Sensor Attack Detection Method for Encrypted State Observers

TL;DR

This paper proposes an encrypted state observer that is capable of detecting sensor attacks without decryption and develops a homomorphic encryption scheme that enables the observer to operate over encrypted data while automatically disclosing the residue signal.

Abstract

This paper proposes an encrypted state observer that is capable of detecting sensor attacks without decryption. We first design a state observer that operates over a finite field of integers with the modular arithmetic. The observer generates a residue signal that indicates the presence of attacks under sparse attack and sensing redundancy conditions. Then, we develop a homomorphic encryption scheme that enables the observer to operate over encrypted data while automatically disclosing the residue signal. Unlike our previous work restricted to single-input single-output systems, the proposed scheme is applicable to general multi-input multi-output systems. Given that the disclosed residue signal remains below a prescribed threshold, the full state can be recovered as an encrypted message.