Limits of Computational Differential Privacy in the Client/Server Setting

Abstract

Abstract. Differential privacy is a well established definition guaranteeing that queries to a database do not reveal "too much" information about specific individuals who have contributed to the database. The standard definition of differential privacy is information theoretic in nature, but it is natural to consider computational relaxations and to explore what can be achieved with respect to such notions. Mironov et al. Left open by prior work was the extent, if any, to which computational differential privacy can help in the usual client/server setting where the entire database resides at the server, and the client poses queries on this data. We show, for queries with output in R n (for constant n) and with respect to a large class of utilities, that any computationally private mechanism can be converted to a statistically private mechanism that is equally efficient and achieves roughly the same utility.

Separating Computational and Statistical Differential Privacy in the Client-Server Model

“…We revisit the techniques of [GKY11] to exhibit a setting in which efficient CDP mechanisms cannot do much better than information-theoretically differentially private mechanisms. In particular, we consider computational tasks with output in some discrete space (or which can be reduced to some discrete space) R k , and with utility measured via functions of the form g : R k × R k → R. We show that if (R k , g) forms a metric space with O(log k)-doubling dimension (and other properties described in detail later), then CDP mechanisms can be efficiently transformed into differentially private ones.…”

“…Beyond just the absence of any techniques for taking advantage of CDP in this setting, results of Groce, Katz, and Yerukhimovich [GKY11] (discussed in more detail below) show that CDP yields no additional power in the client-server model for many basic statistical tasks. An additional barrier stems from the fact that all known lower bounds against computationally efficient differentially private algorithms [DNR + 09, UV11, Ull13, BZ14, BZ16] in the client-server model are proved by exhibiting computationally efficient adversaries.…”

“…Circumventing the impossibility results of [GKY11]. Groce et al showed that in many natural circumstances, computational differential privacy cannot yield any additional power over differential privacy in the client-server model.…”

“…(In Section 4, we revisit the techniques [GKY11] to strengthen the second result in some circumstances. In general, we show that when error is measured in any metric with doubling dimension O(log k), CDP cannot improve utility by more than a constant factor.…”

“…We get around both of these impossibility results by 1) making non-blackbox use of one-way functions via the machinery of zap proofs and 2) relying on a utility function that is far from the form in which the second result of [GKY11] applies. Indeed, our utility function is cryptographic and unnatural from a data analysis point view.…”