中文摘要：

攻击图是一种基于模型的网络脆弱性分析技术，可以自动分析目标网络内脆弱性之间的关系和由此产生的潜在威胁．攻击图主要有状态攻击图和属性攻击图两类．前者由于存在状态爆炸问题不适应于大规模网络，目前主要的研究大多是基于后者．基于属性攻击图研究了含圈攻击路径问题和最优弥补集问题．针对含圈攻击路径问题，定义了反映真实攻击想定的”．有效攻击路径，提出了一种计算关键属性集所有＂．有效攻击路径的迭代算法；针对最优弥补集问题，在定义了所有的风险源为属性攻击图的初始属性的基础上，将该问题转化为带权重的集合覆盖问题，从而归结为NP完全性问题，提出了可应用于大规模攻击图的具有多项式时间复杂度的近似算法．

英文摘要：

An attack graph is a model-based vulnerability analysis technology, which can automatically analyze the interrelation among vulnerabitities in the network and the potential threats resulting from the vulnerabilities. Since the state-based attack graphs can not be applied to the real large networks for the combinatorial explosion in the number of attack paths, the study is now shifted to attribute-based. Based on attribute-based attack graphs, this paper discusses the loop attack paths and the optimization security measures. For the former, an iterative algorithm is presented to find all the non-loop attack paths to the key attributes with their depth less than the given number n. For the latter, it is proved to be an NP-complete problem, and the greedy algorithm is proposed to solve the problem with polynomial time complexity.