Manoj Prabhakaran

Aman Bansal, Rahul Chunduru, Deepesh Data et al.

Differential Privacy (DP) has become a gold standard in privacy-preserving data analysis. While it provides one of the most rigorous notions of privacy, there are many settings where its applicability is limited. Our main contribution is in augmenting differential privacy with {\em Flexible Accuracy}, which allows small distortions in the input (e.g., dropping outliers) before measuring accuracy of the output, allowing one to extend DP mechanisms to high-sensitivity functions. We present mechanisms that can help in achieving this notion for functions that had no meaningful differentially private mechanisms previously. In particular, we illustrate an application to differentially private histograms, which in turn yields mechanisms for revealing the support of a dataset or the extremal values in the data. Analyses of our constructions exploit new versatile composition theorems that facilitate modular design. All the above extensions use our new definitional framework, which is in terms of "lossy Wasserstein distance" -- a 2-parameter error measure for distributions. This may be of independent interest.

Mohammad Mahmoody, Hemanta K. Maji, Manoj Prabhakaran

The seminal result of Impagliazzo and Rudich (STOC 1989) gave a black-box separation between one-way functions and public-key encryption: informally, a public-key encryption scheme cannot be constructed using one-way functions as the sole source of computational hardness. In addition, this implied a black-box separation between one-way functions and protocols for certain Secure Function Evaluation (SFE) functionalities (in particular, Oblivious Transfer). Surprisingly, however, {\em since then there has been no further progress in separating one-way functions and SFE functionalities} (though several other black-box separation results were shown). In this work, we present the complete picture for deterministic 2-party SFE functionalities. We show that one-way functions are black-box separated from {\em all such SFE functionalities}, except the ones which have unconditionally secure protocols (and hence do not rely on any computational hardness), when secure computation against semi-honest adversaries is considered. In the case of security against active adversaries, a black-box one-way function is indeed useful for SFE, but we show that it is useful only as much as access to an ideal commitment functionality is useful. Technically, our main result establishes the limitations of random oracles for secure computation.