1. Advisor: Frank,Yeong-Sung Lin 碩一 冠廷
Influence of attacker’s target recognition ability on defense strategy in homogeneous parallel systems Gregory Levitin , Kjell Hausken 2010
Advisor: Frank,Yeong-Sung Lin
碩一 冠廷

2. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

3. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

4. Introduction Defender distributes its resource：
1. deploying redundant elements
2. protection a subset of the deployed
system elements
Attacker distributes its resource：
1. detect the unprotected elements
(destroyed with negligible effort)
2. (a) evenly among all of the undetected
elements
(b) among elements from a chosen subset of
undetected elements.

5. Introduction
This paper studies the influence of the unprotected element detection probability on the defender’s resource distribution between providing redundancy and protecting the elements in homogeneous parallel systems.

6. Nomenclature

7. Illustration (a) evenly among all of the undetected elements
(b) among elements from a chosen subset of
undetected elements.

8. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

9. The efforts distribution and the vulnerability of a single element
The vulnerability of any element using the attacker– defender contest success function:
x<=r/└F/g┘ (Ng>=F & r>=Nx )

10. The efforts distribution and the vulnerability of a single element
The defender’s objective is to minimize the expected damage using the fixed resource r for deploying system elements and protecting them.
The attacker’s objective is to maximize the expected damage using the fixed resource R for attacking the elements.

11. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

12. Illustration
(a) evenly among all of the undetected elements

13. The defender protects a subset of the elements, the attacker attacks all elements
To decrease the expected damage it may be optimal for the defender to protect M<=N elements.
The defender’s effort per element increases to t=(r-Nx)/(Ma).
The attacker：
1. Tries to detect the unprotected elements
and destroys all the detected unprotected
elements with negligible effort.

14. The defender protects a subset of the elements, the attacker attacks all elements
2. distributes its effort evenly among the
remaining elements (protected ones and
undetected unprotected ones) (N-h)
Let q be the probability that an unprotected element is detected correctly.

15. The defender protects a subset of the elements, the attacker attacks all elements
The probability that the attacker detects correctly h out of N-M unprotected elements is：
Each one of the M protected elements is destroyed with probability ：

16. The defender protects a subset of the elements, the attacker attacks all elements
The probability that k out of M protected elements are destroyed is
The probability that exactly N-M+k elements are destroyed by the attack is

17. The defender protects a subset of the elements, the attacker attacks all elements
The expected damage caused by the attack
The defender chooses its two free choice variables N and M minimize the expected damage D.
The attacker maximizes D.
若g(M-k) > F 表系統能順利運作，故產生的Damage=0;
若g(M-k) < F 表系統無法順利運作，故F-g(M-k)表damage 大小

18. The defender protects a subset of the elements, the attacker attacks all elements
The optimal values M* and N* of M and N can be obtained

19. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

20. Illustration

21. The attacker attacks a subset of the undetected elements
The probability Hs that exactly s elements are destroyed by the attack on Q elements randomly chosen from the set of undetected elements comprising M protected and N-h-M unprotected elements can be obtained as
s=Q-f+k => k=s+f-Q
(其中Q-f 為未被保護的元素)

22. The attacker attacks a subset of the undetected elements
Damage caused by the attack
Assume that for any h the attacker can choose the value of Q=Q*(h) that maximizes the expected damage
若g(N-h-s) > F 表系統能順利運作，故產生的Damage=0;
若g(N-h-s) < F 表系統無法順利運作，故F-g(M-k)表damage 大小

23. The attacker attacks a subset of the undetected elements

24. The attacker attacks a subset of the undetected elements
The defender chooses N and M to minimize the expected damage D
Assume：the attacker chooses for any h the optimal value of Q that maximizes the expected damage d(h,Q).

25. The attacker attacks a subset of the undetected elements

26. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

27. Analysis of the models The first analysis： 1. x=0.3 2. Ɛ=1 3. R=1
5. g=2
6. F=6
7. The attacker attacks all the elements.
=> N>=3
M*, N*,D as functions of q and m

28. Analysis of the models

29. Analysis of the models The second analysis： 1. x=0.6 2. Ɛ=1 3. R=1
5. g=2
6. F=6
7. The attacker attacks all the elements.
=> N>=3
M*, N*,D as functions of q and m.

30. Analysis of the models

31. Analysis of the models The third analysis： 1. x=0.9 2. Ɛ=1 3. R=1
5. g=2
6. F=6
7. The attacker attacks all the elements.
=> N>=3
M*, N*,D as functions of q and m.

32. Analysis of the models

33. Analysis of the models The fourth analysis： 1. x=0.3 2. Ɛ=1 3. R=1
5. g=2
6. F=6
7. The attacker attacks optimal number of
elements.
=> N>=3
M*, N*,D,Q*(0) as functions of q and m.

34. Analysis of the models

35. Analysis of the models The fifth analysis： 1. x=0.6 2. Ɛ=1 3. R=1
5. g=2
6. F=6
7. The attacker attacks optimal number of
elements.
=> N>=3
M*, N*,D,Q*(0) as functions of q and m.

36. Analysis of the models

37. Agenda
Introduction
The efforts distribution and the vulnerability of a single element
The defender protects a subset of the elements, the attacker attacks all elements
The defender protects a subset of the elements, the attacker attacks a subset of the undetected elements
Analysis of the models
Conclusions

38. Conclusions
This paper considers optimal defense resource distribution between two main actions：
1. deployment of separated redundant
system elements
2. protection

39. Conclusions Attacker distributes its resource：
1. detect the unprotected elements
(destroyed with negligible effort)
2. (a) evenly among all of the undetected
elements
(b) among elements from a chosen subset
of undetected elements.

40. Conclusions
With low q the defender may deploy many elements without necessarily protecting all of them.
The higher probability of correct detection for the attacker makes it more important for the defender to protect more elements.

41. Conclusions
The expected damage is insensitive to q when the number of protected elements equals the number of deployed elements.
Free choice of the number of attacked elements makes the defense strategy more sensitive to q.
The decrease of the contest intensity makes the defense strategy insensitive to q because in this case the defender protects all the elements.

42. Thanks for your listening.