Relation To Other Cryptographic Primitives
One-way functions are necessary, but not known to be sufficient, for nontrivial (i.e., with sublinear communication) single database computationally private information retrieval. In fact, such a protocol was proved by G. Di Crescenzo, T. Malkin and R. Ostrovsky in to imply oblivious transfer (see below).
Oblivious transfer, also called symmetric PIR, is PIR with the additional restriction that the user may not learn any item other than the one she requested. It is termed symmetric because both the user and the database have a privacy requirement.
Collision-resistant cryptographic hash functions are implied by any one-round computational PIR scheme, as shown by Ishai, Kushilevitz and Ostrovsky.
Read more about this topic: Private Information Retrieval
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