1 research outputs found
Differential Privacy Via a Truncated and Normalized Laplace Mechanism
When querying databases containing sensitive information, the privacy of
individuals stored in the database has to be guaranteed. Such guarantees are
provided by differentially private mechanisms which add controlled noise to the
query responses. However, most such mechanisms do not take into consideration
the valid range of the query being posed. Thus, noisy responses that fall
outside of this range may potentially be produced. To rectify this and
therefore improve the utility of the mechanism, the commonly used Laplace
distribution can be truncated to the valid range of the query and then
normalized. However, such a data-dependent operation of normalization leaks
additional information about the true query response thereby violating the
differential privacy guarantee.
Here, we propose a new method which preserves the differential privacy
guarantee through a careful determination of an appropriate scaling parameter
for the Laplace distribution. We also generalize the privacy guarantee in the
context of the Laplace distribution to account for data-dependent normalization
factors and study this guarantee for different classes of range constraint
configurations. We provide derivations of the optimal scaling parameter (i.e.,
the minimal value that preserves differential privacy) for each class or
provide an approximation thereof. As a consequence of this work, one can use
the Laplace distribution to answer queries in a range-adherent and
differentially private manner.Comment: This is a pre-print of an article published in Journal of Computer
Science and Technology. The final authenticated version is available online
at: https://doi.org/10.1007/s11390-020-0193-