Recently, the security of state estimation has attracted significant research attention due to the need for trustworthy situation awareness in emerging cyber-physical systems. In this article, we design an encryption-based state estimation (ESE) using partially homomorphically encrypted data. The encryption will enhance the confidentiality not only of data transmitted in the communication network but also critical system information required by the estimator. We adopt a hybrid encryption scheme by jointly using the multiplicatively and additively homomorphic encryption methods. Armed with encryption, ESE is able to conceal comprehensive information (i.e., model parameters, measurements, and estimates) aggregated at the estimator while retaining the correctness of the normal state estimation. Therefore, even if an attacker has gained unauthorized access to the estimator and associated communication channels, he/she will not be able to obtain sufficient knowledge of the system state to guide the attack. Furthermore, due to the encryption-induced quantization error, we give a sufficient stability condition for ESE. Finally, we implement ESE with real-world hardware to illustrate its effectiveness and efficiency.

中文翻译：

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使用混合同态加密方案的安全状态估计

最近，由于在新兴的网络物理系统中需要可信赖的态势感知，状态估计的安全性引起了广泛的研究关注。在本文中，我们使用部分同态加密的数据设计了一种基于加密的状态估计 (ESE)。加密不仅会增强在通信网络中传输的数据的机密性，还会增强估算器所需的关键系统信息的机密性。我们通过联合使用乘法和加法同态加密方法来采用混合加密方案。通过加密，ESE 能够隐藏在估计器中聚合的综合信息（即模型参数、测量和估计），同时保持正常状态估计的正确性。所以，即使攻击者获得了对估计器和相关通信通道的未经授权的访问，他/她也无法获得足够的系统状态知识来指导攻击。此外，由于加密引起的量化误差，我们为 ESE 提供了足够的稳定性条件。最后，我们使用真实世界的硬件实现 ESE，以说明其有效性和效率。