Subgraph query (via subgraph isomorphism) is a fundamental and powerful query in various real graph applications. It has actively been investigated for performance enhancements recently. However, due to the high complexity of subgraph query, hosting efficient subgraph query services has been a technically challenging task, because the owners of graph data may not always possess the IT expertise to offer such services and hence may outsource to query service providers (SP). SPs are often equipped with high performance computing utilities (e.g., a cloud) that offer better scalability, elasticity and IT management. Unfortunately, as SPs may not always be trusted, security (such as the confidentiality of messages exchanged) has been recognized as one of the critical attributes of Quality of Services (QoS) . This influences the willingness of both data owners and query clients to use SP's services. Recently, there is a bloom on the research on query processing with privacy preservation1, e.g., in the context of relational databases, spatial databases and graph databases. However, up to date, private subgraph query has not yet been studied.