A Learning With Errors based encryption scheme for dynamic controllers that discloses residue signal for anomaly detection
It addresses the problem of anomaly detection in encrypted control systems without revealing private data, which is important for secure control applications.
The paper proposes a homomorphic encryption scheme for dynamic controllers that discloses the residue signal for anomaly detection while keeping other signals private, using a Learning With Errors (LWE) based approach. The method enables dynamic controllers with non-integer state matrices without re-encryption.
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 over a finite field of integers and incorporate it into a Learning With Errors (LWE) based scheme. We then present a method to further utilize the disclosed residue signal for implementing dynamic controllers over encrypted data, which does not involve re-encryption even when they have non-integer state matrices.