  The distributed coded caching problem has been studied extensively in the
recent past. While the known coded caching schemes achieve an improved
transmission rate, they violate the privacy of the users since in these schemes
the demand of one user is revealed to others in the delivery phase. In this
paper, we consider the coded caching problem under the constraint that the
demands of the other users remain information theoretically secret from each
user. We first show that the memory-rate pair $(M,\min \{N,K\}(1-M/N))$ is
achievable under information theoretic demand privacy, while using broadcast
transmissions. We then show that a demand-private scheme for $N$ files and $K$
users can be obtained from a non-private scheme that satisfies only a
restricted subset of demands of $NK$ users for $N$ files. We then focus on the
demand-private coded caching problem for $K=2$ users, $N=2$ files. We
characterize the exact memory-rate trade-off for this case. To show the
achievability, we use our first result to construct a demand-private scheme
from a non-private scheme satisfying a restricted demand subset that is known
from an earlier work by Tian. Further, by giving a converse based on the extra
requirement of privacy, we show that the obtained achievable region is the
exact memory-rate trade-off.
