We study the case of searching over encrypted data from a remote server. In order to retrieve the encrypted documents that satisfy a client's criteria, a special index must be built and sent by the client together with encrypted documents. A trapdoor will also be produced to offer the privilege to search on the index. In the area of searchable encryption, many works mainly focused on search criteria consisting of a single keyword or conjunctive keywords. Up until now, searching of the exact documents that contain a phrase, or consecutive keywords still remains an unsolved problem. We first define the model of phrase search over encrypted data with symmetric encryption and its security definition based on the latest security definition raised by R. Curtmola. Then we propose a construction for phrase search with symmetric encryption (PSSE), which meets the functionality of searching a phrase over encrypted documents securely and efficiently. The computing complexity of our scheme when performing a query is linear in the size of the phrase, and at a moderate communication cost between server and client as well. In addition, we prove that our scheme achieves non-adaptive security.
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