We study a security problem for interconnected systems, where each subsystem aims to detect local attacks using local measurements and information exchanged with neighboring subsystems. The subsystems also wish to maintain the privacy of their states and, therefore, use privacy mechanisms that share limited or noisy information with other subsystems. We quantify the privacy level based on the estimation error of a subsystem’s state and propose a novel framework to compare different mechanisms based on their privacy guarantees. We develop a local attack detection scheme without assuming the knowledge of the global dynamics, which uses local and shared information to detect attacks with provable guarantees. Additionally, we quantify a trade-off between security and privacy of the local subsystems. Interestingly, we show that, for some instances of the attack, the subsystems can achieve a better detection performance by being more private. We provide an explanation for this counter-intuitive behavior and illustrate our results with examples.

我们研究了互连系统的安全性问题，其中每个子系统旨在使用本地度量和与相邻子系统交换的信息来检测本地攻击。子系统也希望维护其状态的隐私，因此，使用与其他子系统共享有限或嘈杂信息的隐私机制。我们基于子系统状态的估计误差对隐私级别进行量化，并提出了一个新颖的框架，以基于子系统的隐私保证来比较不同的机制。我们在不假设全局动态的情况下开发了一种本地攻击检测方案，该方案使用本地和共享信息来检测具有可证明保证的攻击。此外，我们量化了本地子系统的安全性和隐私之间的权衡。有趣的是，我们表明 对于某些攻击实例，子系统可以通过更加私有来实现更好的检测性能。我们提供了这种违反直觉的行为的解释，并通过示例说明了我们的结果。