On the Security of OPSI: A Delegated Private Set Intersection on Outsourced Datasets

In recent years, determining the common information privately and efficiently between two mutually mistrusting parties have become an important issue in social networks. Many Private Set Intersection (PSI) protocols have been introduced to address this issue. By applying these protocols, two parties can compute the intersection between their sets without disclosing any information about components that are not in the intersection. Due to the broad range of computational resources that the cloud can provide for its users, determining the set intersection by cloud may decrease the computational cost of the users. The proposed protocols by Abadi et al. are two protocols in this context. In this paper, we show that their protocols are vulnerable to eavesdropping attack. Also, a solution is proposed to secure the protocol against mentioned attack. Moreover, we analyze the performance of both O-PSI and modified O-PSI protocols and show that our scheme is comparable with the O-PSI protocol. Actually, one trivial solution for the Abadi et al.’s proposed schemes is to use a secure channel like TLS. However, in the performance evaluation, we compare our applied modification with this trivial solution, and show that our proposed modification is more efficient as some extra encryptions imposed by TLS are no longer required.