Single-Server Private Linear Transformation: The Joint Privacy Case

This paper introduces the problem of Private Linear Transformation (PLT) which generalizes problems private information retrieval and linear computation. The PLT includes one or more remote server(s) storing (identical copies of) $K$ messages a user who wants to compute notation="LaTeX">$L$ independent combinations notation="LaTeX">$D$ -subset messages. objective is perform computation by downloading minimum possible amount from server(s), while protecting identities required for In this work, we focus on single-server setting when must be protected jointly. We consider two different models, depending whether coefficient matrix generates Maximum Distance Separable (MDS) code. prove that capacity both models given notation="LaTeX">$L/(K-D+L)$ , where defined as supremum all achievable download rates. Our converse proofs are based linear-algebraic information-theoretic arguments. For each model, also present an achievability scheme relies MDS codes.