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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, wedoi:10.1109/tifs.2019.2954652 fatcat:ogow44p4jnag5lahd2d44n4wj4