We propose a similarity index that ensures data privacy and thus is suitable for search systems outsourced in a cloud. The proposed solution can exploit existing efficient metric indexes based on a fixed set of reference points. The method has been fully implemented as a security extension of an existing established approach called M-Index. This Encrypted M-Index supports evaluation of standard range and nearest neighbors queries both in precise and approximate manner. In the first part of this work, we analyze various levels of privacy in existing or future similarity search systems; the proposed solution tries to keep a reasonable privacy level while relocating only the necessary amount of work from server to an authorized client. The Encrypted M-Index has been tested on three real data sets with focus on various cost components.