概率攻击图中主动防御的最优诱饵资源分配
Optimal Decoy Resource Allocation for Proactive Defense in Probabilistic Attack Graphs
摘要：
本文研究了主动防御系统的综合问题，在该系统中，防御者可以分配欺骗性目标，并修改攻击者的行动成本，攻击者的目的是破坏系统中的安全资产。我们使用一个正式的安全模型-概率攻击图来模拟攻击者和系统的交互。通过分配假目标/诱饵，防御者的目的是分散攻击者的注意力，使其无法危及真实目标。通过增加某些攻击行为的成本，防御者旨在阻止攻击者实施某些策略，从而提高防御能力。为了优化防御有限的诱饵资源和操作约束，我们制定的合成问题作为一个双层优化问题，而防御者设计的系统，在攻击者的最佳反应的预期，攻击者有关于系统的虚假信息，由于使用欺骗。虽然一般配方与双层优化是NP-难的，我们表明，在一定的假设下，问题可以转化为一个约束优化问题。我们提出了一种算法，近似解决这个约束优化问题，使用一种新的激励设计方法，预计梯度上升。我们使用大量的数值实验证明了所提出的方法的有效性。
英文摘要：
This paper investigates the problem of synthesizing proactive defense systems in which the defender can allocate deceptive targets and modify the cost of actions for the attacker who aims to compromise security assets in this system. We model the interaction of the attacker and the system using a formal security model -- a probabilistic attack graph. By allocating fake targets/decoys, the defender aims to distract the attacker from compromising true targets. By increasing the cost of some attack actions, the defender aims to discourage the attacker from committing to certain policies and thereby improve the defense. To optimize the defense given limited decoy resources and operational constraints, we formulate the synthesis problem as a bi-level optimization problem, while the defender designs the system, in anticipation of the attacker's best response given that the attacker has disinformation about the system due to the use of deception. Though the general formulation with bi-level optimization is NP-hard, we show that under certain assumptions, the problem can be transformed into a constrained optimization problem. We proposed an algorithm to approximately solve this constrained optimization problem using a novel incentive-design method for projected gradient ascent. We demonstrate the effectiveness of the proposed method using extensive numerical experiments.
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