Limits on the Usefulness of Random Oracles

In their seminal work, Impagliazzo and Rudich (STOC’89) showed that no key-agreement protocol exists in the random-oracle model, yielding that key agreement cannot be black-box reduced to one-way functions. In this work, we generalize their result, showing that, to a large extent, no-private-input, semi-honest, two-party functionalities that can be securely implemented in the random oracle model can be securely implemented information theoretically (where parties are assumed to be all powerful, and no oracle is given). Using a recent information-theoretic impossibility result by McGregor et al. (FOCS’10), our result yields that certain functionalities (e.g. inner product) cannot be computed both in an accurately and in a differentially private manner in the random oracle model, implying that protocols for computing these functionalities cannot be black-box reduced to the existence of one-way functions.