Existing private set intersection (PSI) protocol allows two parties to find intersection of their sets, but restricts learning any other information about each other's set except for its size. In general, the server-aided private set intersection with data transfer technique described herein provides a server-aided private set intersection (PSI) protocol that supports data transfers. The technique pertains to a method for providing a server-aided private set intersection protocol which allows two parties to transfer some of the information about their elements via an untrusted third party. The protocol involves (a) parties applying a shared pseudo-random permutation to each of their sets to create labels of the elements of the set, (b) sending the labels to the third party and (c) the third party performing data transfer between the two parties along with computation of intersection of sets received using a multi-share key.