Verifiable Cloud-Assisted Multi-Party Private Set Intersection Cardinality

Abstract

Private Set Intersection Cardinality (PSI-CA) is a privacy-preserving method designed to compute the size of the intersection between two or more sets without revealing any additional information. In scenarios that require extensive computational resources, outsourcing tasks to cloud servers has emerged as a common solution. Nevertheless, the malicious behavior of cloud servers may lead to incorrect results and pose challenges for clients when verifying correctness. First, for clients with limited computational capabilities, a cloud-assisted multi-party PSI-CA (CMPSI-CA) is introduced, which stores the elements generated by the pseudorandom function generator in a Bloom filter and masks them using the Oblivious Distributed Key PRF (Odk-PRF). Furthermore, to protect against possible malicious behavior of cloud servers, the verifiable cloud-assisted multi-party PSI-CA (VCMPSI-CA) is proposed, leveraging the dual functions with the XOR homomorphic property. When the set size is $2^{18}$ and there are 32 participants, both protocols can be completed in 23.99 and 58.62 s, respectively.