Hardness of non-interactive differential privacy from one-way functions

6Citations
Citations of this article
34Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

A central challenge in differential privacy is to design computationally efficient non-interactive algorithms that can answer large numbers of statistical queries on a sensitive dataset. That is, we would like to design a differentially private algorithm that takes a dataset D∈ Xn consisting of some small number of elements n from some large data universe X, and efficiently outputs a summary that allows a user to efficiently obtain an answer to any query in some large family Q. Ignoring computational constraints, this problem can be solved even when X and Q are exponentially large and n is just a small polynomial; however, all algorithms with remotely similar guarantees run in exponential time. There have been several results showing that, under the strong assumption of indistinguishability obfuscation, no efficient differentially private algorithm exists when X and Q can be exponentially large. However, there are no strong separations between information-theoretic and computationally efficient differentially private algorithms under any standard complexity assumption. In this work we show that, if one-way functions exist, there is no general purpose differentially private algorithm that works when X and Q are exponentially large, and n is an arbitrary polynomial. In fact, we show that this result holds even if X is just subexponentially large (assuming only polynomially-hard one-way functions). This result solves an open problem posed by Vadhan in his recent survey 52].

Cite

CITATION STYLE

APA

Kowalczyk, L., Malkin, T., Ullman, J., & Wichs, D. (2018). Hardness of non-interactive differential privacy from one-way functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10991 LNCS, pp. 437–466). Springer Verlag. https://doi.org/10.1007/978-3-319-96884-1_15

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free