Privacy and Security Trade-off in Cyber-Physical Systems under Utility Consideration

This paper investigates the trade-off between privacy and security under utility consideration in cyber-physical systems. Considering the unreliability of the communication network, we assume that the private data is vulnerable to eaves-dropping and replay attacks. To detect replay attacks, the remote station employs a noisy control method implemented by injecting watermark signals into control inputs. To enhance privacy, the system is equipped with a privacy-preserving mechanism achieved by injecting privacy signals into measurement outputs. Therefore, we first investigate the trade-off between privacy performance and replay attack detection performance, where the privacy level is measured by mutual information. Moreover, both the watermark and privacy signals degrade the control performance, measured by the increment of linear quadratic Gaussian (LQG) cost. Then, we establish an optimization problem to co-design the watermark and privacy signals by minimizing the weighted sum of the mutual information and the LQG cost increment, subject to detection performance constraints. Finally, a numerical example is presented to verify the effectiveness of theoretical results.