A Learning With Errors based Encryption Scheme for Dynamic Controllers that Discloses Residue Signal for Anomaly Detection

Although encrypted control systems ensure confidentiality of private data, it is challenging to detect anomalies without the secret key as all signals remain encrypted. To address this issue, we propose a homomorphic encryption scheme for dynamic controllers that automatically discloses the residue signal for anomaly detection, while keeping all other signals private. To this end, we characterize the zero-dynamics of an encrypted dynamic system defined over a finite field of integers and incorporate it into a Learning With Errors (LWE) based encryption scheme. We then present a method to further utilize the disclosed residue signal for implementing dynamic controllers over encrypted data, without requiring re-encryption even when they have non-integer state matrices.