Private Set Intersection and other Set Operations in the Third Party Setting

We present a collection of protocols to perform privacy-preserving set operations in the third-party private set intersection (PSI) setting. This includes several protocols for multi-party third party PSI. In this model, there are multiple input parties (or clients) each holding a private set of elements and the receiver is an external party (termed as third-party) with no inputs. Multi-party third party PSI enables the receiver to learn only the intersection result of all input clients' private sets while revealing nothing else to the clients and the receiver. Our solutions include constructions that are provably secure against an arbitrary number of colluding parties in the semi-honest model. Additionally, we present protocols for third-party private set difference and private symmetric difference, whereby the learned output by the inputless third-party is the set difference and symmetric difference respectively of two other input parties, while preserving the same privacy guarantees. The motivation in the design of these protocols stems from their utilities in numerous real-world applications. We implemented our protocols and conducted experiments across various input and output set sizes.