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Differentially private noise mechanisms commonly use symmetric noisedistributions. This is attractive both for achieving the differential privacydefinition, and for unbiased expectations in the noised answers. However, thereare contexts in which a noisy answer only has utility if it is conservative,that is, has known-signed error, which we call a padded answer. Seemingly, itis paradoxical to satisfy the DP definition with one-sided error, but we showhow it is possible to bury the paradox into approximate DP's delta parameter.We develop a few mechanisms for one-sided padding mechanisms that always giveconservative answers, but still achieve approximate differential privacy. Weshow how these mechanisms can be applied in a few select areas including makingthe cardinalities of set intersections and unions revealed in Private SetIntersection protocols differential private and enabling multiparty computationprotocols to compute on sparse data which has its exact sizes made differentialprivate rather than performing a fully oblivious more expensive computation.

The Privacy-preserving Padding Problem: Non-negative Mechanisms for Conservative Answers with Differential Privacy