The relationship between public key encryption and oblivious transfer

In this paper we study the relationships among some of the most fundamental primitives and protocols in cryptography: public-key encryption (i.e. trapdoor predicates), oblivious transfer (which is equivalent to general secure multi-party computation), key agreement and trapdoor permutations. Our main results show that public-key encryption and oblivious transfer are incomparable under black-box reductions. These separations are tightly matched by our positive results where a restricted (strong) version of one primitive does imply the other primitive. We also show separations between oblivious transfer and key agreement. Finally, we conclude that neither oblivious transfer nor trapdoor predicates imply trapdoor permutations. Our techniques for showing negative results follow the oracle separations of R. Impagliazzo and S. Rudich (1989).