Efficient Verifiable Cloud-Assisted PSI Cardinality for Privacy-Preserving Contact Tracing

Private set intersection cardinality (PSI-CA) allows two parties to learn the size of the intersection between two private sets without revealing other additional information, which is a promising technique to solve privacy concerns in contact tracing. Efficient PSI protocols typically use oblivious transfer, involving multiple rounds of interaction and leading to heavy local computation overheads and protocol delays, especially when interacting with many receivers. Cloud-assisted PSI-CA is a better solution as it relieves participants' burdens of computation and communication. However, cloud servers may return incorrect or incomplete results for some reason, leading to an incorrectness issue. At present, to our knowledge, existing cloud-assisted PSI-CA protocols cannot address such a concern. To address this, we propose two specific verifiable cloud-assisted PSI-CA protocols: one based on a two-server protocol and the other on a single-server protocol. Further, we employ Cuckoo hashing to optimize these two protocols, enabling the receiver's computational costs independent of the size of the sender's set. We also prove the security of the protocols and implement them. Finally, we analyze and discuss their performance demonstrating that the single-server verifiable PSI-CA protocol does not introduce significant computation or communication costs while adding functionalities.