  We introduce the problem of Private Linear Transformation (PLT). This problem
includes a single (or multiple) remote server(s) storing (identical copies of)
$K$ messages and a user who wants to compute $L$ linear combinations of a
$D$-subset of these messages by downloading the minimum amount of information
from the server(s) while protecting the privacy of the entire set of $D$
messages. This problem generalizes the Private Information Retrieval and
Private Linear Computation problems. In this work, we focus on the
single-server case. For the setting in which the coefficient matrix of the
required $L$ linear combinations generates a Maximum Distance Separable (MDS)
code, we characterize the capacity -- defined as the supremum of all achievable
download rates, for all parameters $K, D, L$. In addition, we present lower
and/or upper bounds on the capacity for the settings with non-MDS coefficient
matrices and the settings with a prior side information.
