Private information retrieval

In cryptography, a private information retrieval (PIR) protocol is a protocol that allows a user to retrieve an item from a server in possession of a database without revealing which item is retrieved. PIR is a weaker version of 1-out-of-n oblivious transfer, where it is also required that the user should not get information about other database items.

One trivial, but very inefficient way to achieve PIR is for the server to send an entire copy of the database to the user. In fact, this is the only possible protocol (in the classical or the quantum setting^[1]) that gives the user information theoretic privacy for their query in a single-server setting.^[2] There are two ways to address this problem: make the server computationally bounded or assume that there are multiple non-cooperating servers, each having a copy of the database.

The problem was introduced in 1995 by Chor, Goldreich, Kushilevitz and Sudan^[2] in the information-theoretic setting and in 1997 by Kushilevitz and Ostrovsky in the computational setting.^[3] Since then, very efficient solutions have been discovered. Single database (computationally private) PIR can be achieved with constant (amortized) communication and k-database (information theoretic) PIR can be done with ${\displaystyle n^{O\left({\frac {\log \log k}{k\log k}}\right)}}$ communication.