Dependence Makes You Vulnberable: Differential Privacy Under Dependent Tuples

Differential privacy (DP) is a widely accepted mathematical framework for protecting data privacy. Simply stated, it guarantees that the distribution of query results changes only slightly due to the modification of any one tuple in the database. This allows protection, even against powerful adversaries, who know the entire database except one tuple. For providing this guarantee, differential privacy mechanisms assume independence of tuples in the database -a vulnerable assumption that can lead to degradation in expected privacy levels especially when applied to real-world datasets that manifest natural dependence owing to various social, behavioral, and genetic relationships between users. In this paper, we make several contributions that not only demonstrate the feasibility of exploiting the above vulnerability but also provide steps towards mitigating it. First, we present an inference attack, using real datasets, where an adversary leverages the probabilistic dependence between tuples to extract users' sensitive information from differentially private query results (violating the DP guarantees). Second, we introduce the notion of dependent differential privacy (DDP) that accounts for the dependence that exists between tuples and propose a dependent perturbation mechanism (DPM) to achieve the privacy guarantees in DDP. Finally, using a combination of theoretical analysis and extensive experiments involving different classes of queries (e.g., machine learning queries, graph queries) issued over multiple large-scale real-world datasets, we show that our DPM consistently outperforms state-of-the-art approaches in managing the privacy-utility tradeoffs for dependent data.