Resistance of IID Noise in Differentially Private Schemes for Trajectory Publishing

Although analyzing and mining user’s trajectory data can provide outstanding benefit, data owners may not be willing to upload their trajectory data because of privacy concerns. Recently, differential privacy technology has achieved a good trade-off between data utility and privacy preserving by publishing noisy outputs, and relevant schemes have been proposed for trajectory release. However, we experimentally find that a relatively accurate estimate of the true data value can still be obtained from the noisy outputs by means of a posterior estimation. But there are no practical mechanisms against current schemes to verify their effectiveness and resistance. To fill this gap, we propose a solution to evaluate the resistance performance of differential privacy on trajectory data release, including a notion of correlation-distinguishability filtering (CDF) and a privacy quantification measurement. Specifically, taking advantage of the principle of filtering that independent noise can be filtered out from correlated sequence, CDF is proposed to sanitize the noise added into the trajectory. To conduct this notion in practice, we attempt to apply a Kalman/particle filter to filter out the corresponding Gaussian/Laplace noise added by differential privacy schemes. Furthermore, to quantify the distortion of privacy strength before and after filtering, an entropy-based privacy quantification metric is proposed, which is used to measure the lost uncertainty of the true locations for an adversary. Experimental results show that the resistance performance of current approaches has a degradation to varying degrees under the filtering attack model in our solution. Moreover, the privacy quantification metric can be regarded as a unified criterion to measure the privacy strength introduced by the noise that does not conform to the form required by differential privacy.