We consider private data analysis in the setting in which a trusted and trustworthy curator, having obtained a large data set containing private information, releases to the public a "sanitization" of the data set that simultaneously protects the privacy of the individual contributors of data and offers utility to the data analyst. The sanitization may be in the form of an arbitrary data structure, accompanied by a computational procedure for determining approximate answers to queries on the original data set, or it may be a "synthetic data set" consisting of data items drawn from the same universe as items in the original data set; queries are carried out as if the synthetic data set were the actual input. In either case the process is non-interactive; once the sanitization has been released the original data and the curator play no further role. For the task of sanitizing with a synthetic dataset output, we map the boundary between computational feasibility and infeasibility with respect to a variety of utility measures. For the (potentially easier) task of sanitizing with unrestricted output format, we show a tight qualitative and quantitative connection between hardness of sanitizing and the existence of traitor tracing schemes.
The definition of differential privacy has recently emerged as a leading standard of privacy guarantees for algorithms on statistical databases. We offer several relaxations of the definition which require privacy guarantees to hold only against efficient—i.e., computationally-bounded—adversaries. We establish various relationships among these notions, and in doing so, we observe their close connection with the theory of pseudodense sets by Reingold et al.. We extend the dense model theorem of Reingold et al. to demonstrate equivalence between two definitions (indistinguishability- and simulatability-based) of computational differential privacy. Our computational analogues of differential privacy seem to allow for more accurate constructions than the standard information-theoretic analogues. In particular, in the context of private approximation of the distance between two vectors, we present a differentially-private protocol for computing the approximation, and contrast it with a substantially more accurate protocol that is only computationally differentially private.