The Hidden Cost of Correlation: Rethinking Privacy Leakage in Local Differential Privacy

Abstract: Local differential privacy (LDP) has emerged as a promising paradigm for privacy-preserving data collection in distributed systems, where users contribute multi-dimensional records with potentially correlated attributes. Recent work has highlighted that correlation-induced privacy leakage (CPL) plays a critical role in shaping the privacy-utility trade-off under LDP, especially when correlations exist among attributes. Nevertheless, it remains unclear to what extent the prevailing assumptions and proposed solutions are valid and how significant CPL is in real-world data. To address this gap, we first perform a comprehensive statistical analysis of five widely used LDP mechanisms -- GRR, RAPPOR, OUE, OLH and Exponential mechanism -- to assess CPL across four real-world datasets. We identify that many primary assumptions and metrics in current approaches fall short of accurately characterising these leakages. Moreover, current studies have been limited to a set of pure LDP (i.e., {\delta = 0}) mechanisms. In response, we develop the first algorithmic framework to theoretically quantify CPL for any general approximated LDP (({\varepsilon},{\delta})-LDP) mechanism. We validate our theoretical results against empirical statistical results and provide a theoretical explanation for the observed statistical patterns. Finally, we propose two novel benchmarks to validate correlation analysis algorithms and evaluate the utility vs CPL of LDP mechanisms. Further, we demonstrate how these findings can be applied to achieve an efficient privacy-utility trade-off in real-world data governance.