Anomaly Detection with LWE Encrypted Control

TL;DR

This paper introduces a novel anomaly detection method that operates directly on LWE encrypted signals using homomorphic properties, avoiding decryption and enhancing security in attack detection.

Contribution

The paper presents a new homomorphic anomaly detection technique for LWE encrypted signals that balances encryption strength and detection performance.

Findings

Detection sensitivity deteriorates polynomially with suboptimal solutions.

Parameter tuning can improve detection at the expense of encryption strength.

Numerical simulations confirm the method's effectiveness in identifying attacks.

Abstract

Detecting attacks using encrypted signals is challenging since encryption hides its information content. We present a novel mechanism for anomaly detection over Learning with Errors (LWE) encrypted signals without using decryption, secure channels, nor complex communication schemes. Instead, the detector exploits the homomorphic property of LWE encryption to perform hypothesis tests on transformations of the encrypted samples. The specific transformations are determined by solutions to a hard lattice-based minimization problem. While the test's sensitivity deteriorates with suboptimal solutions, similar to the exponential deterioration of the (related) test that breaks the cryptosystem, we show that the deterioration is polynomial for our test. This rate gap can be exploited to pick parameters that lead to somewhat weaker encryption but large gains in detection capability. Finally, we conclude the paper by presenting a numerical example that simulates anomaly detection, demonstrating the effectiveness of our method in identifying attacks.