Secure computation of equivalence has fundamental application in many different areas, including health-care. We study this problem in the context of matching an individual's identity to link medical records across systems under the socialist millionaires' problem: Two millionaires wish to determine if their fortunes are equal without disclosing their net worth (Boudot, et al. 2001). In Theorem 2, we show that when a "greater than" algorithm is carried out on a totally ordered set it is easy to achieve secure matching without additional rounds of communication. We present this efficient solution to assess equivalence using a set intersection algorithm designed for "greater than" computation and demonstrate its effectiveness on equivalence of arbitrary data values, as well as demonstrate how it meets regulatory criteria for risk of disclosure.
Keywords: Encrypted data; Record linkage; Secure computation; Set intersection; Socialist millionaires’ problem.