Graph Algorithms over Homomorphic Encryption for Data Cooperatives

"Big data" continues to grow in influence with few competitors able to challenge them. In order to slow the growth of and eventually replace these "data silos", we must enable competition from alternative sources that respect users' privacy, such as data cooperatives. In our previous work, we proposed an architecture for a privacy-preserving data cooperative that relies on homomorphic encryption (HE) to ensure data privacy and demonstrated ring-based BFS, degree centrality, and farness centrality over HE graph data. In this paper we expand our suite of HE graph algorithms to include single-source shortest-path, all-pairs shortest-path, minimum spanning tree, harmonic centrality, random walk, and betweenness centrality over HE graph data. These graph analysis algorithms support the core service of a data cooperative: to provide data and insights (or aggregates) to the service of the cooperative's clients (researchers, companies, governments, etc.) while maintaining the privacy of their users.