A low cost and uncancelled laplace noise based differential privacy algorithm for spatial decompositions Differentially private spatial decompositions split the whole domain into subdomains recursively to generate a hierarchical private tree and add Laplace noise to each nodexe2x80x99s points count. However the Laplace distribution is symmetric about the origin, the mean of a large number of queries may cancel the Laplace noise and reveal privacy. Existing methods take the solution by limiting the number of queries. But in private tree the points count of intermediate node may be real since the summation of all its descendants may cancel the Laplace noise. To address these problems of differentially private spatial decompositions, we propose a more secure algorithm to make the Laplace noise not be canceled. That splits the domains depending on its real points count not noisy, and only adds indefeasible Laplace noise to leaves. That the i th randomly selected leaf of one intermediate node is added noise by (frac left (upbeta i1 right )1upbeta (upbeta i1)upbeta Lap(lambda )). We also propose the definition of Lapmin(xcexbb) whose absolute value is not greater than Sensitivity(f). It is proved that adding Lapmin(xcexbb) noise to query answer guarantees both differential privacy and minimal relative error comparing with unlimited Laplace noise. The experiment results show that our algorithm performs better both on synthetic and real datasets with higher security and data utility, and the noises costs is highly decreased.

Context Aware Laplacian Mechanism for Local Information Privacy In this paper, we consider the problem of designing additive noise mechanisms for data release subject to a local information privacy constraint. While there has been significant prior work on devising additive noise mechanisms for differential privacy (such as Laplacian and Gaussian mechanisms), for the notion of information privacy, which accounts for priorknowledge about the data, there are no such general purpose additive noise mechanisms. To this end, we devise a prioraware Laplacian noise mechanism, which satisfies local information privacy. We show that adding context awareness (i.e., via the knowledge of prior of the data) improves the tradeoff between utility and privacy when compared to contextunaware mechanisms.