P²FRPSI: Privacy-Preserving Feature Retrieved Private Set Intersection.

Private Set Intersection (PSI) protocols can securely compute the intersection of the private sets on the server and the client without revealing additional data. This work introduces the concept of Privacy-Preserving Feature Retrieved Private Set Intersection ( $\mathsf {P^{2}FRPSI}$ ). In $\mathsf {P^{2}FRPSI}$ protocols, the client can obtain the intersection that satisfies a given predicate without revealing the predicate and additional data. We formally define the $\mathsf {P^{2}FRPSI}$ protocol, including its inputs, outputs, functionality, and security. To achieve the privacy guarantee in $\mathsf {P^{2}FRPSI}$ protocols, a new two-party protocol is designed, namely Secure Secret Shared Retrieval ( $\mathsf {S^{3}R}$ ), which can be used to securely determine whether each item on the server satisfies the predicate. We construct an $\mathsf {S^{3}R}$ protocol and prove its security in the semi-honest model. On the basis of this, we design an efficient OT-based $\mathsf {P^{2}FRPSI}$ protocol and an easy-to-implement DH-based $\mathsf {P^{2}FRPSI}$ protocol and prove that they are secure in the semi-honest model. Our implementation shows that the OT-based $\mathsf {P^{2}FRPSI}$ protocol can perform the matching for about 1000K items in 3.8 seconds with a single thread. Moreover, the DH-based $\mathsf {P^{2}FRPSI}$ can perform the matching for about 7000K items in one hour with four threads, with communication totaling 1456 MB, while the OT-based $\mathsf {P^{2}FRPSI}$ protocol requires 1673 MB.