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• W3194565985 abstract "This paper focuses on the Private Linear Transformation (PLT) problem in the multi-server scenario. In this problem, there are $N$ servers, each of which stores an identical copy of a database consisting of $K$ independent messages, and there is a user who wishes to compute $L$ independent linear combinations of a subset of $D$ messages in the database while leaking no information to the servers about the identity of the entire set of these $D$ messages required for the computation. We focus on the setting in which the coefficient matrix of the desired $L$ linear combinations generates a Maximum Distance Separable (MDS) code. We characterize the capacity of the PLT problem, defined as the supremum of all achievable download rates, for all parameters $N, K, D geq 1$ and $L=1$, i.e., when the user wishes to compute one linear combination of $D$ messages. Moreover, we establish an upper bound on the capacity of PLT problem for all parameters $N, K, D, L geq 1$, and leveraging some known capacity results, we show the tightness of this bound in the following regimes: (i) the case when there is a single server (i.e., $N=1$), (ii) the case when $L=1$, and (iii) the case when $L=D$." @default.
• W3194565985 created "2021-08-30" @default.
• W3194565985 creator A5051956168 @default.
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• W3194565985 date "2021-08-22" @default.
• W3194565985 modified "2023-09-27" @default.
• W3194565985 title "Multi-Server Private Linear Transformation with Joint Privacy" @default.
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