Cloud-Assisted Laconic Private Set Intersection Cardinality

Laconic Private Set Intersection (LPSI) is a type of PSI protocols characterized by the requirement of only two-round interactions and by having a reused message in the first round that is independent of the set size. Recently, Aranha et al. (CCS'2022) proposed a LPSI protocol that utilizes the pairing-based accumulator. However, this protocol heavily relies on time-consuming bilinear pairing operations, which can potentially cause a bottleneck. Furthermore, in certain scenarios like contact tracing, it is sufficient to only reveal the intersection cardinality. To tackle this problem and expand on its functionalities, we introduce a cloud-assisted two-party LPSI cardinality (TLPSI-CA) that inherits the properties of LPSI. Interestingly, the cloud-assisted TLPSI-CA eliminates the direct interaction between the sender and receiver, enabling the sender's message to be reused across any number of protocol executions. Besides, we further extend it to the multi-party scenario, which also possesses laconic properties. Then, we prove the two protocols' security in achieving the defined ideal functionalities. Finally, we evaluate the performance of both protocols and find that TLPSI-CA successfully reduces the local computation costs for participants. Additionally, the multi-party protocol performs similarly to TLPSI-CA, with the exception of the higher communication costs incurred by the receiver.