**Multi-Party Privacy-Preserving Set Intersection with Quasi-Linear Complexity**

*Jung Hee Cheon and Stanislaw Jarecki and Jae Hong Seo*

**Abstract: **Secure computation of the set intersection functionality allows $n$
parties to find the intersection between their datasets without
revealing anything else about them. An efficient protocol for such
task could have multiple potential applications, in commerce,
health-care, and security. However, all currently known secure set
intersection protocols for $n>2$ parties have computational costs that
are quadratic in the (maximum) number of entries in the dataset
contributed by each party, rendering secure computation of set
intersection impractical on anything but small datasets.

In this paper we describe the first multi-party protocol for securely computing the set intersection functionality with both the communication and the computation costs that are quasi-linear in the size of the datasets. Specifically, our protocols require $O(n^2k\lambda)$ bits of communication and $\tilde{O}(n^2\lambda+(n\lambda+n^2)k)$ group multiplications per player in the malicious adversary setting, where $k$ is the size of each dataset and $\lambda$ is security parameter. Our protocol follows the basic idea of the protocol proposed by Kissner and Song, but we gain efficiency by using different representation of the polynomials associated with users' datasets, and careful employment of algorithms that interpolate or evaluate polynomials on multiple points more efficiently.

**Category / Keywords: **Privacy-preserving set operation, privacy-preserving set intersection

**Date: **received 6 Oct 2010, last revised 6 Oct 2010

**Contact author: **jhsbhs at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20101007:140646 (All versions of this report)

**Short URL: **ia.cr/2010/512

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