Limits of Random Oracles in Secure Computation
This resolves a long-standing open problem in cryptography by clarifying the limits of computational hardness for secure computation, which is foundational for privacy and security in distributed systems.
The paper tackles the problem of determining which secure function evaluation (SFE) functionalities can be constructed from one-way functions, showing that for deterministic 2-party SFE with semi-honest adversaries, one-way functions are black-box separated from all such functionalities except those with unconditionally secure protocols, and for active adversaries, they are only as useful as an ideal commitment functionality.
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.