Computer Science > Cryptography and Security
[Submitted on 20 Jun 2019 (v1), last revised 21 Aug 2019 (this version, v3)]
Title:Differentially Private Summation with Multi-Message Shuffling
View PDFAbstract:In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for $n$-party real summation in the shuffle model of differential privacy with $O_{\epsilon, \delta}(1)$ error and $\Theta(\epsilon\sqrt{n})$ one-bit messages per party. In contrast, every local model protocol for real summation must incur error $\Omega(1/\sqrt{n})$, and there exist protocols matching this lower bound which require just one bit of communication per party. Whether this gap in number of messages is necessary was left open by Cheu et al.
In this note we show a protocol with $O(1/\epsilon)$ error and $O(\log(n/\delta))$ messages of size $O(\log(n))$ per party. This protocol is based on the work of Ishai et al.\ (FOCS 2006) showing how to implement distributed summation from secure shuffling, and the observation that this allows simulating the Laplace mechanism in the shuffle model.
Submission history
From: Adria Gascon [view email][v1] Thu, 20 Jun 2019 09:45:21 UTC (10 KB)
[v2] Mon, 24 Jun 2019 14:32:33 UTC (10 KB)
[v3] Wed, 21 Aug 2019 18:36:00 UTC (10 KB)
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