Abstract
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.
Original language | English |
---|---|
Title of host publication | Privacy in Dynamical Systems |
Editors | Farhad Farokhi |
Place of Publication | Singapore |
Publisher | Springer |
Chapter | 6 |
Pages | 103-129 |
Number of pages | 27 |
ISBN (Electronic) | 978-981-15-0493-8 |
ISBN (Print) | 978-981-15-0492-1 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Electrical Engineering and Systems Science - Systems and Control