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1. Selection of optimal countermeasure portfolio in IT security planning Adviser: Frank, Yeong-Sung Lin Presenter: Yi-Cin Lin

2. Model • NSP_E • Bi-objective • While this formulation has more variables than ouroriginal non-linear formulation, it should still solve more quicklythan its non-linear counterpart.

3. Problem description • Notation • Total of potential scenarios.

4. Problem description • Denote by the probability of threat . • Notation • The probability of attack scenario in the presence of independent threat events is

5. Problem description • Notation • indicates that countermeasure totally prevents successful attacks of threat . • denotes that countermeasure is totally incapable of mitigating threat .

6. Problem description • Notation • The subset of selected countermeasures must satisfy the available budget constraint

7. Minimization of expected cost- NSP_E • This added level of speciﬁcity is necessary to maintain the linearity ofthe formulation. • Also,it improves the model’s ﬂexibility by allowing for the possibility of a countermeasure being implemented at numerous levels.

8. Minimization of expected cost- NSP_E • Countermeasure is selected at exactly one level i.e., • Notation

9. Minimization of expected cost- NSP_E • Model NSP_E: Minimize Expected Cost (1) Subject to COST

10. Minimization of expected cost- SP_E • NSP_E • Bi-objective • NSP_E

11. Minimization of expected cost- SP_E • The nonlinear objective function (1) can be replaced with a formula

12. Minimization of expected cost- SP_E • In order to compute for each threat , a recursive procedure is proposed below.

13. Minimization of expected cost- SP_E • For each threat and countermeasure can be calculatedrecursively as follows. • The initial conditionis • The remaining terms

14. Minimization of expected cost- SP_E • In order to eliminate nonlinear terms in the right-hand side of Eq. (10), deﬁne an auxiliary variable

15. Minimization of expected cost- SP_E and, in particular, for

16. Minimization of expected cost- SP_E

17. Minimization of expected cost- SP_E

18. Minimization of expected cost- SP_E • Comparison of Eqs. (12) and (15) produces to the following relation

19. Minimization of expected cost- SP_E

20. Minimization of expected cost- SP_E • The above procedure eliminates all variables for each. • Summarizing, the proportion of successful attacks = in Foreach threat can be calculated recursively, using Eqs. (17), (16) and(13) with replaced by.

21. Minimization of expected cost- SP_E • Model SP_E: Minimize Expected Cost (5) subject to 1. Countermeasure selection constraints Eqs. (2) and (3).

22. Minimization of expected cost- SP_E Subject to 2. Surviving threats balance constraints (17) (16) (15)

23. Minimize conditional value-at-risk • NSP_E • Bi-objective • NSP_E

24. Minimize conditional value-at-risk • Notation • Model SP_CV: Minimize

25. Minimize conditional value-at-risk Subject to 1. Countermeasure selection constraints: Eqs. (2)–(3). 2. Surviving threats balance constraints: Eqs. (18)–(21). 3. Risk constraints: 4. Non-negativity and integrality conditions: Eqs. (22)–(24)

26. Minimize conditional value-at-risk • Bi-objective

27. Minimize conditional value-at-risk • Models SP_E and SP_CV can be enhanced for simultaneous optimization of the expenditures on countermeasures and the cost of losses from successful attacks. • Removed constraints (3)

28. Minimize conditional value-at-risk • Model SP_E+B Minimize Required Budget and Expected Cost subject to Eqs. (2), (18)–(24) and (28)

29. Minimize conditional value-at-risk • Model SP_CV+B Minimize Required Budget and CVaR subject to Eqs. (2) and (18)–(28)

30. Agenda • Introduction • Problem description • Model • Single-objective approach • Bi-objective approach • Computational examples • Conclusion

31. Bi-objective approach • NSP_E • Bi-objective • NSP_E

32. Bi-objective approach • In the single objective approach the countermeasure portfolio is selected by minimizing either the expected loss (plus the required budget) or the expected worst-case loss (plus the required budget).

33. Bi-objective approach • Model WSP Minimize Subject to Eqs. (2), (5) and (18)–(28)

34. Bi-objective approach • Decision maker controls • Risk of high losses by choosing the conﬁdence level α • trade-off between expected and worst-case losses by choosing the trade-off parameter λ.

35. Agenda • Introduction • Problem description • Model • Single-objective approach • Bi-objective approach • Computational examples • Conclusion

36. Computational examples • The data set is similar to the one presented in , which was based on the threat set reported on IT security forum EndpointSecurity.org

37. Computational examples

38. Computational examples • =,the number of threats and the number of countermeasures, were equal to 10, and the corresponding number of potential attack scenarios, was equal to 1024.

39. Computational examples

40. Computational examples

41. Computational examples

42. Computational examples

43. Computational examples

44. Computational examples

45. Computational examples

46. Computational examples

47. Computational examples • For the bi-objective approach, the subsets of nondominated solutions were computed by parameterization on λ∈{0.01,0.10,0.25,0.50,0.75,0.90,0.99} the weighted-sum program WSP.

48. Computational examples

49. Computational examples