This paper examines data injection attacks on distributed statistical estimation. We consider a dynamically changing distributed network consisting of N agents exchanging information over time. The N agents share the common goal of minimizing a joint objective function, which is the average of the private objective functions in a distributed manner. The private objective function is a realization of an objective function known to all the agents, but uses private data known to the agent alone. The agents’ data are independent and identically distributed. We have previously proposed a novel data injection attack on the Distributed Projected Gradient (DPG) algorithm which is performed locally by malicious nodes in the network that steer the network’s final state to a state of their choice. The proposed attack cannot be detected using previously described techniques. We propose a new detection and localization scheme, performed in a single instance unlike other methods that require the algorithm to run for many instances to acquire statistics over time. This detection and localization scheme is performed by each agent and is purely local, and does not involve decisions made by other agents. Whenever an agent suspects another agent to be an attacker, it will block its data, and maintain convergence to the true optimal state. We provide exponential bounds for the probability of false alarm and probability of attacker detection and localization. Simulations show that when all the attackers are detected and isolated by each agent, the network will recover and converge to the true optimal state.

中文翻译：

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对分布式 M 估计的数据注入攻击的本地化


本文研究了对分布式统计估计的数据注入攻击。我们考虑一个动态变化的分布式网络，由 N 个代理组成，随着时间的推移交换信息。 N 个代理的共同目标是最小化联合目标函数，该函数是分布式方式的私有目标函数的平均值。私有目标函数是所有智能体已知的目标函数的实现，但使用仅智能体已知的私有数据。代理的数据是独立且同分布的。我们之前提出了一种针对分布式投影梯度（DPG）算法的新型数据注入攻击，该算法由网络中的恶意节点在本地执行，将网络的最终状态引导到他们选择的状态。使用先前描述的技术无法检测到所提出的攻击。我们提出了一种新的检测和定位方案，该方案在单个实例中执行，这与其他需要算法运行多个实例以随时间推移获取统计数据的方法不同。这种检测和定位方案由每个代理执行并且纯粹是本地的，并且不涉及其他代理做出的决策。每当一个代理怀疑另一个代理是攻击者时，它就会阻止其数据，并保持收敛到真正的最佳状态。我们为误报概率以及攻击者检测和定位概率提供指数界限。模拟表明，当所有攻击者都被每个代理检测到并隔离时，网络将恢复并收敛到真正的最优状态。