Paper 2019/175
The Communication Complexity of Threshold Private Set Intersection
Satrajit Ghosh and Mark Simkin
Abstract
Threshold private set intersection enables Alice and Bob who hold sets $A$ and $B$ of size $n$ to compute the intersection $A \cap B$ if the sets do not differ by more than some threshold parameter $t$. In this work, we investigate the communication complexity of this problem and we establish the first upper and lower bounds. We show that any protocol has to have a communication complexity of $\Omega(t)$. We show that an almost matching upper bound of $\tilde{\mathcal{O}}(t)$ can be obtained via fully homomorphic encryption. We present a computationally more efficient protocol based on weaker assumptions, namely additively homomorphic encryption, with a communication complexity of $\tilde{\mathcal{O}}(t^2)$. We show how our protocols can be extended to the multiparty setting. For applications like biometric authentication, where a given fingerprint has to have a large intersection with a fingerprint from a database, our protocols may result in significant communication savings. We, furthermore, show how to extend all of our protocols to the multiparty setting. Prior to this work, all previous protocols had a communication complexity of $\Omega(n)$. Our protocols are the first ones with communication complexities that mainly depend on the threshold parameter $t$ and only logarithmically on the set size $n$.
Note: Minor issue fixed.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- A minor revision of an IACR publication in CRYPTO 2019
- Keywords
- Communication ComplexityPrivate Set IntersectionMultiparty
- Contact author(s)
-
satrajit @ cs au dk
simkin @ cs au dk - History
- 2020-05-27: last of 7 revisions
- 2019-02-26: received
- See all versions
- Short URL
- https://ia.cr/2019/175
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/175, author = {Satrajit Ghosh and Mark Simkin}, title = {The Communication Complexity of Threshold Private Set Intersection}, howpublished = {Cryptology {ePrint} Archive, Paper 2019/175}, year = {2019}, url = {https://eprint.iacr.org/2019/175} }