Selective private function evaluation with applications to private statistics

Motivated by the application of private statistical analysis of large databases, we consider the problem of <i>selective private function evaluation</i> (SPFE). In this problem, a client interacts with one or more servers holding copies of a database <i>x</i> = <i>x</i><subscrpt>1</subscrpt>, … , <i>x<subscrpt>n</subscrpt></i> in order to compute <i>f</i>(<i>x</i><subscrpt><i>i</i><subscrpt>1</subscrpt></subscrpt>, … , <i>x</i><subscrpt><i>i</i><subscrpt><i>m</i></subscrpt></subscrpt>), for some function <i>f</i> and indices <i>i</i> = <i>i</i><subscrpt>1</subscrpt>, … , <i>i<subscrpt>m</subscrpt></i> chosen by the client. Ideally, the client must learn nothing more about the database than <i>f</i>(<i>x<subscrpt>i</subscrpt></i>, … , <i>x</i><subscrpt><i>i</i><subscrpt><i>m</i></subscrpt></subscrpt>), and the servers should learn nothing. Generic solutions for this problem, based on standard techniques for secure function evaluation, incur communication complexity that is at least linear in <i>n</i>, making them prohibitive for large databases even when <i>f</i> in relatively simple and <i>m</i> is small. We present various approaches for constructing sublinear-communication SPFE protocols, both for the general problem and for special cases of interest. Our solutions not only offer sublinear communication complexity, but are also practical in many scenarios.

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