EO-PSI-CA: Efficient outsourced private set intersection cardinality

Private set intersection cardinality (PSI-CA) is a useful cryptographic primitive for many data analysis techniques, e.g. in genomic computations and data mining. In the last few years, several classical multi-party PSI-CA protocols have been designed where parties jointly compute the PSI-CA and at the end of the protocol none of them learns more than their private input sets and the output. The computation complexity of these multi-party protocols is quadratic in the size of the input sets and linear in the number of the parties involved in the protocol. In addition, the communication complexity scales quadratically as the number of parties increases. With the advent of cloud computing, it is now necessary to gain the benefits of the computation and storage capabilities of the cloud for outsourcing private input sets and PSI-CA computation. For the first time, in this paper, we design an efficient outsourced private set intersection cardinality named EO-PSI-CA in the multi-party setting. This protocol computes PSI-CA by employing the Bloom filter (BF) technique and the exponential ElGamal cryptosystem over encrypted Bloom filters. In our protocol, two or more parties outsource their private input sets to the cloud and finally one of the parties requests the EO-PSI-CA value. Due to the use of Bloom filter, the size of the parties’ sets is independent of each other, and the computational and communication complexity of each party is independent of the total number of parties. We formally prove the security of our protocol in the semi-honest adversarial model and we claim that our scheme addresses the intersection size hiding. On a more positive note, our EO-PSI-CA is the first in its kind with linear complexity supporting outsourcing in a multi-party setting.