CN111343180B - Multi-type malicious program attack and defense method based on nonlinear chargeable sensor network model - Google Patents

Multi-type malicious program attack and defense method based on nonlinear chargeable sensor network model Download PDF

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CN111343180B
CN111343180B CN202010115515.1A CN202010115515A CN111343180B CN 111343180 B CN111343180 B CN 111343180B CN 202010115515 A CN202010115515 A CN 202010115515A CN 111343180 B CN111343180 B CN 111343180B
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CN111343180A (en
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刘贵云
彭百豪
钟晓静
舒聪
唐冬
向建化
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Guangzhou University
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    • H—ELECTRICITY
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Abstract

The invention relates to a multi-type malicious program attacking and defending method based on a nonlinear chargeable sensor network model, which comprises the following steps: s1, constructing a multi-type malicious program propagation model based on the wirelessly rechargeable sensor network, wherein the malicious program propagation model takes a logistic growth rate as a node number growth rate of the wirelessly rechargeable sensor network; s2, constructing a state flow chart of the wireless chargeable sensor network node, and writing differential equations of each state according to the state flow chart; s3, constructing a cost function under the malicious program propagation model; and S4, constructing a Hamiltonian equation according to the differential equation of each state and the cost function. The invention not only further considers the problem of energy consumption, but also introduces nonlinear logistic input and nonlinear infection rate, thereby further conforming to the working environment of the actual wireless sensor network.

Description

Multi-type malicious program attack and defense method based on nonlinear chargeable sensor network model
Technical Field
The invention relates to the technical field of wireless chargeable sensor networks, in particular to a multi-type malicious program attacking and defending method based on a nonlinear chargeable sensor network model.
Background
With the continuous update of the corresponding technologies of wireless sensor networks, the related fields are also wider and wider, such as military fields, medical health, environmental monitoring, building safety, earthquake monitoring, intelligent transportation and the like, so that the importance and the expandability of the wireless sensor networks can be seen. The traditional wireless sensor network can also be composed of nodes for collecting surrounding information, and the nodes and a base station or a remote data center complete the transmission of processing information in a multi-hop mode. Due to the relatively simple structure of the wireless sensor network, once the wireless sensor network is attacked by a malicious program without any defense measures, the malicious program can quickly infect the whole network, so that network paralysis and information leakage caused by the malicious program can cause huge economic hidden danger and loss.
The spread of the malicious program in the wireless sensor network gradually increases from the most basic SIS model, namely a susceptible state, an infected state and a susceptible state on the basis, namely an R state, namely a repair state; q state, i.e. isolated state; the E state, i.e., the exposed state, and various dormant states, etc., are discussed in detail from the node infection level.
In the traditional malicious program propagation model, the released nodes are disposable, however, many nodes will die over time, and the total presentation is that the number of nodes is reduced. The continuous reduction of the number of nodes inevitably causes the wireless sensor network not to work normally. In the infection process, that is, the node state is from a susceptible state to an infected state, the traditional malicious program propagation model is a linear growth model and a single type of malicious program propagation, and in the single type of malicious program propagation model, after the susceptible node is infected, the susceptible node is finally dead or becomes an immune node. However, as a practical matter, a malicious program cannot be of one type, and like a computer virus, a computer also needs to update a protection measure in real time to target a new virus.
In summary, the traditional malicious program propagation model cannot adopt accurate infection rate and face various malicious programs, cannot maintain normal work of the sensor network, and does not conform to the working environment of the actual wireless sensor network.
Disclosure of Invention
Aiming at the problems of the multi-type malicious program attacking and defending method based on the nonlinear chargeable sensor network model in the prior art, the invention provides the multi-type malicious program attacking and defending method based on the nonlinear chargeable sensor network model.
The specific scheme of the application is as follows:
a multi-type malicious program attack and defense method based on a nonlinear chargeable sensor network model comprises the following steps:
s1, constructing a multi-type malicious program propagation model based on the wirelessly rechargeable sensor network, wherein the malicious program propagation model takes a logistic growth rate as a node number growth rate of the wirelessly rechargeable sensor network;
s2, constructing a state flow chart of the wireless chargeable sensor network node, and writing differential equations of each state according to the state flow chart;
s3, constructing a cost function under the malicious program propagation model;
s4, constructing a Hamiltonian equation according to the differential equation of each state and the cost function;
and S5, further solving an equation set meeting the condition of the covariates and a corresponding attack and defense strategy according to the Hamiltonian.
Preferably, the malware propagation model adopts a non-linear infection rate, which is:
m＝[1-(1-PSI)nI(t)]
wherein P isSIRepresents the probability of the node transferring from the susceptible state to the infected state and satisfies 0 ≦ PSI≦ 1, where I (t) is the number of infected nodes and the number n represents the degree of the node.
Preferably, the logistic growth rate is:
Figure BDA0002391374610000031
where r represents the degree of the node, k represents the capacity of the wireless chargeable sensor network, and n (t) is the number of surviving nodes at the current time t.
Preferably, the differential equations for the various states are:
Figure BDA0002391374610000032
Figure BDA0002391374610000033
Figure BDA0002391374610000034
Figure BDA0002391374610000035
Figure BDA0002391374610000036
wherein, S (t), I (t), R (t), L (t), D (t) respectively represent that the node is in a susceptible state, an infected state, an immune full-energy state, a low-energy state and a death state; pSIIs the probability of transition from a susceptible state to an infected state; n is the degree of the node, namely the node has information communication with a plurality of surrounding nodes; i (t) is the number of nodes in an infected state at time t; pSLIs the transition probability from a susceptible state to a low energy state; a. theRSThe degree of control over the migration of an immune full-capable node from an immune full-capable state to a susceptible state for another type of malicious program; pRSThe transition probability of the immune full-energy state to the susceptible state; r (t) is the number of nodes in the immune full-energy state at the time t; dSRThe control degree of the wireless sensor system for transferring the node in the susceptible state from the susceptible state to the immune full-energy state is provided; pSRThe transition probability of the node from the susceptible state to the immune full-energy state is defined; dIRA degree of control for the node wireless sensor network to migrate the node in the infected state from the infected state to an immune-full state; pIRA transition probability for a node to transition from an infected state to an immune-full state; a. theILIs a malicious program pairA degree of control to migrate an infected node to a low energy node; pILA transition probability for a node to transition from an infected state to a low energy state; dLRA degree of control for the system to migrate nodes in a low energy state to nodes in an immune full energy state; pLRA transition probability for a node to transition from a low energy state to an immune full energy state; pRLIs the transition probability representing the node to transition from the immune full energy state to the low energy state; pLDA transition probability for a node to transition from a low energy state to a death state; l (t) is the number of nodes in a low energy state at time t; d (t) is the number of nodes in the death state at the moment t.
Preferably, the cost function is:
Figure BDA0002391374610000041
wherein, cNCost factors for logistic growth; c. CIA cost factor for an infected node due to infection with a malware; c. CRThe cost coefficient brought by downloading and installing patches for the immune full-energy node and simultaneously charging energy is increased; c. CDCost coefficient brought by the fact that the sensor network can not work normally due to the fact that the dead nodes die; c. CLThe cost coefficient is brought by the fact that certain functions cannot be normally started due to the fact that the low-energy node is in a low-energy state; c. CILCost coefficient brought by functional disorder caused by running malicious programs on infected nodes; c. CSRPositive income coefficient brought by patching for the susceptible nodes; c. CIRPositive profit coefficient for infected node due to patching; c. CLRPositive gain coefficients for low energy nodes due to patching and charging;
Figure BDA0002391374610000052
the cost coefficient brought by dead nodes at the final moment.
Preferably, the hamiltonian equation is:
Figure BDA0002391374610000051
wherein λ isS(t) is a covariate corresponding to the susceptible node; lambda [ alpha ]I(t) is a co-modal variable corresponding to the infected node; lambda [ alpha ]R(t) is a covariate corresponding to the immune full energy node; lambda [ alpha ]D(t) is a co-modal variable corresponding to the dead node; lambda [ alpha ]LAnd (t) is a covariate corresponding to the low-energy node.
Preferably, the hamiltonian equation is:
Figure BDA0002391374610000061
wherein: n (t) ═ s (t) + i (t) + r (t) + l (t).
Preferably, the optimal control strategy is obtained according to the bilateral maximum principle, and each collaborative equation must satisfy the following conditions:
Figure BDA0002391374610000062
λS(T)＝0
Figure BDA0002391374610000071
λI(T)＝0
Figure BDA0002391374610000072
λR(T)＝0
Figure BDA0002391374610000073
Figure BDA0002391374610000074
Figure BDA0002391374610000075
λL(T)＝0
according to the bilateral extremum principle, and considering that the following inequality holds:
ASImin≤ASI≤ASImax
ARSmin≤ARS≤ARSmax
AILmin≤AIL≤AILmax
DSRmin≤DSR≤DSRmax
DIRmin≤DIR≤DIRmax
DLRmin≤DLR≤DLRmax
wherein A isSIminMinimal control that a malicious program can exert over the transition of a node from a susceptible state to an infected state; a. theSImaxMaximum control that a malicious program can exert over the node moving from a susceptible state to an infected state; a. theRSminMinimal control that a malicious program can exert over the transition of the node from the immune full-energy state to the susceptible state; a. theRSmaxMaximum control that a malicious program can exert on a node to transition from an immune full-energy state to a susceptible state; a. theILminMinimal control that a malicious program can exert over the transition of a node from an infected state to a low energy state; a. theILmaxMaximum control that a malicious program can exert over the transition of a node from an infected state to a low energy state; dSRminMinimum control which can be exerted on the node from a susceptible state to an immune full-energy state is provided for the wireless sensor network; dSRmaxMaximum control that a malicious program can exert on a node to transition from a susceptible state to an immune full-energy state; dIRminMinimal control that a malicious program can exert over the transition of a node from an infected state to an immune full-energy state; dIRmaxIs aversion toMaximum control that the program can exert over the transition of the node from the infected state to the immune-full state; dLRminMinimal control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state; dLRmaxMaximum control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state;
the optimal attack and defense strategy is as follows:
when-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＞0， ASI＝ASImax；
When-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＜0， ASI＝ASImin；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＞0，ARS＝ARSmax；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＜0，ARS＝ARSmin；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＞0，AIL＝AILmax；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＜0，AIL＝AILmin；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＜0，DSR＝DSRmax；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＞0，DSR＝DSRmin；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＜0，DIR＝DIRmax；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＞0，DIR＝DIRmin(ii) a When-lambdaLPLRL(t)+λRPLRL(t)-cP&RPLRL(t)＜0，DLR＝DLRmax；
When-lambdaLPLRL(t)+λRPLRL(t)-cP&RPLRL(t)＞0，DLR＝DLRmin。
Compared with the prior art, the invention has the following beneficial effects:
the wireless chargeable sensor network is based on a differential game, utilizes a bilateral maximum value principle, adopts the wireless chargeable sensor network containing nonlinear logistic input, nonlinear infection rate and various malicious program intrusions, takes the wireless chargeable sensor network and the malicious programs as attacking and defending objects, and provides an optimal attacking and defending strategy of the wireless chargeable sensor network to various malicious programs. Compared with a traditional malicious program propagation model, the model not only further considers the problem of energy consumption, but also introduces the conditions of nonlinear logistic input, nonlinear infection rate and attack of various malicious programs, so that the model further conforms to the working environment of an actual wireless sensor network.
Drawings
Fig. 1 is a schematic flow chart of a multi-type malicious program attacking and defending method based on a nonlinear chargeable sensor network model according to the embodiment.
Fig. 2 is a state flow chart of the present embodiment.
Detailed Description
The invention is further illustrated by the following figures and examples.
The scheme provides an attack and defense strategy for a wireless chargeable sensor network containing nonlinear factors to various types of malicious programs based on differential game.
Referring to fig. 1, a multi-type malicious program attack and defense method based on a nonlinear chargeable sensor network model includes:
s1, constructing a multi-type malicious program propagation model based on the wirelessly rechargeable sensor network, wherein the malicious program propagation model takes a logistic growth rate as a node number growth rate of the wirelessly rechargeable sensor network; where the malware propagation model appears to transition from an immune full-capable state to a vulnerable state, previous patches do not work against new malware.
According to the traditional malicious program propagation model, the released nodes are disposable, however, many nodes are obliterated along with the time, and the total presentation is that the number of the nodes is reduced. The continuous reduction of the number of the nodes can certainly prevent the wireless sensor network from working normally, so that the charging factor is introduced and the number of times of node throwing is further introduced. That is, not only can the normal work of the sensing network be maintained by relieving node decay, but also the normal operation of the network can be maintained by continuously increasing nodes from the input. The scheme adopts the logistic growth model as the increasing rate of the input newly added nodes, and the logistic growth model is established on the premise that the birth rate and the death rate of the population are only considered, but external factors of the population, such as natural enemies, bacteria, viruses and the like, are not considered. Therefore, the scheme takes the logistic equation as the premise that the growth rate of the release node can meet the logistic growth, can better accord with the biological growth rule, and further saves the release cost. Compared with the traditional linear increment, the logical stutty growth model has the advantages that after the population number is increased to a certain degree, the growth rate is reduced, because the resources are limited, too many individuals exceed the bearing capacity of the system, and a part of individuals are eliminated. For the wireless sensor network, in order to further save the putting cost, namely reduce the resource waste caused by the appearance of unnecessary nodes, a logistic growth model is adopted as the increasing rate of the newly added nodes. The logistic growth rate is:
Figure BDA0002391374610000111
wherein R represents the degree of the nodes, k represents the capacity of the wireless chargeable sensor network, and n (t) is the number of the surviving nodes at the current time t, namely the sum of the numbers of the four types of nodes including the susceptible node S, the infected node I, the immune full-energy node R and the low-energy node L.
Similarly, in the infection process, namely the process of the node state from the susceptible state to the infected state, the scheme also adopts a nonlinear growth model. Compared with the common linear infection rate, the non-linear infection can reflect the actual situation. It can be assumed that in the wireless sensor network, the probability that a susceptible node is infected by a surrounding node is definitely smaller than the probability that the susceptible node is infected by a surrounding group of nodes, and the latter situation is definitely more dominant as the infection increases, so that the infection rate of the model cannot be linear as time increases. And as the surrounding infection situation changes, an upper bound is reached, namely the infection is ensured, and the infection probability is 1. A similar growth model can be described as a state where, starting from 0, the infection rate increases rapidly to slowly over time and finally reaches saturation. Therefore, the malicious program propagation model of the scheme adopts the nonlinear infection rate which is as follows:
m＝[1-(1-PSI)nI(t)]
wherein P isSIRepresents the probability of the node transferring from the susceptible state to the infected state and satisfies 0 ≦ PSI≦ 1, where I (t) is the number of infected nodes and the number n represents the degree of the node.
It can be seen from the infection rate model that as the number of infected nodes increases, the infection rate increases rapidly, then increases slowly, and finally reaches a balance, which completely conforms to the above-described situation, so that the infection rate model has a certain practical significance.
Meanwhile, compared with a single type of malicious program propagation model, the scheme further discusses a multi-type malicious program propagation model. In a single type of malware propagation model, susceptible nodes are infected and eventually either die or become immunized nodes. However, as a practical matter, a malicious program cannot be of one type, and like a computer virus, a computer also needs to update a protection measure in real time to target a new virus. Therefore, based on actual conditions, the malicious program propagation model discusses the situation given to multiple types of malicious programs, but all the malicious programs have the common characteristic that the consumption of the nodes is further accelerated, so that the nodes are dead due to the fact that the energy is consumed, the modes and the processes are different, the energy can be consumed more quickly by increasing the information collection frequency, the transmission path of the information of the malicious programs is changed, the information is disseminated and propagated, the loss is increased, and the like. The multi-type malicious program propagation model has realistic guiding significance.
S2, constructing a state flow chart of the wireless chargeable sensor network node, and writing differential equations of each state according to the state flow chart; in FIG. 2, S (t), I (t), R (t), L (t), D (t) respectively indicate that the node is in a susceptible state, an infected state, an immune full-energy state, a low-energy state and a death state; the differential equations for each state are:
Figure BDA0002391374610000131
Figure BDA0002391374610000132
Figure BDA0002391374610000133
Figure BDA0002391374610000134
Figure BDA0002391374610000135
wherein, PSIIs the probability of transition from a susceptible state to an infected state; n is the degree of the node, i.e. how many surrounding nodes the node hasInformation exchange; i (t) is the number of nodes in an infected state at time t; pSLIs the transition probability from a susceptible state to a low energy state; a. theRSThe degree of control over the migration of an immune full-capable node from an immune full-capable state to a susceptible state for another type of malicious program; pRSThe transition probability of the immune full-energy state to the susceptible state; r (t) is the number of nodes in the immune full-energy state at the time t; dSRThe control degree of the wireless sensor system for transferring the node in the susceptible state from the susceptible state to the immune full-energy state is provided; pSRThe transition probability of the node from the susceptible state to the immune full-energy state is defined; dIRA degree of control for the node wireless sensor network to migrate the node in the infected state from the infected state to an immune-full state; pIRA transition probability for a node to transition from an infected state to an immune-full state; a. theILA degree of control over the migration of a node in an infected state to a low energy node for a malicious program; pILA transition probability for a node to transition from an infected state to a low energy state; dLRA degree of control for the system to migrate nodes in a low energy state to nodes in an immune full energy state; pLRA transition probability for a node to transition from a low energy state to an immune full energy state; pRLIs the transition probability representing the node to transition from the immune full energy state to the low energy state; pLDA transition probability for a node to transition from a low energy state to a death state; l (t) is the number of nodes in a low energy state at time t; d (t) is the number of nodes in the death state at the moment t.
S3, constructing a cost function under the malicious program propagation model; the cost function is:
Figure BDA0002391374610000141
wherein, cNCost factor for logistic growth, cNIs greater than zero; c. CICost factor for infected nodes due to infection with malicious programs, cIIs greater than zero; c. CRCost factor due to downloading and installing patches for immunization of a fully charged node, cRIs greater than zero; c. CDCost coefficient for dead nodes due to node extinction causing sensor network not to work normally, cDIs greater than zero; c. CLCost factor for low energy nodes due to low energy state, some functions can not be normally started, cLIs greater than zero; c. CILCost factor due to dysfunction caused by malicious program running on infected node, cILIs greater than zero; c. CSRPositive yield coefficient for susceptible nodes due to patching, cSRIs greater than zero; c. CIRPositive profit coefficient for infected node due to patching; c. CLRPositive gain coefficients for low energy nodes due to patching and charging;
Figure BDA0002391374610000142
the cost factor brought by the dead node at the final moment,
Figure BDA0002391374610000143
greater than zero.
S4, constructing a Hamiltonian equation according to the differential equation of each state and the cost function; the Hamiltonian equation is:
Figure BDA0002391374610000151
wherein λ isS(t) is a covariate corresponding to the susceptible node; lambda [ alpha ]I(t) is a co-modal variable corresponding to the infected node; lambda [ alpha ]R(t) is a covariate corresponding to the immune full energy node; lambda [ alpha ]D(t) is a co-modal variable corresponding to the dead node; lambda [ alpha ]LAnd (t) is a covariate corresponding to the low-energy node.
Further, the hamiltonian equation is:
Figure BDA0002391374610000152
wherein: n (t) ═ s (t) + i (t) + r (t) + l (t).
And S5, further solving an equation set meeting the condition of the covariates and a corresponding attack and defense strategy according to the Hamiltonian.
According to the bilateral maximum principle, an optimal control strategy is obtained, and each collaborative equation and the final value condition thereof must satisfy the following conditions:
Figure BDA0002391374610000161
λS(T)＝0
Figure BDA0002391374610000162
λI(T)＝0
Figure BDA0002391374610000163
λR(T)＝0
Figure BDA0002391374610000164
Figure BDA0002391374610000165
Figure BDA0002391374610000171
λL(T)＝0
according to the bilateral extremum principle, and considering that the following inequality holds:
ASImin≤ASI≤ASImax
ARSmin≤ARS≤ARSmax
AILmin≤AIL≤AILmax
DSRmin≤DSR≤DSRmax
DIRmin≤DIR≤DIRmax
DLRmin≤DLR≤DLRmax
wherein A isSIminMinimal control that a malicious program can exert over the transition of a node from a susceptible state to an infected state; a. theSImaxMaximum control that a malicious program can exert over the node moving from a susceptible state to an infected state; a. theRSminMinimal control that a malicious program can exert over the transition of the node from the immune full-energy state to the susceptible state; a. theRSmaxMaximum control that a malicious program can exert on a node to transition from an immune full-energy state to a susceptible state; a. theILminMinimal control that a malicious program can exert over the transition of a node from an infected state to a low energy state; a. theILmaxMaximum control that a malicious program can exert over the transition of a node from an infected state to a low energy state; dSRminMinimum control which can be exerted on the node from a susceptible state to an immune full-energy state is provided for the wireless sensor network; dSRmaxMaximum control that a malicious program can exert on a node to transition from a susceptible state to an immune full-energy state; dIRminMinimal control that a malicious program can exert over the transition of a node from an infected state to an immune full-energy state; dIRmaxMaximum control that a malicious program can exert over the transition of a node from an infected state to an immune full-energy state; dLRminMinimal control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state; dLRmaxMaximum control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state;
the optimal attack and defense strategy is as follows:
when-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＞0， ASI＝ASImax；
When-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＜0， ASI＝ASImin；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＞0，ARS＝ARSmax；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＜0，ARS＝ARSmin；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＞0，AIL＝AILmax；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＜0，AIL＝AILmin；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＜0，DSR＝DSRmax；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＞0，DSR＝DSRmin；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＜0，DIR＝DIRmax；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＞0，DIR＝DIRmin；
When-lambdaLPLRL(t)+λRPLRL(t)-cP&RPLRL(t)＜0，DLR＝DLRmax；
When-lambdaLPLRL(t)+λRPLRL(t)-cP&RPLRL(t)＞0，DLR＝DLRmin。
In conclusion, the attack and defense strategy of the wireless chargeable sensor network containing the nonlinear factors on the multi-type malicious programs based on the differential game in the scheme controls the wireless sensor network to charge or patch the susceptible nodes, the infected nodes and the low-energy nodes. Meanwhile, the control of the malicious programs is to infect the susceptible nodes and bring the susceptible nodes into a low-energy state quickly, and the fact that the nodes are still likely to become susceptible nodes due to the appearance of the different malicious programs even though the susceptible nodes are in an immune full-energy state is reflected in the three aspects.
The above examples only show some embodiments of the present invention, and the description thereof is specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims (2)

1. A multi-type malicious program attack and defense method based on a nonlinear chargeable sensor network model is characterized by comprising the following steps:
s1, constructing a multi-type malicious program propagation model based on the wirelessly rechargeable sensor network, wherein the malicious program propagation model takes a logistic growth rate as a node number growth rate of the wirelessly rechargeable sensor network;
s2, constructing a state flow chart of the wireless chargeable sensor network node, and writing differential equations of each state according to the state flow chart;
s3, constructing a cost function under the malicious program propagation model;
s4, constructing a Hamiltonian equation according to the differential equation of each state and the cost function;
s5, further solving an equation set meeting a collaborative variable condition and a corresponding attack and defense strategy according to the Hamiltonian;
the malicious program propagation model adopts a nonlinear infection rate which is as follows:
m＝[1-(1-PSI)nI(t)]
wherein P isSIRepresents the probability of the node transferring from the susceptible state to the infected state and satisfies 0 ≦ PSI≦ 1, where I (t) is the number of infected nodes and the number n represents the degree of the node;
the logistic growth rate was:
Figure FDA0003320674500000011
wherein r represents the degree of the node, k represents the capacity of the wireless chargeable sensor network, and N (t) is the number of surviving nodes in the current time t; the differential equations for each state are:
Figure FDA0003320674500000012
Figure FDA0003320674500000013
Figure FDA0003320674500000021
Figure FDA0003320674500000022
Figure FDA0003320674500000023
wherein, S (t), I (t), R (t), L (t),d (t) respectively represents that the node is in a susceptible state, an infected state, an immune full-energy state, a low-energy state and a death state; pSIIs the probability of transition from a susceptible state to an infected state; n is the degree of the node, namely the node has information communication with a plurality of surrounding nodes; i (t) is the number of nodes in an infected state at time t; pSLIs the transition probability from a susceptible state to a low energy state; a. theRSThe degree of control over the migration of an immune full-capable node from an immune full-capable state to a susceptible state for another type of malicious program; pRSThe transition probability of the immune full-energy state to the susceptible state; r (t) is the number of nodes in the immune full-energy state at the time t; dSRThe control degree of the wireless sensor system for transferring the node in the susceptible state from the susceptible state to the immune full-energy state is provided; pSRThe transition probability of the node from the susceptible state to the immune full-energy state is defined; dIRA degree of control for the node wireless sensor network to migrate the node in the infected state from the infected state to an immune-full state; pIRA transition probability for a node to transition from an infected state to an immune-full state; a. theILA degree of control over the migration of a node in an infected state to a low energy node for a malicious program; pILA transition probability for a node to transition from an infected state to a low energy state; dLRA degree of control for the system to migrate nodes in a low energy state to nodes in an immune full energy state; pLRA transition probability for a node to transition from a low energy state to an immune full energy state; pRLIs the transition probability representing the node to transition from the immune full energy state to the low energy state; pLDA transition probability for a node to transition from a low energy state to a death state; l (t) is the number of nodes in a low energy state at time t; d (t) is the number of nodes in a death state at the moment t;
the cost function is:
Figure FDA0003320674500000031
wherein, cNCost factors for logistic growth; c. CIA cost factor for an infected node due to infection with a malware; c. CRThe cost coefficient brought by downloading and installing patches for the immune full-energy node and simultaneously charging energy is increased; c. CDCost coefficient brought by the fact that the sensor network can not work normally due to the fact that the dead nodes die; c. CLThe cost coefficient is brought by the fact that certain functions cannot be normally started due to the fact that the low-energy node is in a low-energy state; c. CILCost coefficient brought by functional disorder caused by running malicious programs on infected nodes; c. CSRPositive income coefficient brought by patching for the susceptible nodes; c. CIRPositive profit coefficient for infected node due to patching; c. CLRPositive gain coefficients for low energy nodes due to patching and charging;
Figure FDA0003320674500000032
cost coefficients brought to dead nodes at the final moment;
the Hamiltonian equation is:
Figure FDA0003320674500000033
wherein λ isS(t) is a covariate corresponding to the susceptible node; lambda [ alpha ]I(t) is a co-modal variable corresponding to the infected node; lambda [ alpha ]R(t) is a covariate corresponding to the immune full energy node; lambda [ alpha ]D(t) is a co-modal variable corresponding to the dead node; lambda [ alpha ]L(t) is a covariate corresponding to the low energy node;
according to the bilateral maximum principle, an optimal control strategy is obtained, and each collaborative equation must meet the following conditions:
Figure FDA0003320674500000041
λS(T)＝0
Figure FDA0003320674500000042
λI(T)＝0
Figure FDA0003320674500000043
λR(T)＝0
Figure FDA0003320674500000044
Figure FDA0003320674500000045
Figure FDA0003320674500000046
λL(T)＝0
according to the bilateral extremum principle, and considering that the following inequality holds:
ASImin≤ASI≤ASImax
ARSmin≤ARS≤ARSmax
AILmin≤AIL≤AILmax
DSRmin≤DSR≤DSRmax
DIRmin≤DIR≤DIRmax
DLRmin≤DLR≤DLRmax
wherein A isSIminMinimal control that a malicious program can exert over the transition of a node from a susceptible state to an infected state; a. theSImaxTransition from susceptible state to infection for malicious program to nodeMaximum control that the state can exert; a. theRSminMinimal control that a malicious program can exert over the transition of the node from the immune full-energy state to the susceptible state; a. theRSmaxMaximum control that a malicious program can exert on a node to transition from an immune full-energy state to a susceptible state; a. theILminMinimal control that a malicious program can exert over the transition of a node from an infected state to a low energy state; a. theILmaxMaximum control that a malicious program can exert over the transition of a node from an infected state to a low energy state; dSRminMinimum control which can be exerted on the node from a susceptible state to an immune full-energy state is provided for the wireless sensor network; dSRmaxMaximum control that a malicious program can exert on a node to transition from a susceptible state to an immune full-energy state; dIRminMinimal control that a malicious program can exert over the transition of a node from an infected state to an immune full-energy state; dIRmaxMaximum control that a malicious program can exert over the transition of a node from an infected state to an immune full-energy state; dLRminMinimal control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state; dLRmaxMaximum control that a malicious program can exert over the transition of a node from a low energy state to an immune full energy state;
the optimal attack and defense strategy is as follows:
when-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＞0，ASI＝ASImax；
When-lambdaS(t)[1-(1-PNI)nI(t)]S(t)+λI(t)[1-(1-PNI)nI(t)]S(t)＜0，ASI＝ASImin；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＞0，ARS＝ARSmax；
When lambda isS(t)PRSR(t)-λR(t)PRSR(t)＜0，ARS＝ARSmin；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＞0，AIL＝AILmax；
When-lambdaI(t)PILI(t)+-λL(t)PILI(t)+cILPILI(t)＜0，AIL＝AILmin；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＜0，DSR＝DSRmax；
When-lambdaS(t)PSRS(t)+λR(t)PSRS(t)-cPATCHPSRS(t)＞0，DSR＝DSRmin；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＜0，DIR＝DIRmax；
When-lambdaI(t)PIRI(t)+λR(t)PIRI(t)-cPATCHPIRI(t)＞0，DIR＝DIRmin；
When-lambdaLPLRL(t)+λRPLRL(t)-cP&RPLRL(t)＜0，DLR＝DLRmax；
When-lambdaLPLRL(t)+λRPLRL(t)-CP&RPLRL(t)＞0，DLR＝DLRmin。
2. The multi-type malicious program attack and defense method based on the nonlinear chargeable sensor network model according to claim 1, characterized in that the Hamiltonian equation is as follows:
Figure FDA0003320674500000071
wherein: n (t) ═ s (t) + i (t) + r (t) + l (t).
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