Revealing information while preserving privacy

We examine the tradeoff between privacy and usability of statistical databases. We model a statistical database by an n-bit string d₁,.,d_n, with a query being a subset q ⊆ [n] to be answered by Σ_iεq d_i. Our main result is a polynomial reconstruction algorithm of data from noisy (perturbed) subset sums. Applying this reconstruction algorithm to statistical databases we show that in order to achieve privacy one has to add perturbation of magnitude (Ω√n). That is, smaller perturbation always results in a strong violation of privacy. We show that this result is tight by exemplifying access algorithms for statistical databases that preserve privacy while adding perturbation of magnitude Õ(√n).For time-T bounded adversaries we demonstrate a privacypreserving access algorithm whose perturbation magnitude is ≈ √T.