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Geo-indistinguishability and expected inference error are two complementarynotions for location privacy. The joint guarantee of differential privacy(indistinguishability) and distortion privacy (inference error) limits theinformation leakage. In this paper, we analyze the differential privacy ofPIVE, a dynamic location obfuscation mechanism proposed by Yu, Liu and Pu (NDSS2017), and show that PIVE fails to offer either of the privacy guarantees onadaptive Protection Location Sets (PLSs) as claimed. Specifically, wedemonstrate that different PLSs could intersect with one another due to thedefined search algorithm, and then different apriori locations in the same PLScould have different protection diameters. As a result, we can show that theproof of local differential privacy for PIVE is problematic. Besides, thecondition introduced in PIVE is confirmed to be not sufficient for boundingexpected inference errors in general, which makes the user-defined inferenceerror threshold invalid. To address these issues, we propose a couple ofcorrection approaches, analyze theoretically their satisfied privacycharacteristics and detail their respective merits and demerits.

On the differential privacy of dynamic location obfuscation with personalized error bounds