  We address the problem of synthesizing distorting mechanisms that maximize
privacy of stochastic dynamical systems. Information about the system state is
obtained through sensor measurements. This data is transmitted to a remote
station through an unsecured/public communication network. We aim to keep part
of the system state private (a private output); however, because the network is
unsecured, adversaries might access sensor data and input signals, which can be
used to estimate private outputs. To prevent an accurate estimation, we pass
sensor data and input signals through a distorting (privacy-preserving)
mechanism before transmission, and send the distorted data to the trusted user.
These mechanisms consist of a coordinate transformation and additive dependent
Gaussian vectors. We formulate the synthesis of the distorting mechanisms as a
convex program, where we minimize the mutual information (our privacy metric)
between an arbitrarily large sequence of private outputs and the disclosed
distorted data for desired distortion levels -- how different actual and
distorted data are allowed to be.
