Perfect data privacy seems to be in fundamental opposition to the economical
and scientific opportunities associated with extensive data exchange. Defying
this intuition, this paper develops a framework that allows the disclosure of
collective properties of datasets without compromising the privacy of
individual data samples. We present an algorithm to build an optimal disclosure
strategy/mapping, and discuss it fundamental limits on finite and
asymptotically large datasets. Furthermore, we present explicit expressions to
the asymptotic performance of this scheme in some scenarios, and study cases
where our approach attains maximal efficiency. We finally discuss suboptimal
schemes to provide sample privacy guarantees to large datasets with a reduced
computational cost.