Attribute-based encryption enables data owners to share their information by specifying access control policies while outsourcing their encrypted data to the cloud. However, there are no efficient searchable schemes over encrypted data in attribute-based setting. In this paper, we propose a novel primitive called deterministic attribute-based encryption DABE, which simultaneously supports data sharing and retrieving in time logarithmic in the size of the database. We formalise the security properties for DABE with respect to auxiliary inputs. Furthermore, we propose a generic construction in the random oracle model and a selectively secure concrete key-policy DABE in the standard model under decisional bilinear Diffie-Hellman assumption.