Efficient and Collusion Resistant Multi-party Private Set Intersection Protocols for Large Participants and Small Sets Setting

Abstract

Multi-party private set intersection (MP-PSI) allows m participants with private sets to calculate their intersection without revealing any information, which is quite different from the traditional two-party PSI. Although some efficient MP-PSI protocols already exist, the efficiency of these protocols decreases significantly in the scenarios with the increasing number of participants for the small sets setting. In this paper, we propose efficient MP-PSI protocols based on one-round two-party key agreement embedding with unconditional zero sharing technique and prove secure by resisting up to $m-2$ parties collision in the semi-honest model and $m-1$ parties collision in the malicious model. Compared with the current efficient MP-PSI, our protocol performs better in terms of the communication round, communication cost and the running time in small sets setting. Extensive experiments show that as the number of participants m increases from 5 to 50 and the upbound of the set size n scales from $2^8$ to $2^{10}$, the running time of our MP-PSI protocol is faster than those of the most efficient MP-PSI protocol [14] and the recent work [4]. Take the set size at $2^{7}$ for example, as the number of the participants increases from 10 to 50, our protocol only requires 4–26$\times$ less running time and 8–11$\times$ less communication cost than those of [14], respectively. We conclude that our protocols are practical solutions suitable for the scenarios in small set setting with increasing participants.

This work is supported in part by National Natural Science Foundation of China under Grant 61972241, in part by Natural Science Foundation of Shanghai under Grant 22ZR1427100 and 18ZR1417300, and in part by Luo-Zhaorao College Student Science and Technology Innovation Foundation of Shanghai Ocean University.