  We study a class of private information retrieval (PIR) methods that we call
one-shot schemes. The intuition behind one-shot schemes is the following. The
user's query is regarded as a dot product of a query vector and the message
vector (database) stored at multiple servers.
  Privacy, in an information theoretic sense, is then achieved by encrypting
the query vector using a secure linear code, such as secret sharing.
  Several PIR schemes in the literature, in addition to novel ones constructed
here, fall into this class. One-shot schemes provide an insightful link between
PIR and data security against eavesdropping. However, their download rate is
not optimal, i.e., they do not achieve the PIR capacity. Our main contribution
is two transformations of one-shot schemes, which we call refining and lifting.
We show that refining and lifting one-shot schemes gives capacity-achieving
schemes for the cases when the PIR capacity is known. In the other cases, when
the PIR capacity is still unknown, refining and lifting one-shot schemes gives
the best download rate so far.
