Differential Privacy Via a Truncated and Normalized Laplace Mechanism

TL;DR

This paper introduces a method for applying the Laplace mechanism in differential privacy that accounts for query range constraints by carefully choosing a scaling parameter, thus improving utility without compromising privacy.

Contribution

It proposes a new approach to normalize truncated Laplace noise in differential privacy, ensuring privacy guarantees are maintained with range constraints.

Findings

Derived optimal scaling parameters for different range configurations.

Extended privacy guarantees to include data-dependent normalization.

Enabled range-adherent, differentially private query responses.

Abstract

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.