  Verifying user attributes to provide fine-grained access control to databases
is fundamental to an attribute-based authentication system. In such systems,
either a single (central) authority verifies all attributes, or multiple
independent authorities verify individual attributes distributedly to allow a
user to access records stored on the servers. While a \emph{central} setup is
more communication cost efficient, it causes privacy breach of \emph{all} user
attributes to a central authority. Recently, Jafarpisheh et al. studied an
information theoretic formulation of the \emph{distributed} multi-authority
setup with $N$ non-colluding authorities, $N$ attributes and $K$ possible
values for each attribute, called an $(N,K)$ distributed attribute-based
private access control (DAPAC) system, where each server learns only one
attribute value that it verifies, and remains oblivious to the remaining $N-1$
attributes. We show that off-loading a subset of attributes to a central server
for verification improves the achievable rate from $\frac{1}{2K}$ in
Jafarpisheh et al. to $\frac{1}{K+1}$ in this paper, thus \emph{almost doubling
the rate} for relatively large $K$, while sacrificing the privacy of a few
possibly non-sensitive attributes.
