Private Set Intersection (PSI) is a cryptographic primitive that allows two network connected parties with hidden inputs to jointly compute the intersection of these inputs while keeping their specific inputs secret. PSI can be used as a building block for a variety of applications, most notably querying a remote relational database without revealing the query or the database. Many constructions of PSI exist, each building off of a subset of an assortment of cryptographic primitives such as: oblivious transfer, hash functions, garbled circuits, public key encryption and signature schemes, and basic number theoretic hardness assumptions. In this dissertation, we study variations of PSI and their practicality to modern day applications. Specifically, we study new security constraints for PSI that arise from applications such as genomics, consumer applications, and inter-agency information sharing. These constraints lead to several novel secure computation protocols. Through actualized prototypes of these schemes we conclude that, specialized PSI protocols are fast enough for use today, even on resource constrained hardware
