In this paper, we introduce the imperfect shuffle differential privacy model, where messages sent from users are shuffled in an almost uniform manner before being observed by a curator for private aggregation. We then consider the private summation problem. We show that the standard split-and-mix protocol by Ishai et. al. [FOCS 2006] can be adapted to achieve near-optimal utility bounds in the imperfect shuffle model. Specifically, we show that surprisingly, there is no additional error overhead necessary in the imperfect shuffle model.
@article{arxiv.2308.14733,
title = {Differentially Private Aggregation via Imperfect Shuffling},
author = {Badih Ghazi and Ravi Kumar and Pasin Manurangsi and Jelani Nelson and Samson Zhou},
journal= {arXiv preprint arXiv:2308.14733},
year = {2023}
}