Correlated pseudorandomness and the complexity of private computations

The race to find the weakest possible assumptions on which to base cryptographic primitives such aa oblivious transfer was abruptly baited by Impagliazzo’s and Rudich’s surprising result: basing oblivious transfer or other related problems on a black-box one-way permutation (as opposed to a one-way trapdoor permutation ) is tantamount to showing P#NP. In contrast, we show how to generate OT – in the sense of random number generation – using any one-way function in a black-box manner. That is, an initial “seed” of k OT’S suffices to generate O(kc) OT’S. In turn, we show that such generation is impossible in an information-theoretic setting, thus placing OT on an equal footing with random number generation, and resolving an artificial asymmetry in the analysis of randomness and partiallycorrelated randomness.