Frequency Estimation in the Shuffle Model with Almost a Single Message. (arXiv:2111.06833v2 [cs.CR] UPDATED)

We present a protocol in the shuffle model of differential privacy (DP) for
the \textit{frequency estimation} problem that achieves error $\omega(1)\cdot
O(\log n)$, almost matching the central-DP accuracy, with $1+o(1)$ messages per
user. This exhibits a sharp transition phenomenon, as there is a lower bound of
$\Omega(n^{1/4})$ if each user is allowed to send only one message. Previously,
such a result is only known when the domain size $B$ is $o(n)$. For a large
domain, we also need an efficient …

message shuffle single