We introduce Private Set Matching (PSM) problems, in which a client aims to
determine whether a collection of sets owned by a server matches her interest.
Existing privacy-preserving cryptographic primitives cannot solve PSM problems
efficiently without harming privacy. We propose a new modular framework that
enables designers to build privacy-friendly PSM systems that output one bit:
whether a server set or collection of server sets matches the client's set,
while guaranteeing privacy of client and server sets. The communication cost of
our protocols scales linearly with the size of the client's set and is
independent of the number of server sets and their total size. We demonstrate
the potential of our framework by designing and implementing novel solutions
for two real-world PSM problems: determining whether a dataset has chemical
compounds of interest, and determining whether a document collection has
relevant documents. Our evaluation shows that our privacy gain comes at a
reasonable communication and computation cost
