Private Linear Transformation: The Joint Privacy Case
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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.
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