On the Capacity of Private Nonlinear Computation for Replicated Databases

Sarah A. Obead, Hsuan Yin Lin, Eirik Rosnes, Jorg Kliewer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publication2019 IEEE Information Theory Workshop, ITW 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538669006
DOIs
StatePublished - Aug 2019
Event2019 IEEE Information Theory Workshop, ITW 2019 - Visby, Sweden
Duration: Aug 25 2019Aug 28 2019

Publication series

Name2019 IEEE Information Theory Workshop, ITW 2019

Conference

Conference2019 IEEE Information Theory Workshop, ITW 2019
Country/TerritorySweden
CityVisby
Period8/25/198/28/19

All Science Journal Classification (ASJC) codes

  • Software
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Information Systems

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