2022-01-01T19:27
We consider distributed private data analysis, where n parties each holding some sensitive data wish to compute some aggregate statistics over all parties’ data. We prove a tight lower bound for the private distributed summation problem. Our lower bound is strictly stronger than the prior lower-bound result by Beimel, Nissim, and Omri published in CRYPTO 2008. In particular, we show that any n-party protocol computing the sum with sparse communication graph must incur an additive error of \documentclass[12pt]{minimal}
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\begin{document}$\Omega(\sqrt{n})$\end{document} with constant probability, in order to defend against potential coalitions of compromised users. Furthermore, we show that in the client-server communication model, where all users communicate solely with an untrusted server, the additive error must be \documentclass[12pt]{minimal}
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\begin{document}$\Omega(\sqrt{n})$\end{document}, regardless of the number of messages or rounds. Both of our lower-bounds, for the general setting and the client-to-server communication model, are strictly stronger than those of Beimel, Nissim and Omri, since we remove the assumption on the number of rounds (and also the number of messages in the client-to-server communication model). Our lower bounds generalize to the (ε, δ) differential privacy notion, for reasonably small values of δ.
aggregate statistics
differential privacy notion
Beimel
sensitive data wish
data wish
277-288
2012-01-01
summation problem
communication graph
aggregation
additive error
optimal lower bounds
analysis
Multi-party Aggregation
order
data
assumption
en
values
probability
true
OMRI
https://doi.org/10.1007/978-3-642-33090-2_25
lower bounds
sum
messages
server
parties
constant probability
untrusted server
2012
CRYPTO 2008
sparse communication graph
statistics
privacy notion
coalition
error
rounds
private data analysis
bounds
potential coalitions
general setting
chapters
https://scigraph.springernature.com/explorer/license/
number of rounds
small values
model
number of messages
Nissim
chapter
data analysis
protocol
server communication model
Private Multi-party Aggregation
notion
party protocol
wishes
setting
Optimal Lower Bound for Differentially Private Multi-party Aggregation
number
users
results
communication model
client-server communication model
graph
clients
problem
Springer Nature - SN SciGraph project
Song
Dawn
doi
10.1007/978-3-642-33090-2_25
Elaine
Shi
Chan
T-H. Hubert
dimensions_id
pub.1012086337
Algorithms – ESA 2012
978-3-642-33089-6
978-3-642-33090-2
Data Format
University of Maryland, College Park, USA
University of Maryland, College Park, USA
Information and Computing Sciences
Epstein
Leah
UC Berkeley, USA
UC Berkeley, USA
The University of Hong Kong, Hong Kong
The University of Hong Kong, Hong Kong
Ferragina
Paolo
Springer Nature