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.
@InProceedings{ghazi_et_al:LIPIcs.ITC.2023.17, author = {Ghazi, Badih and Kumar, Ravi and Manurangsi, Pasin and Nelson, Jelani and Zhou, Samson}, title = {{Differentially Private Aggregation via Imperfect Shuffling}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {17:1--17:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.17}, URN = {urn:nbn:de:0030-drops-183453}, doi = {10.4230/LIPIcs.ITC.2023.17}, annote = {Keywords: Differential privacy, private summation, shuffle model} }
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