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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, 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 paper, the authors present the complete picture for deterministic 2-party SFE functionalities.
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