  We present a private information retrieval (PIR) scheme that allows a user to
retrieve a single message from an arbitrary number of databases by colluding
with other users while hiding the desired message index. This scheme is of
particular significance when there is only one accessible database -- a special
case that turns out to be more challenging for PIR in the multi-database case.
The upper bound for privacy-preserving capacity for these scenarios is
$C=(1+\frac{1}{S}+\cdots+\frac{1}{S^{K-1}})^{-1}$, where $K$ is the number of
messages and $S$ represents the quantity of information sources such as
$S=N+U-1$ for $U$ users and $N$ databases. We show that the proposed
information retrieval scheme attains the capacity bound even when only one
database is present, which differs from most existing works that hinge on the
access to multiple databases in order to hide user privacy. Unlike the
multi-database case, this scheme capitalizes on the inability for a database to
cross-reference queries made by multiple users due to computational complexity.
