Approximate Privacy: PARs for Set Problems

TL;DR

This paper analyzes the privacy guarantees of protocols for set disjointness and intersection problems using the Privacy Approximation Ratio (PAR), revealing exponential privacy loss and identifying fairer protocols.

Contribution

It extends the PAR framework to multiple protocols for set problems, proving exponential privacy loss and comparing protocol fairness.

Findings

Privacy loss is necessarily exponential in set size k.

Some protocols are significantly fairer, affecting both players similarly.

The PAR framework effectively measures privacy in set problem protocols.

Abstract

In previous work (arXiv:0910.5714), we introduced the Privacy Approximation Ratio (PAR) and used it to study the privacy of protocols for second-price Vickrey auctions and Yao's millionaires problem. Here, we study the PARs of multiple protocols for both the disjointness problem (in which two participants, each with a private subset of {1,...,k}, determine whether their sets are disjoint) and the intersection problem (in which the two participants, each with a private subset of {1,...,k}, determine the intersection of their private sets). We show that the privacy, as measured by the PAR, provided by any protocol for each of these problems is necessarily exponential (in k). We also consider the ratio between the subjective PARs with respect to each player in order to show that one protocol for each of these problems is significantly fairer than the others (in the sense that it has a similarly bad effect on the privacy of both players).