  This paper considers the secretive coded caching problem with shared caches
in which no user must have access to the files that it did not demand. In a
shared cache network, the users are served by a smaller number of helper caches
and each user is connected to exactly one helper cache. To ensure the secrecy
constraint in shared cache networks, each user is required to have an
individual cache of at least unit file size. For this setting, a secretive
coded caching scheme was proposed recently in the literature
(\enquote{Secretive Coded Caching with Shared Caches}, in \textit{IEEE
Communications Letters}, 2021), and it requires a subpacketization level which
is in the exponential order of the number of helper caches. By utilizing the
PDA constructions, we propose a procedure to obtain new secretive coded caching
schemes for shared caches with reduced subpacketization levels. We also show
that the existing secretive coded caching scheme for shared caches can be
recovered using our procedure. Furthermore, we derive a lower bound on the
secretive transmission rate using cut-set arguments and demonstrate the
order-optimality of the proposed secretive coded caching scheme.
