  We investigate the problems of identity and closeness testing over a discrete
population from random samples. Our goal is to develop efficient testers while
guaranteeing Differential Privacy to the individuals of the population. We
describe an approach that yields sample-efficient differentially private
testers for these problems. Our theoretical results show that there exist
private identity and closeness testers that are nearly as sample-efficient as
their non-private counterparts. We perform an experimental evaluation of our
algorithms on synthetic data. Our experiments illustrate that our private
testers achieve small type I and type II errors with sample size sublinear in
the domain size of the underlying distributions.
