Single Database Private Information Retrieval Implies Oblivious Transfer
Giovanni Di Crescenzo, Tal Malkin and Rafail Ostrovsky
Abstract: A Single-Database Private Information Retrieval (PIR, for short) is a protocol that allows a user to privately retrieve from a database an entry with as small as possible communication complexity. We call any PIR protocol non-trivial if its total communication complexity is strictly less than the total size of the database (i.e., a PIR protocol is non-trivial even if the total communication is just one bit less then the total size of the database). Non-trivial PIR is an important cryptographic primitive with many applications. Thus, understanding which assumptions are necessary for implementing such a primitive is an important task, although (so far) not a well-understood one. In this paper we show that any non-trivial PIR implies Oblivious Transfer, a far better understood primitive. Our result not only significantly clarifies our understanding of any non-trivial PIR protocol, but also yields the following consequences:
-- Any non-trivial PIR is complete for all two-party and multi-party secure computations.
-- There exists a communication-efficient reduction from any PIR protocol to a $1$-out-of-$n$ Oblivious Transfer protocol (also called SPIR).
-- There is a strong evidence that the assumption of the existence of a one-way function is necessary but not sufficient for any non-trivial PIR implementation.
comment: Appeared in Proceedings of Advances in Cryptology B. Preneel (ED.): EUROCRYPT 2000, LNCS 1807, pp. 122-138, 2000. Springer-Verlag.
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