More Efficient, Privacy-Enhanced, and Powerful Privacy-Preserving Feature Retrieval Private Set Intersection

Private Set Intersection (PSI) allows two parties, the sender and the receiver, each possessing a private set, to compute the intersection of their sets, with only the receiver learning the intersection and without revealing any additional information. Privacy-Preserving Feature Retrieval PSI ( $\mathsf {P^{2}FRPSI}$ ) is a variant of PSI. In $\mathsf {P^{2}FRPSI}$ , the receiver designs a predicate and obtains the intersection of private sets that satisfy this predicate, while the sender learns nothing about the predicate. However, the existing two $\textsf {PRFPSI}$ protocols ( $\textsf {TIFS 2024}$ ), based respectively on the DH key agreement and Oblivious Pseudo-Random Function (OPRF), are not highly efficient due to their reliance on expensive homomorphic encryption. Moreover, the existing DH-based $\mathsf {P^{2}FRPSI}$ protocol reveals the output size and the original intersection size to the sender. We also observed that the existing $\mathsf {P^{2}FRPSI}$ protocols do not support threshold retrieval and the logical connective $\textsf {OR}$ and can only work when feature values of the sender have very low dimensionality. This paper also proposes two new $\mathsf {P^{2}FRPSI}$ protocols, one based on DH key agreement and the other based on OPRF, to fully address the issues present in existing $\mathsf {P^{2}FRPSI}$ protocols. Our DH-based $\mathsf {P^{2}FRPSI}$ is $30 \times $ faster than the existing DH-based protocol, with only a 36% increase in communication overhead. Furthermore, our OPRF-based $\mathsf {P^{2}FRPSI}$ protocol is $2 \times $ as fast as existing OPRF-based protocol and reduces communication overhead by a factor of 4.6. Our DH-based $\mathsf {P^{2}FRPSI}$ protocol completely eliminates the leakage of the original intersection size and the output size. Meanwhile, our protocols support the logical connective $\textsf {OR}$ for linking sub-predicates and also enable threshold-based retrieval. They are proven to be secure in the semi-honest model. Our open-source implementations can be found at https://github.com/ShallMate/pfrpsi, which can help readers understand our protocols and reproduce the experiments.