On the Capacity of Private Nonlinear Computation for Replicated Databases

Document Type

Conference Proceeding

Publication Date

8-1-2019

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.

Identifier

85081109977 (Scopus)

ISBN

[9781538669006]

Publication Title

2019 IEEE Information Theory Workshop Itw 2019

External Full Text Location

https://doi.org/10.1109/ITW44776.2019.8989267

Grant

CNS-1526547

Fund Ref

National Science Foundation

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