Searchable encryption allows one to store encrypted documents on a remote honest-but-curious server, and query that data at the server itself without requiring the documents to be decrypted prior to searching. This not only protects the data from the prying eyes of the server, but can also reduce the communication overhead between the server and the user and local processing at the latter. Previous research in searchable encryption have investigated exact match search on keywords and boolean expression search on keywords. In this work, we first propose a novel secure and efficient multi-keyword similarity searchable encryption (MKSim) that returns the matching data items in a ranked order manner. Unlike many existing schemes, our search complexity is sublinear to the total number of documents that contain the queried set of keywords. Our theoretical analysis demonstrates that the proposed scheme is provably secure against adaptive chosen-keyword attacks, the strongest form of security sought in searchable encryption. Next, we develop a proof-of-concept prototype that we use for experimentation on a large-scale real-world dataset and evaluate the efficiency and scalability of our solution. Finally, we extend the MKSim protocol to the multi-user setting in which the data owner wishes to provide selective access to his encrypted document corpus to more than one user.