The recently proposed file-injection type attacks are highlighting the importance of forward security in dynamic searchable symmetric encryption (DSSE). Forward security enables to thwart those attacks by hiding the information about the newly added files matching a previous search query. However, there are still only a few DSSE schemes that provide forward security, and they have factors that hinder efficiency. In particular, all of these schemes do not support actual data deletion, which increments both storage space and computational complexity. In this paper, we design and implement a forward secure DSSE scheme with optimal search and update complexity, for both computation and communication point of view. As a starting point, we propose a new, simple, theoretical data structure, called dual dictionary that can take advantage of both the inverted and the forward indexes at the same time. This data structure allows to delete data explicitly and in real time, which greatly improves efficiency compared to previous works. In addition, our scheme provides forward security by encrypting the newly added data with fresh keys not related with the previous search tokens. We implemented our scheme for Enron email and Wikipedia datasets and measured its performance. The comparison with Sophos shows that our scheme is very efficient in practice, for both searches and updates in dynamic environments.