  We introduce the problem of learning-based attacks in a simple abstraction of
cyber-physical systems---the case of a discrete-time, linear, time-invariant
plant that may be subject to an attack that overrides the sensor readings and
the controller actions. The attacker attempts to learn the dynamics of the
plant and subsequently override the controller's actuation signal, to destroy
the plant without being detected. The attacker can feed fictitious sensor
readings to the controller using its estimate of the plant dynamics and mimic
the legitimate plant operation. The controller, on the other hand, is
constantly on the lookout for an attack; once the controller detects an attack,
it immediately shuts the plant off. In the case of scalar plants, we derive an
upper bound on the attacker's deception probability for any measurable control
policy when the attacker uses an arbitrary learning algorithm to estimate the
system dynamics. We then derive lower bounds for the attacker's deception
probability for both scalar and vector plants by assuming a specific
authentication test that inspects the empirical variance of the system
disturbance. We also show how the controller can improve the security of the
system by superimposing a carefully crafted privacy-enhancing signal on top of
the "nominal control policy." Finally, for nonlinear scalar dynamics that
belong to the Reproducing Kernel Hilbert Space (RKHS), we investigate the
performance of attacks based on nonlinear Gaussian-processes (GP) learning
algorithms.
