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arXiv · 2307.01772

On the Capacity of Private Nonlinear Computation for Replicated Databases

Sarah A. Obead·Hsuan-Yin Lin·Eirik Rosnes·Jörg Kliewer
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Abstract

We consider the problem of private computation (PC) in a distributed storage system. In such a setting a user wishes to compute a function of $f$ messages replicated across $n$ noncolluding databases, while revealing no information about the desired function to the databases. We provide an information-theoretically accurate achievable PC rate, which is the ratio of the smallest desired amount of information and the total amount of downloaded information, for the scenario of nonlinear computation. For a large message size the rate equals the PC capacity, i.e., the maximum achievable PC rate, when the candidate functions are the $f$ independent messages and one arbitrary nonlinear function of these. When the number of messages grows, the PC rate approaches an outer bound on the PC capacity. As a special case, we consider private monomial computation (PMC) and numerically compare the achievable PMC rate to the outer bound for a finite number of messages.

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Sarah A. Obead, Hsuan-Yin Lin, Eirik Rosnes, Jörg Kliewer. 2023-07-04. On the Capacity of Private Nonlinear Computation for Replicated Databases. https://doi.org/10.1109/itw44776.2019.8989267

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