Scalable min-max multi-objective cyber-security optimisation over probabilistic attack graphs
Scalable min-max multi-objective cyber-security optimisation over probabilistic attack graphs
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DOI：
10.1016/j.ejor.2019.04.035
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
M. Khouzani;Zheng-Long Liu;P. Malacaria
中科院分区：
文献类型：
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作者：
M. Khouzani;Zheng-Long Liu;P. Malacaria
我们提出了一个框架，以有效地解决网络安全防御的多目标优化问题。面对可以发起多阶段攻击（使用攻击图建模）的攻击者，防御问题是选择一个安全控制组合，以最大限度地降低安全风险和控制组合的（直接和间接）成本。优化的主要挑战是：（a）安全控制的效果通常是概率性的，例如，员工反网络钓鱼培训的效果;此外，一些控制，如定期备份，不具有攻击预防效果，而是减轻成功攻击的损失;（B）每个控制可能影响多个漏洞;并且每个漏洞可能受到多个控制的影响;（c）可能存在大量的攻击途径，每个途径涉及利用不同的漏洞。我们的数学框架处理所有这些问题。特别是，我们模型的问题作为一个最小最大的多目标优化。使用技术，如ILP转换，精确LP松弛和对偶，我们转换成一个非常有效的MILP的问题。例如，它通常在不到四分钟的时间内返回具有20，000个节点的攻击图的最佳解决方案。
We present a framework to efficiently solve a multi-objective optimisation problem for cyber-security defence. Facing an attacker who can mount a multi-stage attack (modelled using attack graphs), the defence problem is to select a portfolio of security controls which minimises the security risk and the (direct and indirect) costs of the portfolio of controls. The main challenges for the optimisation are: (a) the effect of the security controls is in general probabilistic, for example, the effect of staff anti-phishing training; moreover, some controls like taking regular back-ups do not have an attack-preventing effect, but rather, mitigate the losses of a successful attack; (b) each control may affect multiple vulnerabilities; and each vulnerability may be affected by multiple controls; (c) there can be a prohibitively large number of attack paths, each involving exploitation of different vulnerabilities. Our mathematical framework deals with all these problems. In particular, we model the problem as a min-max multi-objective optimisation. Using techniques such as ILP conversion, exact LP relaxation and dualisation, we convert the problem into a very efficient MILP. For instance, it returns the optimal solution for attack graphs with 20,000 nodes in less than four minutes typically.