Optimal Linear Encryption Against Stealthy Attacks on Remote State Estimation

Abstract

Defending against malicious attacks has become increasingly important in various cyber-physical systems. This article presents an encryption-based countermeasure against stealthy attacks on remote state estimation. Smart sensors transmit data to a remote estimator through a wireless communication network, in which data packets can be intercepted and compromised by attackers. The remote end is equipped with a false data detector that monitors the system. To avoid being detected, the attack should follow the stealthiness constraint. A linear encryption scheme is proposed to reduce the influence of potential stealthy attacks. For arbitrary linear encryption, the worst-case linear attack that yields the largest estimation error is derived. Accordingly, the optimal linear encryption, which minimizes the worst-case estimation error, is designed based on the Stackelberg game analysis. The above optimal strategies are considered in both the complete and partial measurement information scenarios for the attacker. Moreover, the generalization to nonlinear encryption strategies is also discussed. Comparisons of attack and encryption strategies through numerical examples are provided to illustrate the theoretical results.