Information-theoretic stealth attacks are data injection attacks that minimize the amount of information acquired by the operator about the state variables, while simultaneously limiting the Kullback-Leibler divergence between the distribution of the measurements under attack and the distribution under normal operation with the aim of controling the probability of detection. For Gaussian distributed state variables, attack construction requires knowledge of the second order statistics of the state variables, which is estimated from a finite number of past realizations using a sample covariance matrix. Within this framework, the attack performance is studied for the attack construction with the sample covariance matrix. This results in an analysis of the amount of data required to learn the covariance matrix of the state variables used on the attack construction. The ergodic attack performance is characterized using asymptotic random matrix theory tools, and the variance of the attack performance is bounded. The ergodic performance and the variance bounds are assessed with simulations on IEEE test systems.
翻译:信息理论隐形攻击是数据注入攻击,最大限度地减少操作者获得的关于国家变量的信息数量,同时限制Kullback-Leebler在攻击测量分布和正常操作分布之间的差异,以控制探测概率。对于高西亚分布的州变量,攻击构造需要了解国家变量的第二顺序统计,该统计是利用一个抽样共变矩阵从过去有限数目的实现中估算出来的。在此框架内,与样本共变矩阵一起研究攻击性能,从而分析为学习攻击建筑中使用的州变量的共变矩阵所需的数据数量。攻击性能的特征是使用随机随机矩阵理论工具,攻击性能的差异是捆绑在一起的。对攻击性能和差异界限进行评估时,要对IEE测试系统进行模拟。