  Secure computation protocols combine inputs from involved parties to generate
an output while keeping their inputs private. Private Set Intersection (PSI) is
a secure computation protocol that allows two parties, who each hold a set of
items, to learn the intersection of their sets without revealing anything else
about the items. Private Intersection Sum (PIS) extends PSI when the two
parties want to learn the cardinality of the intersection, as well as the sum
of the associated integer values for each identifier in the intersection, but
nothing more. Finally, Private Join and Compute (PJC) is a scalable extension
of PIS protocol to help organizations work together with confidential data
sets. The extensions proposed in this paper include: (a) extending PJC protocol
to additional data columns and applying columnar aggregation based on supported
homomorphic operations, (b) exploring Ring Learning with Errors (RLWE)
homomorphic encryption schemes to apply arithmetic operations such as sum and
sum of squares, (c) ensuring stronger security using mutual authentication of
communicating parties using certificates, and (d) developing a Website to
operationalize such a service offering. We applied our results to develop a
Proof-of-Concept solution called JingBing, a voter list validation service that
allows different states to register, acquire secure communication modules,
install it, and then conduct authenticated peer-to-peer communication. We
conclude our paper with directions for future research to make such a solution
scalable for practical real-life scenarios.
