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Enterprises outsourcing their databases to the cloud and authorizing multiple users for access represents a typical use scenario of cloud storage services. In such a case of database outsourcing, data encryption is a good approach enabling the data owner to retain its control over the outsourced data. Searchable encryption is a cryptographic primitive allowing for private keyword based search over the encrypted database. The above setting of enterprise outsourcing database to the cloud requires multi-user searchable encryption, whereas virtually all of the existing schemes consider the single-user setting. To bridge this gap, we are motivated to propose a practical multi-user searchable encryption scheme, which has a number of advantages over the known approaches. The associated model and security requirements are also formulated. We further discuss to extend our scheme in several ways so as to achieve different search capabilities.