We study the problem of maximizing privacy of data sets by adding random
vectors generated via synchronized chaotic oscillators. In particular, we
consider the setup where information about data sets, queries, is sent through
public (unsecured) communication channels to a remote station. To hide private
features (specific entries) within the data set, we corrupt the response to
queries by adding random vectors. We send the distorted query (the sum of the
requested query and the random vector) through the public channel. The
distribution of the additive random vector is designed to minimize the mutual
information (our privacy metric) between private entries of the data set and
the distorted query. We cast the synthesis of this distribution as a convex
program in the probabilities of the additive random vector. Once we have the
optimal distribution, we propose an algorithm to generate pseudo-random
realizations from this distribution using trajectories of a chaotic oscillator.
At the other end of the channel, we have a second chaotic oscillator, which we
use to generate realizations from the same distribution. Note that if we obtain
the same realizations on both sides of the channel, we can simply subtract the
realization from the distorted query to recover the requested query. To
generate equal realizations, we need the two chaotic oscillators to be
synchronized, i.e., we need them to generate exactly the same trajectories on
both sides of the channel synchronously in time. We force the two chaotic
oscillators into exponential synchronization using a driving signal.
Simulations are presented to illustrate our results.Comment: arXiv admin note: text overlap with arXiv:1809.03133 by other author