A stochastic approach in private information retrieval

We propose a novel scheme that achieves the capacity of the PIR, which is the maximum number of bits of the desired messages that can be privately retrieved by a single bit information download from the databases. The proposed scheme is based on the stochastic approach, where the queries are generated randomly and the downloading information is the random linear combinations of the message bits. Consequently, we claim that one-shot query generation, based on the stochastic approach, can guarantee the privacy of the user and the correctness of the retrieved information while achieving the capacity, when the number of answering bits are sufficiently large.