### Finding One Common Item, Privately

##### Abstract

Private set intersection (PSI) allows two parties, who each hold a set of items, to learn which items they have in common, without revealing anything about their other items. Some applications of PSI would be better served by revealing only one common item, rather than the entire set of all common items. In this work we develop simple special-purpose protocols for privately finding one common item (FOCI) from the intersection of two sets. The protocols differ in how that item is chosen --- e.g., uniformly at random from the intersection; the "best" item in the intersection according to one party's ranking; or the "best" item in the intersection according to the sum of both party's scores. All of our protocols are proven secure against semi-honest adversaries, under the Decisional Diffie-Hellman (DDH) assumption and assuming a random oracle. All of our protocols leak a small amount of information (e.g., the cardinality of the intersection), which we precisely quantify.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. SCN 2022
Keywords
private set intersection
Contact author(s)
trb4137 @ truman edu
janabel @ mit edu
rosulekm @ eecs oregonstate edu
History
2022-07-04: revised
See all versions
Short URL
https://ia.cr/2022/573

CC BY

BibTeX

@misc{cryptoeprint:2022/573,
author = {Tyler Beauregard and Janabel Xia and Mike Rosulek},
title = {Finding One Common Item, Privately},
howpublished = {Cryptology ePrint Archive, Paper 2022/573},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/573}},
url = {https://eprint.iacr.org/2022/573}
}

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