  For a class of Cyber-Physical Systems (CPSs), we address the problem of
performing computations over the cloud without revealing private information
about the structure and operation of the system. We model CPSs as a collection
of input-output dynamical systems (the system operation modes). Depending on
the mode the system is operating on, the output trajectory is generated by one
of these systems in response to driving inputs. Output measurements and driving
inputs are sent to the cloud for processing purposes. We capture this
"processing" through some function (of the input-output trajectory) that we
require the cloud to compute accurately - referred here as the trajectory
utility. However, for privacy reasons, we would like to keep the mode private,
i.e., we do not want the cloud to correctly identify what mode of the CPS
produced a given trajectory. To this end, we distort trajectories before
transmission and send the corrupted data to the cloud. We provide mathematical
tools (based on output-regulation techniques) to properly design distorting
mechanisms so that: 1) the original and distorted trajectories lead to the same
utility; and the distorted data leads the cloud to misclassify the mode.
