Private Linear Transformation: The Joint Privacy Case

In this paper, 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 that 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 for all parameters K, D, L, where the capacity is defined as the supremum of all achievable download rates. 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.