Security threat assessment of an Internet security system using attack tree and vague sets.

Chang KH - ScientificWorldJournal (2014)

Related In: Results  -  Collection

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fig2: “AND” node and “OR” node.
Mentions: If we let xj be a random variable such that xj = 1 corresponds to the accomplishments of subtask j and xj = 0 corresponds to the failure of task j, then P(x1, x2,…, xn) is the joint probability distribution. In an “AND” node (see Figure 2), it must have P(x1 = 1, x2 = 1,…, xn = 1). The accomplishment for the parent goal requires the success of all children—that is, Pand = ∏j=1npj—which is the product of the probability of accomplishments of all children. In an “OR” node (see Figure 2), this is essentially the negation of the probability that all subtasks fail: 1 − P(x1 = 0, x2 = 0,…, xn = 0). The accomplishment for the parent goal requires the success of any one of the children—that is, Por = 1 − ∏j=1n(1 − pj)—which is the product of the probability of an accomplishment of any one of the children. It assumes that the attacker can try all available subtasks until he finds one that succeeds. This is an unrealistic assumption in attack modeling, because if an attacker needs to try more than one subtask, he has manifested at least one failure. This is a situation that may be untenable in an attack. Therefore, Yager [23] assumed that in an “OR” node, where the attacker needs only to succeed at one subtask, he cannot try all possibilities but must try one. Thus, the probability of success at an “OR” node without any failure is POR = Maxj[Pj]. It is also clear that POR = Maxj[Pj] ≥ PAND = ∏j=1npj.

Bottom Line: Security threat assessment of the Internet security system has become a greater concern in recent years because of the progress and diversification of information technology.Moreover, it does not consider the failure probability of the bottom events suffered in the attack, which may bias conclusions.In order to effectively solve the problem above, this paper proposes a novel technique, integrating attack tree and vague sets for security threat assessment.

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Affiliation: Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan.

ABSTRACT
Security threat assessment of the Internet security system has become a greater concern in recent years because of the progress and diversification of information technology. Traditionally, the failure probabilities of bottom events of an Internet security system are treated as exact values when the failure probability of the entire system is estimated. However, security threat assessment when the malfunction data of the system's elementary event are incomplete--the traditional approach for calculating reliability--is no longer applicable. Moreover, it does not consider the failure probability of the bottom events suffered in the attack, which may bias conclusions. In order to effectively solve the problem above, this paper proposes a novel technique, integrating attack tree and vague sets for security threat assessment. For verification of the proposed approach, a numerical example of an Internet security system security threat assessment is adopted in this paper. The result of the proposed method is compared with the listing approaches of security threat assessment methods.

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