Searchable symmetric encryption (SSE) enables clients to outsource their encrypted documents into a remote server and allows them to search the outsourced data efficiently without violating the privacy of the documents and search queries. Dynamic SSE schemes (DSSE) include performing update queries, where documents can be added or removed at the expense of leaking more information to the server. Two important privacy notions are addressed in DSSE schemes: forward and backward privacy. The first one prevents associating the newly added documents with previously issued search queries. While the second one ensures that the deleted documents cannot be linked with subsequent search queries. Backward has three formal types of leakage ordered from strong to weak security: Type-I, Type-II, and Type-III. In this paper, we propose a new DSSE scheme that achieves Type-II backward and forward privacy by generating fresh keys for each search query and preventing the server from learning the underlying operation (del or add) included in update query. Our scheme improves I/O performance and search cost. We implement our scheme and compare its efficiency against the most efficient backward privacy DSSE schemes in the literature of the same leakage: MITRA and MITRA*. Results show that our scheme outperforms the previous schemes in terms of efficiency in dynamic environments. In our experiments, the server takes 699ms to search and return (100,000) results.