Asymptotic Learning Requirements for Stealth Attacks on Linearized State Estimation
Asymptotic Learning Requirements for Stealth Attacks on Linearized State Estimation
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DOI：
10.1109/tsg.2023.3236785
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发表时间：
2021-12
影响因子：
9.6
通讯作者：
Ke Sun;I. Esnaola;A. Tulino;H. Vincent Poor
中科院分区：
文献类型：
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作者：
Ke Sun;I. Esnaola;A. Tulino;H. Vincent Poor
信息论隐形攻击是一种数据注入攻击，它最大限度地减少了操作员获取的关于状态变量的信息量，同时限制了攻击下测量值分布与正常操作下测量值分布之间的Kullback-Leibler散度，目的是控制攻击检测的概率。对于高斯分布的状态变量，攻击构造需要了解状态变量的二阶统计量，该统计量是使用样本协方差矩阵根据有限数量的过去实现来估计的。在此框架内，攻击性能的样本协方差矩阵的攻击结构进行了研究。这导致分析学习攻击构造上使用的状态变量的协方差矩阵所需的数据量。利用渐近随机矩阵理论刻画了遍历攻击性能，并证明了攻击性能的方差是有界的。遍历性能和方差界进行了评估与IEEE测试系统的模拟。
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 attack 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.