Efficient and Practical Multi-party Private Set Intersection Cardinality Protocol

We present an efficient and simple multi-party private set intersection cardinality (PSI-CA) protocol that allows several parties to learn the intersection size of their private sets without revealing any other information. Our protocol is highly efficient because it only utilizes the Oblivious Key-Value Store and zero-sharing techniques, without incorporating components such as OPPRF (Oblivious Programmable Pseudorandom Function) which is the main building block of multi-party PSI-CA protocol by Gao et al. (PoPETs 2024). Our protocol exhibits better communication and computational overhead than the state-ofthe-art. To compute the intersection between 16 parties with a set size of 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> each, our PSI-CA protocol only takes 5.84 seconds and 326.6 MiB of total communication, which yields a reduction in communication by a factor of up to 2.4× compared to the state-of-the-art multi-party PSI-CA protocol of Gao et al. (PoPETs 2024). We prove that our protocol is secure in the presence of a semi-honest adversary who may passively corrupt any (t−2)-out-of-t parties once two specific participants are non-colluding.