  In this paper, we propose GraphSE$^2$, an encrypted graph database for online
social network services to address massive data breaches. GraphSE$^2$ preserves
the functionality of social search, a key enabler for quality social network
services, where social search queries are conducted on a large-scale social
graph and meanwhile perform set and computational operations on user-generated
contents. To enable efficient privacy-preserving social search, GraphSE$^2$
provides an encrypted structural data model to facilitate parallel and
encrypted graph data access. It is also designed to decompose complex social
search queries into atomic operations and realise them via interchangeable
protocols in a fast and scalable manner. We build GraphSE$^2$ with various
queries supported in the Facebook graph search engine and implement a
full-fledged prototype. Extensive evaluations on Azure Cloud demonstrate that
GraphSE$^2$ is practical for querying a social graph with a million of users.
