Security of Random Output Perturbation for Statistical Databases

Abstract

We prove that, with respect to a database query response privacy mechanism employing output perturbation with i.i.d. random noise addition, an adversary can, allowed a sufficiently large number of queries, exactly determine all records in an n-record database up to overwhelming probability of success, and establish corresponding quantitative confidence bounds for the attack success probability. These confidence bounds do not depend on the cardinality |D| of the data domain D ⊂ R, where the database ${\mathcal{D}}$ is a member of the set D ⁿ, and they even admit some unbounded data domains D of (countably) infinite cardinality. Within the context of differential privacy, we show that our results also imply a lower bound on the variance of independent, Laplace-distributed noise that can be added to user queries if database privacy is to be preserved. Our results do not require the additive noise to be bounded by $o(\sqrt{n})$ as assumed in Dinur & Nissim (2003) and Dwork & Yekhanin (2008), which, on the other hand, do admit correlated noise.