Optimal defence of single object with imperfect false targets

Optimal defence of single object with imperfect false targets
Presented by YI-CHIN LIN

Agenda Introduction Problem Description(Goal) The model
Resource Distribution Single type of false targets Multiple types of false targets Uncertain contest intensity Conclusion

r (Defender’s resources)
Introduction The paper considers an object exposed to external intentional attacks. Protecting the object r (Defender’s resources) Deploying false targets

Introduction The aim of deploying false targets is to mislead the attacker so that the genuine target will be attacked with less probability or less-attacking effort. The false targets are not perfect and there is a nonzero probability that a false target can be detected by the attacker.

Introduction Once the attacker has detected a certain number of false targets( ), it ignores them and chooses such number of undetected targets ( ) to attack that maximizes the probability of the object destruction. - Genuine element - False Target - Detected false target

Introduction Single type of the false target Optimal strategy
Assuming that the attacker uses the most harmful strategy to attack. Optimal strategy Single type of the false target Multiple types of the false targets

Problem Description(Goal)
How many false targets to deploy in order to minimize the probability of the object destruction assuming that the attacker uses the most harmful strategy to attack? Suggests a conservative methodology of determining the optimal defence strategy under conditions of uncertain contest intensity.

The model Assumptions 1.The defender uses identical false targets with the same detection probability. 2.The attacker can detect each false target independently of other false targets. 3.The defender’s and the attacker’s resources are known to each other.

The model Assumptions 4.The attacker knows the defender’s effort distribution and decides how many elements to attack. 5.The attacker distributes its resources evenly among the attacked elements.

The model The defender and the attacker’s resources, and , are ﬁxed.
The defender distributes its resource among deploying false elements and protecting the genuine element.

The model If the attacker detects false elements with probability the attacker ignores the detected false elements and attacks randomly chosen elements out of elements remaining undetected.

The model The vulnerability (destruction probability) of the attacked object is determined by the attacker– defender contest success function modelled with the common ratio form as

The model For each the attacker solves the optimization problem and chooses the that maximizes the object vulnerability The entire expected damage is .

The model The entire expected damage is
The defender solves the min–max problem: ﬁnds that minimizes the maximal expected damage given that for any the attacker chooses vector that maximizes the vulnerability .

Single type of false targets
Since false targets are deployed , the genuine element protection effort is Constants

If false targets are detected and the attacker
attacks targets the attack effort allocated to each target is -1 -H -K

The vulnerability of the genuine target is obtained as,

The attacker chooses the that maximizes the probability of object destruction.

For the convenience of later discussion, we denote where is the maximal integer not greater than x. Since cannot be greater than , we have:

Figure 1 presents the most harmful attack strategies and different

The attacker tends to attack more elements when it has more resource. With the growth of the contest intensity it becomes more important for the attacker to achieve the effort superiority over the defender. Therefore the attacker concentrates greater per- target efforts by attacking fewer targets and tends to decrease with . When the attacker detects all the false targets and attacks single-defended object:

It can be seen that decreases with the increase of Indeed, it is not cost-effective to build too many false targets if they are too expensive or can be rather easily detected by the attacker. increases with the increase of

Figure 3 represents as functions as functions of and different values of

When the defender’s resource is superior , the defender beneﬁts from the increase of the contest intensity and decreases with

When the defender’s resource is inferior , the attacker beneﬁts from the increase of the contest intensity and increases with

For and high contest intensity is almost insensitive to because in this case and that results in the effort equality and for any Only when all ﬁve false targets are detected and the attacker achieves the effort superiority. However the probability of this case is rather small:

When take close values, as function of demonstrates non-monotonic behaviour. This can be explained by the fact that changes in optimal values of can make the defender’s object protection effort either inferior or superior.

Figure 4 represents the false targets deployment efﬁciency curves for

For any pair of above the curve the deployment of any false target is not beneﬁcial for the defender It can be seen that when the attacker’s resource increases, the deployment of the false targets becomes justiﬁed for greater Indeed, with the decreasing ratio the protection becomes less effective and the defender tends to apply false targets even when they are less effective and more expensive.

Multiple types of false targets
In situations when different types of false elements are available, the defender may consider With smaller detection probability With higher detection probability

We assume that the defender can deploy different types of false targets and each type is characterized by its cost and detection probability The defender’s optimal strategy is how to choose the number and type of the false targets.

If type false targets are deployed , the genuine element protection effort is If false targets are detected (with probability ) and the attacker attacks targets the attack effort allocated to each target is

For the expected object vulnerability is, The optimal number and type of false targets are

For the expected probability of object destruction is, The optimal number and type of false targets are

Consider a numerical example with We assume that ﬁve types of false targets are available. These false targets are characterized by respectively.

It can be seen that the optimal type and number of false targets change drastically with the change of and . With the growth of the attacker’s resource superiority the defender tends to deploy cheaper and less-effective false targets.

When increases above 7 both approach 1 and the difference between approach 0.

This means that under the overwhelming attacker’s superiority the optimization of number and type of the false targets cannot help the defender much. It can be seen that when neither attacker nor the defender has overwhelming resource superiority, the availability of different types of the false targets can improve the object survivability.

Uncertain contest intensity
In many practical situations the values of the contest intensities cannot be exactly determined. Therefore it would be useful to suggest a practical way to determine the rational defence strategy for certain intervals of the contest intensity .

The most conservative defence strategy is to assume that the actual value of (belonging to an exogenously deﬁned interval) is the most favourable for the attacker. This approach is equivalent to assuming that the attacker can choose within the given interval as a free strategic variable.

The min–max defence strategy, thus, minimizes the maximal object vulnerability associated with combination of the most unfavourable circumstances (contest intensity ) and the most harmful attacker’s strategy

Let be the attacker’s strategy that maximizes for the given The defender’s strategy is to choose the parameters that minimize the greatest object vulnerability in the range of contest intensities assuming that the attacker always chooses the optimal strategy

One can see that is higher when the contest intensity is uncertain. This is because we have assumed that the actual value of is the most favourable for the attacker. The range of variation of the optimal number of false targets increases when the contest intensity is uncertain.

The effect of ﬂexibility in choosing the type of false targets increases when the contest intensity is uncertain. In analogy with Section 4 as functions of were compared for It was shown that under conditions of uncertain contest intensity the difference between can reach about 14.5% which is bigger than the case of ﬁxed contest intensity.

Conclusion In the case when there is only one type of false targets available to the defender: The attacker attacks more targets as its resource increases and the contest intensity is not high. The optimal number of false targets deployed by the defender decreases with the increase of the detection probability and the unit cost of each false target. With the increase of the attacker’s resource the deployment of more expensive and more easily detectable false targets become effective for the defender.

Conclusion In the case when multiple types of false targets are available to the defender: A numerical example shows that the optimal type and number of false targets largely depend on the the attacker’s relative resource and the contest intensity. The ﬂexibility of choosing the type of false targets can result in a smaller probability of object destruction.

Conclusion It is shown that the ﬂexibility in choosing the type of false targets gives the defender more beneﬁt when the contest intensity is uncertain.

Thanks for your attention!!

Optimal defence of single object with imperfect false targets

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