How Sensor Attacks Transfer Across Lie Groups
Sensor spoofing analysis in cyber-physical systems is predominantly confined to linear state spaces, where attack transferability is trivial. On Lie groups, however, the noncommutativity of the dynamics can distort certain sensor attacks, exposing nominally stealthy attacks during complex maneuvers. We present a geometric framework characterizing when a sensor attack can transfer across operating conditions, preserving both its physical impact and stealthiness. We prove that successful transfer requires the attack to commute with the nominal dynamics (a Lie bracket condition), which isolates transferable attacks to an invariant subspace, while attacks outside this subspace identifiably alter residuals. For small deviations from ideal transferable attacks, our decomposition theorem reveals a fundamental asymmetry: the flow's Adjoint action amplifies the physical impact of the bracket-violating component. Furthermore, although the attack perturbs the innovation linearly, the accumulated error drift undergoes distortion via the Adjoint action. Finally, we demonstrate how turning maneuvers on a Dubins unicycle collapse the transferable subspace to a single direction, verifying that imperfect attacks remain within theoretical detection bounds.