  Coded caching is a technique where we utilize multi-casting opportunities to
reduce rate in cached networks. One limitation of coded caching schemes is that
they reveal the demands of all users to their peers. In this work, we consider
coded caching schemes that assure privacy for user demands with a particular
focus on reducing subpacketization. For the 2-user, 2-file case, we present a
new linear demand-private scheme with the lowest possible subpacketization.
This is done by presenting the scheme explicitly and proving impossibility
results under lower subpacketization. Additionally, when only partial privacy
is required, we show that subpacketization can be significantly reduced when
there are a large number of files.
