z*(-c-e I )+x*(1-z)*(-e I )+(1-x)*z*(-c-e I )+(1-x)*(1-z)*(-e I ))
E uR(SIR) ＝z*(x*y*(2*c-e R )+x*(1-y)*(2*c-e R )+(1-x)*y*(c-e R )+(1-x)*(1-y)*(c-e R ))
in SIR three-party attack and defense game, the final result E of the three-party attack and defense game is easy to know uR(SIR) Is maximum, i.e. when z =1, E uR(SIR) To the maximum, there are:
E uS(SIR) ＝x*(y*(a-e S )+(c+e S )*(y-1))
E uI(SIR) ＝c*y-e I -c-a*x*y-c*x*y
E uR(SIR) ＝c-e R +c*x；
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure BDA0002875548170000111
Comprises the following steps:
Figure BDA0002875548170000112
Figure BDA0002875548170000113
Figure BDA0002875548170000114
there is a system of equations:
Figure BDA0002875548170000115
the solution to the system of equations is:
Figure BDA0002875548170000116
(where c > e) S ) Namely, the hybrid Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model is obtained;
wherein E is uS(SIR) 、E uI(SIR) 、E uR(SIR) Respectively as the revenue functions of susceptible nodes, malicious nodes and immune nodes;
in SIR three-party attack and defense game, the profit of R is always positive profit as known by the function profit table and the profit function thereof, namely when z =1,c > e S When E is greater uI(SIR) To the maximum, in this case:
when the temperature is higher than the set temperature
Figure BDA0002875548170000121
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000122
the expected income of attack initiated by the malicious node is equal to the expected income of no attack;
when in use
Figure BDA0002875548170000123
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000124
the expected income of attack initiated by the malicious node is larger than that of non-attack;
when in use
Figure BDA0002875548170000125
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000126
the expected income of attack initiated by the malicious node is less than that of non-attack;
when in use
Figure BDA0002875548170000127
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000128
the expected benefit of the susceptible node for detection is equal to the expected benefit of the node for no detection;
when in use
Figure BDA0002875548170000129
When the temperature of the water is higher than the set temperature,
Figure BDA00028755481700001210
the expected benefit of the susceptible node for detection is larger than the expected benefit of the node without detection;
when in use
Figure BDA00028755481700001211
When the temperature of the water is higher than the set temperature,
Figure BDA00028755481700001212
the expected benefit of the susceptible node for detection is less than the expected benefit of the node without detection;
from the above analysis, when the SIR three-party attack and defense game is performed, since the expected yield of the immune node is always positive, the susceptible node can determine whether to perform detection according to the attack probability of the malicious node, and the malicious node also determines whether to initiate attack according to the probability of detecting the susceptible node,
Figure BDA00028755481700001213
and the method is a mixed Nash equilibrium strategy for carrying out attack and defense game by a susceptible node, a malicious node and an immune node. And finishing the verification.
If the participants of the malicious program propagation model are both SI parties, the revenue function is as follows:
E uS(SI) ＝x*(y*(a-e S )+(1-y)(-e S ))+(1-x)*y*(-b)
E uI(sI) ＝y*(x*(-a-e I )+(1-x)*(b-e I ))+(1-y)*(x*(-e I )+(1-x)*(-e I ))
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure BDA0002875548170000131
Comprises the following steps:
Figure BDA0002875548170000132
Figure BDA0002875548170000133
there is a system of equations:
Figure BDA0002875548170000134
the solution to the system of equations is:
Figure BDA0002875548170000135
namely, the hybrid Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model.
When the SI parties attack and defense game, the function gain table and the gain function thereof can know that whether S is detected is related to whether R is attacked or not in order to pursue the maximization of the gains of the two parties, as follows:
when in use
Figure BDA0002875548170000136
When the utility model is used, the water is discharged,
Figure BDA0002875548170000137
the expected income of attack initiated by the malicious node is equal to the expected income of no attack;
when in use
Figure BDA0002875548170000138
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000139
the expected income of attack initiated by the malicious node is larger than that of non-attack;
when in use
Figure BDA00028755481700001310
When the temperature of the water is higher than the set temperature,
Figure BDA00028755481700001311
the expected income of attack initiated by the malicious node is less than that of non-attack;
when in use
Figure BDA00028755481700001312
When the temperature of the water is higher than the set temperature,
Figure BDA00028755481700001313
the expected benefit of the susceptible node for detection is equal to the expected benefit of the node for no detection;
when in use
Figure BDA0002875548170000141
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000142
the expected benefit of the susceptible node for detection is larger than the expected benefit of the node without detection;
when in use
Figure BDA0002875548170000143
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000144
the expected benefit of the susceptible node for detection is less than the expected benefit of the node without detection;
from the above analysis, when SI two-party attack and defense game, the susceptible node will determine whether to detect according to the attack probability of the malicious node, and the malicious node should also determine whether to launch the attack according to the probability of the susceptible node,
Figure BDA0002875548170000145
the method is a mixed Nash equilibrium strategy for carrying out attack and defense game on the susceptible nodes and the malicious nodes. And finishing the verification.
If the participants of the malicious program propagation model are SR parties, the revenue function is as follows:
E uS(SR) ＝x*(z*(-c-e S )+(1-z)*(-e S ))
E uR(SR) ＝z*(x*(c-e R )+(1-x)*(-e R ))
when both SR parties attack and defense game, according to the function income table and the income function thereof, the income of the susceptible node is always negative, E uS(SR) To achieve maximum, i.e. when z =0, E uS(SR) The maximum is reached, and for the benefit of the immune node, there are:
order to
Figure BDA0002875548170000146
Comprises the following steps:
Figure BDA0002875548170000147
get through solution
Figure BDA0002875548170000148
In order to maximize the profit of both parties, whether to detect S and whether to detect R are related to each other, as follows:
when in use
Figure BDA0002875548170000151
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000152
the expected benefit of the immune node for detection is equal to the expected benefit of the immune node for non-attack;
when the temperature is higher than the set temperature
Figure BDA0002875548170000153
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000154
the expected benefit of the immune node for detection is larger than that of the immune node without attack;
when the temperature is higher than the set temperature
Figure BDA0002875548170000155
When the temperature of the water is higher than the set temperature,
Figure BDA0002875548170000156
the expected income of the immune node for detection is less than the expected income of the immune node without attack;
when z =0, the expected benefit of the susceptible node is maximized;
from the above analysis, when the two parties of the SR attack and defense game play, the susceptible node determines whether to perform detection according to the detection probability of the immune node, and the immune node also determines whether to perform detection according to the detection probability of the susceptible node,
Figure BDA0002875548170000157
the method is a mixed Nash equilibrium strategy for the susceptible node and the immune node to carry out attack and defense game. And finishing the verification.
If the participants of the malicious program propagation model are both IR parties, the revenue function is:
E uI(IR) ＝y*(z*(-c-e I )+(1-z)*(-e I ))+(1-y)*(z*(-c-e I )+(1-z)*(-e I ))
E uR(IR) ＝z*(y*(c-e R )+(1-y)*(c-e R ))
when the two IR parties attack and defense game, according to the function income table and the income function thereof,the yield of the malicious node is always negative, E uI(IR) To achieve maximum, i.e. when z =0, E uI(IR) The maximum is reached, for the benefit of the immune node, the function benefit table and the benefit function thereof can show that the value of y (y is more than or equal to 0 and less than or equal to 1) does not influence the benefit of the immune node, and the benefit of the immune node is always positive.
From the analysis, when the IR three-party attack and defense game is carried out, because the expected income of the malicious node is negative forever and the expected income of the immune node is positive forever,
Figure BDA0002875548170000161
the method is a mixed Nash equilibrium strategy for carrying out attack and defense game on susceptible nodes, malicious nodes and immune nodes. And finishing the verification.
The invention analyzes the micro mechanism of WSN malicious program propagation from the angle of game theory, establishes an attack and defense game model of the WSN, solves the mixed Nash equilibrium solution of the game model, and determines the infection probability of the malicious program according to the mixed Nash equilibrium strategy of both game parties, thereby establishing the malicious program propagation model of the WSN. The method carries out simulation on the spreading process of the WSN malicious program, reveals the relation between the spreading speed of the malicious program and the game parameters, and has theoretical guiding significance for inhibiting the spreading of the WSN malicious program according to research results.
The above-mentioned embodiments are preferred embodiments of the present invention, and the present invention is not limited thereto, and any other modifications or equivalent substitutions that do not depart from the technical spirit of the present invention are included in the scope of the present invention.

Claims (5)

1. A WSN attack and defense game method based on a non-cooperative game is characterized by comprising the following steps:
s1, constructing a malicious program propagation model of the WSN; judging the participants of the malicious program propagation model;
s2, listing a function income table according to the functional relation among the participants of the malicious program propagation model;
s3, constructing a profit function of each participant under the model according to the function profit table; performing mixed Nash equilibrium strategy solution on the revenue function to obtain a mixed Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model;
the participating parties are SIR three parties, SI two parties, SR two parties and IR two parties, and S is a susceptible node; i is a malicious node; r is an immune node;
if the participants of the malicious program propagation model are SIR three parties, the gain function is as follows:
E uS(SIR) ＝x*(y*z*(a-e S )+y*(1-z)*(a-e S )+(1-y)*z*(-c-e S )+(1-y)*(1-z)*(-e S ))+(1-x)*y*(1-z)*(-b)
E uI(SIR) ＝y*(x*z*(-a-c-e I )+x*(1-z)*(-a-e I )+(1-x)*z*(-e I )+(1-x)*(1-z)*(b-e I ))+(1-y)*(x*z*(-c-e I )+x*(1-z)*(-e I )+(1-x)*z*(-c-e I )+(1-x)*(1-z)*(-e I ))
E uR(SIR) ＝z*(x*y*(2*c-e R )+x*(1-y)*(2*c-e R )+(1-x)*y*(c-e R )+(1-x)*(1-y)*(c-e R ))
in SIR three-party attack and defense game, the final result E of the three-party attack and defense game is easy to know uR(SIR) Is maximum, i.e. when z =1, E uR(SIR) To the maximum, then:
E uS(SIR) ＝x*(y*(a-e S )+(c+e S )*(y-1))
E uI(SIR) ＝c*y-e I -c-a*x*y-c*x*y
E uR(SIR) ＝c-e R +c*x；
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure FDA0004000189520000021
Comprises the following steps:
Figure FDA0004000189520000022
Figure FDA0004000189520000023
Figure FDA0004000189520000024
there is a system of equations:
Figure FDA0004000189520000025
the solution to the system of equations is:
Figure FDA0004000189520000026
wherein c > e S Namely, the hybrid Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model is obtained;
wherein E is uS(SIR) 、E uI(SIR) 、E uR(SIR) Respectively as the revenue functions of susceptible nodes, malicious nodes and immune nodes; a is the profit of the susceptible node detecting the malicious program and the loss of the malicious node attacking the identified susceptible node, b is the profit of the malicious node attacking the susceptible node successfully and the loss of the susceptible node infected by the malicious program; c, the yield of the immune node for converting the malicious node into the susceptible node, the loss of the malicious node converted into the susceptible node by the immune node, the yield of the immune node converted into the susceptible node by the immune node and the loss of the susceptible node converted into the immune node by the immune node are obtained; e.g. of a cylinder s Detecting energy costs of malicious programs for susceptible nodes, e I Energy cost of sending general information or malicious programs for malicious nodes, e R The method comprises the steps of sending common information or energy cost of an immune recovery program for an immune node, wherein x is the probability of detecting a malicious program by a susceptible node, y is the probability of attacking by a malicious node, z is the probability of converting the malicious node into the susceptible node by the immune node, and the probability of converting the susceptible node into the immune node by the immune node.
2. The WSN attacking and defending gaming method based on the non-cooperative gaming of claim 1, wherein if the participants of the malicious program propagation model are SI parties, the revenue function is:
E uS(SI) ＝x*(y*(a-e S )+(1-y)(-e S ))+(1-x)*y*(-b)
E uI(SI) ＝y*(x*(-a-e I )+(1-x)*(b-e I ))+(1-y)*(x*(-e I )+(1-x)*(-e I ))
the step of performing a hybrid Nash equalization strategy solution on the revenue function includes:
order to
Figure FDA0004000189520000031
Comprises the following steps:
Figure FDA0004000189520000032
Figure FDA0004000189520000033
there is a system of equations:
Figure FDA0004000189520000034
the solution to the system of equations is:
Figure FDA0004000189520000035
namely, the hybrid Nash equilibrium strategy solution of the attack and defense game of the malicious program propagation model.
3. The WSN attacking and defending game method based on the non-cooperative game as claimed in claim 1, wherein if the participants of the malicious program propagation model are SR parties, the revenue function is:
E uS(SR) ＝x*(z*(-c-e S )+(1-z)*(-e S ))
E uR(SR) ＝z*(x*(c-e R )+(1-x)*(-e R ))
when both SR parties attack and defense game, according to the function income table and the income function thereof, the income of the susceptible node is always negative, E uS(SR) To achieve maximum, i.e. when z =0, E uS(SR) The maximum is reached, and for the benefit of the immune node, there are:
order to
Figure FDA0004000189520000041
Comprises the following steps:
Figure FDA0004000189520000042
get it solved
Figure FDA0004000189520000043
4. The WSN attacking and defending gaming method based on the non-cooperative gaming of claim 1, wherein if the participants of the malicious program propagation model are IR parties, the revenue function is:
E uI(IR) ＝y*(z*(-c-e I )+(1-z)*(-e I ))+(1-y)*(z*(-c-e I )+(1-z)*(-e I ))
E uR(IR) ＝z*(y*(c-e R )+(1-y)*(c-e R ))
when the two IR parties attack and defense game, the profits of the malicious nodes are known to be negative forever according to the function gain table and the gain function thereof, and E uI(IR) To achieve maximum, i.e. when z =0, E uI(IR) The maximum is reached, for the benefit of the immune node, the value of y (y is more than or equal to 0 and less than or equal to 1) does not influence the benefit of the immune node, and the benefit of the immune node is positive benefit forever.
5. The WSN attacking and defending game method based on the non-cooperative game as claimed in claim 1, wherein when a susceptible node is in a detection state, the immune node converts the susceptible node into the immune node.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103152345A (en) * 2013-03-07 2013-06-12 南京理工大学常熟研究院有限公司 Network safety optimum attacking and defending decision method for attacking and defending game
CN108898010A (en) * 2018-06-25 2018-11-27 北京计算机技术及应用研究所 A method of establishing the attacking and defending Stochastic Game Model towards malicious code defending

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB0622792D0 (en) * 2006-11-15 2006-12-27 Cognima Ltd Apparatus for transferring advertising content to a mobile telephone
US20140114746A1 (en) * 2012-10-19 2014-04-24 Adobe Systems Incorporated Selection of Creatives Based on Performance Analysis and Predictive Modeling

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103152345A (en) * 2013-03-07 2013-06-12 南京理工大学常熟研究院有限公司 Network safety optimum attacking and defending decision method for attacking and defending game
CN108898010A (en) * 2018-06-25 2018-11-27 北京计算机技术及应用研究所 A method of establishing the attacking and defending Stochastic Game Model towards malicious code defending

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
"基于博弈的能量获取传感器网络分布式估计算法";刘贵云;《广州大学学报(自然科学版)》;20140215;全文 *

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