Founding crytpography on oblivious transfer

Abstract

Suppose your netmail is being erratically censored by Captain Yossarian. Whenever you send a message, he censors each bit of the message with probability 1/2, replacing each censored bit by some reserved character. Well versed in such concepts as redundancy, this is no real problem to you. The question is, can it actually be turned around and used to your advantage? We answer this question strongly in the affirmative. We show that this protocol, more commonly known as oblivious transfer, can be used to simulate a more sophisticated protocol, known as oblivious circuit evaluation([Y]). We also show that with such a communication channel, one can have completely noninteractive zero-knowledge proofs of statements in NP. These results do not use any complexity-theoretic assumptions. We can show that they have applications to a variety of models in which oblivious transfer can be done.