CN110166437A - The method that mobile target defence optimal policy based on DS evidential reasoning is chosen - Google Patents
The method that mobile target defence optimal policy based on DS evidential reasoning is chosen Download PDFInfo
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- H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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- H—ELECTRICITY
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract
The method that the mobile target defence optimal policy based on DS evidential reasoning that the invention discloses a kind of is chosen.Steps are as follows by the present invention: establishing attacking and defending betting model；Attacker selects attack strategies；Defender observes attack strategies, and attacking and defending both sides calculate income；Perfect Bayesian Equilibrium solution obtains optimal defence policies；Defender corrects attacker's type posterior probability by DS evidential reasoning.Wherein establishing attacking and defending betting model includes: to define attacking and defending betting model；Define the quantization of attacking and defending income.It includes: the attack strategies calculating posterior probability that defender arrives according to the observation that attacking and defending both sides, which calculate income step,；Attacking and defending both sides calculate respective income；Attack type inductive decision table is formed according to the characteristic attribute of previous attack record；The Basic Probability As-signment of evidence of attack is determined according to decision table.The present invention compensates for the shortcoming of prior probability in existing model, keeps defence policies income more reasonable, improves the defence success rate of system early period.
Description
Technical field
The present invention should belong to network security, information security field, main to study mobile target defence optimal policy selection, mention
A kind of method that the mobile target defence optimal policy based on DS evidential reasoning is chosen out.
Background technique
Being all based on incomplete information dynamic game establishes attacking and defending game greatly for existing mobile target defence optimal policy selection
Model, in this class model, defender generally according to experience or thinks specified to the prior probability of attacker's type, subjectivity compared with
By force, the posterior probability of defender and defence policies income calculation are affected as a result, it is anti-in early period so as to cause system of defense
Imperial success rate decline.Therefore, this paper presents a kind of incomplete information dynamic game model based on D-S evidential reasoning, the moulds
Type is repaired on the basis of incomplete information dynamic game by constructing attack type decision table, and using the method for D-S evidential reasoning
Positive defender infers the posteriority of attack type, so that probability updating is more objective, compensates for prior probability in existing model
Shortcoming keeps defence policies income more reasonable, improves the defence success rate of system early period.
Summary of the invention
The present invention is directed in mobile target system of defense optimal defence policies problem of choosing, and open one kind is pushed away based on DS evidence
The method that the mobile target defence optimal policy of reason is chosen.A kind of deficiency making up prior probability in existing model, defender's choosing
Optimal defence policies are selected to which defence system early period can be improved into the method for rate.
For technical purpose more than realization, the present invention will take technical solution below:
The method that mobile target defence optimal policy based on DS evidential reasoning is chosen, carries out in accordance with the following steps:
Step (1) establishes attacking and defending betting model；
Step (2) attacker selects attack strategies；
Step (3) defender observes attack strategies, and attacking and defending both sides calculate income；
The solution of step (4) Perfect Bayesian Equilibrium obtains optimal defence policies；
Step (5) defender corrects attacker's type posterior probability by DS evidential reasoning；
Wherein step (1) is implemented as follows:
Step (1-1): attacking and defending betting model is defined；
Step (1-2): the quantization of attacking and defending income is defined；
Step (3) is implemented as follows:
Step (3-1): the attack strategies that defender arrives according to the observation calculate posterior probability；
Step (3-2): attacking and defending both sides calculate respective income.
Step (5) is implemented as follows:
Step (5-1): attack type inductive decision table is formed according to the characteristic attribute of previous attack record；
Step (5-2): the Basic Probability As-signment (BPA) of evidence of attack is determined according to decision table；
Step (5-3): evidence is synthesized according to D-S Evidential reasoning algorithm；
Step (5-4): the conversion of pignistic probability is carried out according to the BPA after Evidence Combination Methods, obtains the type θ of attackeri
Posterior probability.
The technical solution that the present invention further limits are as follows:
Step (1-1) specifically: betting model is established based on incomplete information dynamic game, model uses eight tuplesDescription.Respectively correspond game participant, the type space of participant, attack strategies collection, defence plan
Slightly collection, prior probability set, posterior probability set, revenue function set.
Further, step (1-2) specifically: define intrusion scene AC；Cost DC is defendd, attack face is shifted by defender
Cost ASSC, negative effect cost NC and attack recognition cost AIC three parts composition；System loss cost SLC indicates that certain class is attacked
Hit the extent of damage to target resource.Usually using target resource significance level Criticaiity, attack criticality AL and safety
Attribute damage SAD is described；
In summary definition can obtain attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
Further, step (3-1) specifically: the attack strategies that defender arrives according to the observation calculate posterior probability, according to
Bayes rule calculates posterior probability, posterior probability calculation formula are as follows:
Further, step (3-2) specifically: attacking and defending both sides calculate respective income.
Attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)；
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
The game theory of first stage can be calculated by attacking and defending income formula.
Further, step (4) is specially that the attacking and defending both sides in the attack strategies and step (3) arrived according to the observation receive
The calculating of benefit, solves the game using Perfect Bayesian Equilibrium, may there is pooling equilibrium and two kinds of separating equilibrium solutions respectively.Defence
Person infers optimal defence policies d*(aj), that is, pass through calculating
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
Attacker infers optimal attack strategies a*(θi), attacker θ, which predicts defender, can observe the attack strategies of oneself
On the basis of a, optimal policy d is selected*(aj), therefore select optimal attack strategies a*(θi), make the game profit expectation U of oneselfaIt takes
Maximum value passes through calculating
a*(θi)∈max Ua(aj, dh, θi)
Perfect Bayesian Equilibrium solves
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, the attack of m kind is may be selected in attacker
Strategy, ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
Further, step (5-1) specifically: attack type reasoning is formed according to the characteristic attribute of previous attack record and is determined
Plan table.It is different according to corresponding attacker's type under the combination of the numerical value of each evidence and different numerical value in attack record, by it
It records, forms decision table, evidence uses ckIt indicates, attack type uses θu1It indicates.
Further, step (5-2) specifically:
The Basic Probability As-signment (BPA) of each evidence in the attack strategies is determined according to decision table.Defender is according to detecting
Evidence of attack concentrates ckValue, will be with ckIt is worth identical historical record from corresponding U/ { ck, θurIn mark off come, be counted as Bk, most
Afterwards according to BkThe corresponding attack type of middle historical record u is different, by BkIt is divided into Bk={ { Bk1, { Bk2... { Bkz, then
ckTo BkIn all types of decision rule strength calculation formula are as follows:
ckTo BkIn all attack types expansion decision rule strength calculation formula are as follows:
Evidence ckThe Basic Probability As-signment of corresponding each attack type are as follows:
Evidence ckTo the Basic Probability As-signment of all attack types are as follows:
Further, step (5-3) specifically:
K evidence ck,For its Basic Probability As-signment, then k evidence are as follows:
Further, step (5-4) specifically:
The conversion of pignistic probability is carried out to the BPA after step (5-3) resulting combination, obtains the type θ of attackeri
Posterior probability.Wherein pignistic probability conversion formula are as follows:
The present invention has the beneficial effect that:
The prior probability of defender generally according to experience or thinks specified in existing model, subjective, as a result, to anti-
The posterior probability and defence policies income calculation of driver affects, so as to cause system of defense in the case where early period defends success rate
Drop.This paper presents a kind of incomplete information dynamic game model based on D-S evidential reasoning, the model is dynamic in imperfect information
On the basis of state game, by constructing attack type decision table, and using the method for D-S evidential reasoning amendment defender to attack class
The posteriority of type is inferred, so that probability updating is more objective, compensates for the shortcoming of prior probability in existing model, makes to defend plan
Slightly income is more reasonable, improves the defence success rate of system early period.
Detailed description of the invention
Fig. 1 is the flow diagram of the method for the invention.
Fig. 2 is that the present invention establishes attacking and defending betting model flow diagram.
Fig. 3 is that attacker of the present invention selects attack strategies flow diagram.
Fig. 4 is attacking and defending income quantization flow block diagram of the present invention
Fig. 5 is the flow diagram of defence policies decision of the present invention.
Fig. 6 is that defender of the present invention corrects attack type posterior probability flow diagram.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
As shown in Figure 1, initially set up attacking and defending betting model, parameters in Definition Model, subsequent attacker in systems
Offensive attack, the attack strategies that defender arrives according to the observation calculate income, are solved by refining Bayesian and select optimal defence plan
Slightly.
It is illustrated in figure 2 the present invention and establishes attacking and defending betting model flow diagram.It is primarily based on incomplete information dynamic game
Betting model is established, model uses eight tuplesDescription.Respectively correspond game participant, participant
Type space, attack strategies collection, defence policies collection, prior probability set, posterior probability set, revenue function set；Then
Carry out model parameter initialization.
It is illustrated in figure 3 attacker of the present invention and selects attack strategies flow diagram." nature " participant is introduced, first " from
Attack type so " is selected, attacker observes attack type and selects specific attack strategies.
It is illustrated in figure 4 attacking and defending income quantization flow block diagram of the present invention.Defender prevents after observing attack strategies
Driver calculates posterior probability according to attack strategies, and calculates the defence policies risk income under this attack strategies, finally obtains anti-
Driver's income.
It is illustrated in figure 5 the flow diagram of defence policies decision of the present invention.Infer respectively after obtaining attacking and defending income by upper figure
From optimal policy, optimal solution is finally obtained by Perfect Bayesian Equilibrium solution.It is illustrated in figure 6 defender's amendment of the present invention
Attack type posterior probability is prepared for next step attacking and defending.
Referring to Fig.1, a method of the mobile target based on game theory defends optimal defence policies to choose, including following step
It is rapid:
Step 1. establishes attacking and defending betting model, referring to Fig. 2；
1.1 define attacking and defending betting model, establish betting model based on incomplete information dynamic game, model uses eight tuplesDescription.Respectively correspond game participant, the type space of participant, attack strategies collection, defence plan
Slightly collection, prior probability set, posterior probability set, revenue function set.
1.2 define the quantization of attacking and defending income, define intrusion scene AC；Defend cost DC；System loss cost SLC；It is comprehensive with
Upper definition can obtain attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)；
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh；
Step 2 attacker selects attack strategies, referring to Fig. 3；
2.1 " natures " press certain probability from attacker NaType space ΘnOne type θ of middle selectioni, attacker Na
Know θi, defender NdDo not know, but defender NdPossess to θiDeduction, i.e. defender's prior probability for knowing attack type.
2.2 attacker NaObserving θiAn attack strategies a is selected from its policy space A afterwardsw
Step 3. defender observes attack strategies, and attacking and defending both sides calculate income, referring to Fig. 4；
The attack strategies that 3.1 defenders arrive according to the observation calculate posterior probability, calculate posterior probability according to bayes rule
3.2 attacking and defending both sides calculate respective income, attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)；
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh；
The game theory of first stage can be calculated by attacking and defending income formula.
The solution of step 4 Perfect Bayesian Equilibrium obtains optimal defence policies, referring to Fig. 5
Defender infers optimal defence policies d*(aj), that is, pass through calculating
Attacker infers optimal attack strategies a*(θ), attacker θ, which predicts defender, can observe the attack strategies of oneself
On the basis of a, optimal policy d is selected*(a), therefore optimal attack strategies a is selected*(θ) makes the game profit expectation U of oneselfaIt takes most
Big value, that is, pass through calculating
a*(θi)∈max Ua(aj, dh, θi)
Perfect Bayesian Equilibrium solvesFor different attack strategies, by
In by intruding detection system the quantization of defender's income may be improved, reality is more in line with there is a situation where erroneous judgement, misjudgement
Border situation, then the defence policies chosen in equilibrium solution are optimal defence policies.
Step 5 defender corrects attack type posterior probability using DS just reasoning, referring to Fig. 6
5.1: attack type inductive decision table is formed according to the characteristic attribute of previous attack record.According to each in attack record
Corresponding attacker's type is different under the combination of the numerical value of evidence and different numerical value, is recorded, and decision table, card are formed
According to using ckIt indicates, attack type uses θu1It indicates.
5.2 determine the Basic Probability As-signment (BPA) of each evidence in the attack strategies according to decision table.Defender is according to detection
C is concentrated to evidence of attackkValue, will be with ckIt is worth identical historical record from corresponding U/ { ck, θurIn mark off come, be counted as Bk,
Finally according to BkThe corresponding attack type of middle historical record u is different, by BkIt is divided into Bk={ { Bk1, { Bk2... { Bkz, that
CkTo BkIn all types of decision rule strength calculation formula are as follows:
ckTo BkIn all attack types expansion decision rule strength calculation formula are as follows:
Evidence ckThe Basic Probability As-signment of corresponding each attack type are as follows:
Evidence ckTo the Basic Probability As-signment of all attack types are as follows:
5.3:k evidence ck,For its Basic Probability As-signment, then k evidence are as follows:
5.4: the conversion of pignistic probability being carried out to the BPA after step 3. resulting combination, obtains the type θ of attackeri
Posterior probability.Wherein pignistic probability conversion formula are as follows:
Claims (4)
1. the method that the mobile target defence optimal policy based on DS evidential reasoning is chosen, it is characterised in that include the following steps:
Step (1) establishes attacking and defending betting model；
Step (2) attacker selects attack strategies；
Step (3) defender observes attack strategies, and attacking and defending both sides calculate income；
The solution of step (4) Perfect Bayesian Equilibrium obtains optimal defence policies；
Step (5) defender corrects attack type posterior probability by DS evidential reasoning；
Step (1) includes the following steps:
(1-1) defines attacking and defending betting model；
(1-2) defines the quantization of attacking and defending income；
Step (1-1) specifically: betting model is established based on incomplete information dynamic game, model uses eight tuplesDescription；Respectively correspond game participant, the type space of participant, attack strategies collection, defence plan
Slightly collection, prior probability set, posterior probability set, revenue function set；
Step (1-2) specifically: define intrusion scene AC；Cost DC is defendd, by defender's transfer attack face cost ASSC, negatively
Influence cost NC and attack recognition cost AIC three parts composition；System loss cost SLC indicates the attack of certain class to target resource
The extent of damage；SAD is damaged usually using target resource significance level Criticality, attack criticality AL and security attribute
It is described；
In summary definition can obtain attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, m kind attack strategies are may be selected in attacker,
ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k；
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, m kind attack strategies are may be selected in attacker,
ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k.
2. the method that the mobile target according to claim 1 based on game theory defends optimal defence policies to choose, special
Sign is that step (3) includes the following steps:
Step (3-1): the attack strategies that defender arrives according to the observation calculate posterior probability；
Step (3-2): attacking and defending both sides calculate respective income；
Step (3-1) specifically: the attack strategies that defender arrives according to the observation calculate posterior probability, are calculated according to bayes rule
Posterior probability, posterior probability calculation formula are as follows:
Step (3-2) specifically: attacking and defending both sides calculate respective income；
Attacker's profit calculating formula are as follows:
Ua(θi, aj, dh)=SLC (aj)+DC(dh, θi)-AC(aj, θi)；
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, m kind attack strategies are may be selected in attacker,
ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k；
Defender's profit calculating formula are as follows:
Ud(aj, dh, θi)=SLC (aj)+AC(aj, θi)-DCh
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, m kind attack strategies are may be selected in attacker,
ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k；
The game theory of first stage can be calculated by attacking and defending income formula.
3. the method that the mobile target according to claim 2 based on game theory defends optimal defence policies to choose, special
Sign is that step (4) according to the attacking and defending game theory in step (3), obtains optimal defence plan by Perfect Bayesian Equilibrium solution
Slightly, pooling equilibrium solution and separating equilibrium solution are separately included, defender infers optimal defence policies d*(aj), that is, pass through calculating:
Wherein, attacker includes n kind attack type, θiFor attacker's type, 1≤i≤n, m kind attack strategies are may be selected in attacker,
ajFor attack strategies, 1≤j≤m, k kind attack strategies, d is may be selected in defenderhFor defence policies, 1≤h≤k；
Attacker infers optimal attack strategies a*(θ), attacker θ predict the base that defender can observe the attack strategies a of oneself
On plinth, optimal policy d is selected*(a), therefore optimal attack strategies a is selected*(θ) makes the game profit expectation U of oneselfaIt is maximized,
Pass through calculating:
a*(θ)∈max Ua(a, d*(a), θ)
Perfect Bayesian Equilibrium solves, and for different attack strategies, the strategy for making oneself maximum revenue is selected, then
Defence policies in the solution that weighs are optimal defence policies.
4. the method that the mobile target according to claim 3 based on game theory defends optimal defence policies to choose, special
Sign is that step (5) includes the following steps:
Step (5-1): attack type inductive decision table is formed according to the characteristic attribute of previous attack record；
Step (5-2): the Basic Probability As-signment (BPA) of evidence of attack is determined according to decision table；
Step (5-3): evidence is synthesized according to D-S Evidential reasoning algorithm；
Step (5-4): the conversion of pignistic probability is carried out according to the BPA after Evidence Combination Methods, obtains the type θ of attackeriAfter
Test probability；
Step (5-1) specifically: attack type inductive decision table is formed according to the characteristic attribute of previous attack record；According to attack
Corresponding attacker's type is different under the combination of the numerical value of each evidence and different numerical value in record, is recorded, and is formed
Decision table, evidence use ckIt indicates, attack type uses θu1It indicates；
Step (5-2) specifically:
The Basic Probability As-signment (BPA) of each evidence in the attack strategies is determined according to decision table；Defender according to detect attack
Evidence concentrates ckValue, will be with ckIt is worth identical historical record from corresponding U/ { ck, θurIn mark off come, be counted as Bk, finally press
According to BkThe corresponding attack type of middle historical record u is different, by BkIt is divided into Bk={ { Bk1, { Bk2... { Bkz, then ckTo Bk
In all types of decision rule strength calculation formula are as follows:
ckTo BkIn all attack types expansion decision rule strength calculation formula are as follows:
Evidence ckThe Basic Probability As-signment of corresponding each attack type are as follows:
Evidence ckTo the Basic Probability As-signment of all attack types are as follows:
Step (5-3) specifically:
K evidence ck,For its Basic Probability As-signment, then k evidence are as follows:
Step (5-4) specifically: the conversion of pignistic probability is carried out to the BPA after step (5-3) resulting combination, is attacked
The type θ for the person of hittingiPosterior probability；Wherein pignistic probability conversion formula are as follows:
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Application publication date: 20190823 Assignee: Hangzhou Greentown Information Technology Co.,Ltd. Assignor: HANGZHOU DIANZI University Contract record no.: X2023330000109 Denomination of invention: A Method for Selecting the Optimal Strategy of Mobile Target Defense Based on DS Evidence Reasoning Granted publication date: 20200519 License type: Common License Record date: 20230311 |