# Pure Differentially Private Summation from Anonymous Messages

@article{Ghazi2020PureDP,
title={Pure Differentially Private Summation from Anonymous Messages},
author={Badih Ghazi and Noah Golowich and Ravi Kumar and Pasin Manurangsi and R. Pagh and Ameya Velingker},
journal={ArXiv},
year={2020},
volume={abs/2002.01919}
}
• Published 1 February 2020
• Computer Science, Mathematics
• ArXiv
The shuffled (aka anonymous) model has recently generated significant interest as a candidate distributed privacy framework with trust assumptions better than the central model but with achievable errors smaller than the local model. We study pure differentially private (DP) protocols in the shuffled model for summation, a basic and widely used primitive: - For binary summation where each of n users holds a bit as an input, we give a pure $\epsilon$-DP protocol for estimating the number of…

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## References

SHOWING 1-10 OF 45 REFERENCES
On the Power of Multiple Anonymous Messages
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2019
A nearly tight lower bound on the error of locally-private frequency estimation in the low-privacy (aka high $\epsilon$) regime is obtained and implies that the protocols obtained from the amplification via shuffling work of Erlingsson et al. are essentially optimal for single-message protocols.
Differentially Private Summation with Multi-Message Shuffling
• Computer Science, Mathematics
ArXiv
• 2019
This note shows a protocol with O(1/\epsilon)$error and$O(\log(n/\delta)$messages of size$O(n)$per party, based on the work of Ishai et al.\ (FOCS 2006) showing how to implement distributed summation from secure shuffling. Distributed Differential Privacy via Shuffling • Computer Science, Mathematics IACR Cryptol. ePrint Arch. • 2019 Evidence that the power of the shuffled model lies strictly between those of the central and local models is given: for a natural restriction of the model, it is shown that shuffled protocols for a widely studied selection problem require exponentially higher sample complexity than do central-model protocols. Improved Summation from Shuffling • Computer Science ArXiv • 2019 Improved analysis achieving a dependency of the form$O(1+\sigma/\log n)$addresses the intuitive question left open by Ishai et al. of whether the shuffling step in their protocol provides a "hiding in the crowd" amplification effect as$n$increases. Optimal Lower Bound for Differentially Private Multi-party Aggregation • Computer Science, Mathematics ESA • 2012 It is shown that any n-party protocol computing the sum with sparse communication graph must incur an additive error of$\Omega(\sqrt{n})\$ with constant probability, in order to defend against potential coalitions of compromised users.
Local, Private, Efficient Protocols for Succinct Histograms
• Computer Science, Mathematics
STOC
• 2015
Efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy are given and it is shown that each user need only send 1 bit to the server in a model with public coins.
Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity
• Computer Science
SODA
• 2019
It is shown, via a new and general privacy amplification technique, that any permutation-invariant algorithm satisfying e-local differential privacy will satisfy [MATH HERE]-central differential privacy.
Scalable and Differentially Private Distributed Aggregation in the Shuffled Model
• Computer Science
ArXiv
• 2019
A simple and more efficient protocol for aggregation in the shuffled model, where communication as well as error increases only polylogarithmically in the number of users, is proposed.
Our Data, Ourselves: Privacy Via Distributed Noise Generation
• Computer Science
EUROCRYPT
• 2006
This work provides efficient distributed protocols for generating shares of random noise, secure against malicious participants, and introduces a technique for distributing shares of many unbiased coins with fewer executions of verifiable secret sharing than would be needed using previous approaches.
Heavy Hitters and the Structure of Local Privacy
• Computer Science, Mathematics
PODS
• 2018
We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work