Kushilevitz,“General constructions for information-theoretic private information retrieval

Abstract A Private Information Retrieval (PIR) protocol enables a user to retrieve a data item from a database while hiding the identity of the item being retrieved; specifically, in a t-private k-server PIR protocol the database is replicated among k servers, and the user's privacy is protected from any collusion of up to t servers. The main costmeasure of such protocols is the communication complexity of retrieving a single bit of data. This work addresses the information-theoretic setting for PIR, where the user's privacy should be unconditionally protected against computationally unbounded servers. We present a general construction, whose abstract components can be instantiated to yield both old and new families of PIR protocols. A main ingredient in the new protocols is a generalization of a solution by Babai, G'al, Kimmel, and Lokam for a communication complexity problem in the multiparty simultaneous messages model