How Sensor Attacks Transfer Across Lie Groups

Researchers Rijad Alisic and Saurabh Amin have published a groundbreaking paper, 'How Sensor Attacks Transfer Across Lie Groups,' introducing a geometric framework for analyzing sensor spoofing in complex cyber-physical systems. While prior analysis was confined to linear systems where attack transferability is straightforward, this work tackles the noncommutative dynamics of systems operating on Lie groups, such as drones or autonomous vehicles performing complex maneuvers. The core finding is a mathematical condition for stealth: for an attack to transfer across different operating conditions while remaining undetected, it must commute with the system's nominal dynamics—a condition expressed through the Lie bracket. Attacks that violate this condition are provably detectable because they identifiably alter the system's residuals.

The framework reveals critical asymmetries in how imperfect attacks behave. For small deviations from the ideal 'transferable' attack, the physical impact of the non-commuting component is amplified by the system's own dynamics through the Adjoint action. Although the attack perturbs sensor readings linearly, the accumulated error in the system's state estimation undergoes nonlinear distortion. The researchers demonstrated this concretely using a Dubins unicycle model, showing how a simple turning maneuver collapses the subspace of transferable attacks to just a single direction. This mathematically verifies that even sophisticated, nearly-perfect attacks have theoretical detection bounds, providing a new foundation for designing more robust anomaly detection systems in autonomous platforms.