On the Capacity of Private Nonlinear Computation for Replicated Databases
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 messages replicated across 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 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.
Cite
@article{arxiv.2307.01772,
title = {On the Capacity of Private Nonlinear Computation for Replicated Databases},
author = {Sarah A. Obead and Hsuan-Yin Lin and Eirik Rosnes and Jörg Kliewer},
journal= {arXiv preprint arXiv:2307.01772},
year = {2023}
}
Comments
5 pages, 1 figure, 1 table. Presented at the 2019 IEEE Information Theory Workshop (ITW). Figure 1 is updated as it contained incorrect data-points for $f=2$ and $g=3$. arXiv admin note: text overlap with arXiv:2003.10007