An Optimal Noise Mechanism for Cross-Correlated IoT Data Releasing

Cross correlations are ubiquitous in time-series IoT data sets such as trajectories from smartphones and smart meters data in smart grids. Conventional privacy methods have difficulty to protect cross correlation privacy within such correlated data set. Here we propose a novel Correlated noise mechanism for Cross-correlated Data Privacy (CCDP). Because the Fourier coefficients of the cross correlation of two data records are the linear product of those of the two data records, the sanitizing Fourier coefficients noise is used for efficient optimization. Also, the noise is added via the Geometric sum method, which is proved to provide the required Laplace distribution. We perform rigorous mathematical analysis of the CCDP and prove that it satisfies epsilon-Pufferfish privacy. We also prove that the CCDP can achieve the optimal data utility for a given privacy budget epsilon. What's more important, we further derive the mathematical procedure to obtain the optimal Laplace noise scale parameter to achieve better data utility. Simulations show that the proposed CCDP outperforms the independent Fourier coefficients noise mechanism, as well as two other state-of-the-art time-domain privacy mechanisms in the literature, for three types of data sets: computer-generated data, real-world trajectory data, and smart meter data.