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.

翻译：安全计算协议通过整合各参与方的输入生成输出，同时保护其输入隐私。私有集交集（PSI）是一种安全计算协议，允许持有各自数据集的两方在不泄露其他信息的前提下，获知双方集合的交集。私有交集和（PIS）扩展了PSI功能，使双方不仅能获知交集基数，还能计算交集中每个标识符关联整数值的总和，且不泄露其他信息。最后，私有连接与计算（PJC）作为PIS协议的可扩展扩展，可帮助组织协作处理机密数据集。本文提出的扩展包括：(a) 将PJC协议扩展至多数据列，并基于支持的同态操作实现列聚合；(b) 探索基于环上带误差学习（RLWE）的同态加密方案，以执行求和及平方和等算术运算；(c) 通过使用证书实现通信双方的相互认证，增强安全性；(d) 开发实现此类服务的运营网站。我们基于研究成果开发了名为"静兵"的概念验证解决方案——选民名单验证服务，允许各州进行注册、获取安全通信模块、安装并完成认证的点对点通信。文章最后提出了未来研究方向，以使此类解决方案在现实场景中具备可扩展性。