Optimal finite-time watermark signal design for replay attack detection using zonotopes

This paper analyzes the injection of finite sequences as a physical watermarking method for the detection of sensor replay attacks under an unknown but zonotopically bounded uncertainty description. A temporal mismatch between the watermark sequences that are injected during the record and replay phases of the attack is achieved by splitting the input space into a pre-established number of sets. These sets are designed offline by solving an optimization problem whose solution guarantees that, in each set, there exists a finite sequence that ensures attack detection for all possible recorded watermarks belonging to any of the remaining sets. Additionally, several approaches for reducing the complexity of the optimization problem are discussed. The results are validated in simulation using a four-tanks system.Peer ReviewedPostprint (published version