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Paper: Private Aggregation from Fewer Anonymous Messages

Authors:
Badih Ghazi , Google Research
Pasin Manurangsi , Google Research
Rasmus Pagh , Google Research and IT University of Copenhagen
Ameya Velingker , Google Research
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DOI: 10.1007/978-3-030-45724-2_27 (login may be required)
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Conference: EUROCRYPT 2020
Abstract: Consider the setup where $n$ parties are each given an element~$x_i$ in the finite field $\F_q$ and the goal is to compute the sum $\sum_i x_i$ in a secure fashion and with as little communication as possible. We study this problem in the \emph{anonymized model} of Ishai et al.~(FOCS 2006) where each party may broadcast anonymous messages on an insecure channel. We present a new analysis of the one-round ``split and mix'' protocol of Ishai et al. In order to achieve the same security parameter, our analysis reduces the required number of messages by a $\Theta(\log n)$ multiplicative factor. We also prove lower bounds showing that the dependence of the number of messages on the domain size, the number of parties, and the security parameter is essentially tight. Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an $\left(\varepsilon, \delta\right)$-differentially private protocol for aggregation that, for any constant $\varepsilon > 0$ and any $\delta = \frac{1}{\poly(n)}$, incurs only a constant error and requires only a \emph{constant number of messages} per party. Previously, such a protocol was known only for $\Omega(\log n)$ messages per party.
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BibTeX
@inproceedings{eurocrypt-2020-30191,
  title={Private Aggregation from Fewer Anonymous Messages},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  keywords={Secure Aggregation;Anonymous Channel;Shuffled Model;Differential Privacy},
  volume={12105},
  doi={10.1007/978-3-030-45724-2_27},
  author={Badih Ghazi and Pasin Manurangsi and Rasmus Pagh and Ameya Velingker},
  year=2020
}