## CryptoDB

#### Publications

Year
Venue
Title
2020
EUROCRYPT
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.

#### Coauthors

Pasin Manurangsi (1)
Rasmus Pagh (1)
Ameya Velingker (1)