Symmetric Searchable Encryption (SSE) allows users to outsource encrypted data to a possibly untrusted remote location while simultaneously being able to perform keyword search directly through the stored ciphertexts. An ideal SSE scheme should reveal no information about the content of the encrypted information nor about the searched keywords and their mapping to the stored files. However, most of the existing SSE schemes fail to fulfil this property since in every search query, some information potentially valuable to a malicious adversary is leaked. The leakage becomes even bigger if the underlying SSE scheme is dynamic. In this paper, we minimize the leaked information by proposing a forward and backward private SSE scheme in a multi-client setting. Our construction achieves optimal search and update costs. In contrast to many recent works, each search query only requires one round of interaction between a user and the cloud service provider. In order to guarantee the security and privacy of the scheme and support the multi-client model (i.e. synchronization between users), we exploit the functionality offered by AMD’s Secure Encrypted Virtualization (SEV).