Concerns on location privacy frequently arise with the rapid development of GPS enabled devices and location-based applications. While spatial transformation techniques such as location perturbation or generalization have been studied extensively, most techniques rely on syntactic privacy models without rigorous privacy guarantee. Many of them only consider static scenarios or perturb the location at single timestamps without considering temporal correlations of a moving user's locations, and hence are vulnerable to various inference attacks. While differential privacy has been accepted as a standard for privacy protection, applying differential privacy in location based applications presents new challenges, as the protection needs to be enforced on the fly for a single user and needs to incorporate temporal correlations between a user's locations.In this paper, we propose a systematic solution to preserve location privacy with rigorous privacy guarantee. First, we propose a new definition, "δ-location set" based differential privacy, to account for the temporal correlations in location data. Second, we show that the well known 1-norm sensitivity fails to capture the geometric sensitivity in multidimensional space and propose a new notion, sensitivity hull, based on which the error of differential privacy is bounded. Third, to obtain the optimal utility we present a planar isotropic mechanism (PIM) for location perturbation, which is the first mechanism achieving the lower bound of differential privacy. Experiments on real-world datasets also demonstrate that PIM significantly outperforms baseline approaches in data utility.

Abstract. Differential privacy is a strong notion for protecting individual privacy in privacy preserving data analysis or publishing. In this paper, we study the problem of differentially private histogram release based on an interactive differential privacy interface. We propose two multidimensional partitioning strategies including a baseline cell-based partitioning and an innovative kd-tree based partitioning. In addition to providing formal proofs for differential privacy and usefulness guarantees for linear distributive queries , we also present a set of experimental results and demonstrate the feasibility and performance of our method.

Differential Privacy (DP) has received increasing attention as a rigorous privacy framework. Many existing studies employ traditional DP mechanisms (e.g., the Laplace mechanism) as primitives, which assume that the data are independent, or that adversaries do not have knowledge of the data correlations. However, continuous generated data in the real world tend to be temporally correlated, and such correlations can be acquired by adversaries. In this paper, we investigate the potential privacy loss of a traditional DP mechanism under temporal correlations in the context of continuous data release. First, we model the temporal correlations using Markov model and analyze the privacy leakage of a DP mechanism when adversaries have knowledge of such temporal correlations. Our analysis reveals that the privacy loss of a DP mechanism may accumulate and increase over time. We call it temporal privacy leakage. Second, to measure such privacy loss, we design an efficient algorithm for calculating it in polynomial time. Although the temporal privacy leakage may increase over time, we also show that its supremum may exist in some cases. Third, to bound the privacy loss, we propose mechanisms that convert any existing DP mechanism into one against temporal privacy leakage. Experiments with synthetic data confirm that our approach is efficient and effective.

Differential Privacy (DP) has received increasing attention as a rigorous privacy framework. Many existing studies employ traditional DP mechanisms (e.g., the Laplace mechanism) as primitives to continuously release private data for protecting privacy at each time point (i.e., event-level privacy), which assume that the data at different time points are independent, or that adversaries do not have knowledge of correlation between data. However, continuously generated data tend to be temporally correlated, and such correlations can be acquired by adversaries. In this paper, we investigate the potential privacy loss of a traditional DP mechanism under temporal correlations. First, we analyze the privacy leakage of a DP mechanism under temporal correlation that can be modeled using Markov Chain. Our analysis reveals that, the event-level privacy loss of a DP mechanism may increase over time. We call the unexpected privacy loss temporal privacy leakage (TPL). Although TPL may increase over time, we find that its supremum may exist in some cases. Second, we design efficient algorithms for calculating TPL. Third, we propose data releasing mechanisms that convert any existing DP mechanism into one against TPL. Experiments confirm that our approach is efficient and effective.