We introduce SCiFI, a system for Secure Computation of Face Identification. The system performs face identification which compares faces of subjects with a database of registered faces. The identification is done in a secure way which protects both the privacy of the subjects and the confidentiality of the database. A specific application of SCiFI is reducing the privacy impact of camera based surveillance. In that scenario, SCiFI would be used in a setting which contains a server which has a set of faces of suspects, and client machines which might be cameras acquiring images in public places. The system runs a secure computation of a face recognition algorithm, which identifies if an image acquired by a client matches one of the suspects, but otherwise reveals no information to neither of the parties. Our work includes multiple contributions in different areas: • A new face identification algorithm which is unique in having been specifically designed for usage in secure computation. Nonetheless, the algorithm has face recognition performance comparable to that of state of the art algorithms. We ran experiments which show the algorithm to be robust to different viewing conditions, such as illumination, occlusions, and changes in appearance (like wearing glasses). . A secure protocol for computing the new face recognition algorithm. In addition, since our goal is to run an actual system, considerable effort was made to optimize the protocol and minimize its online latency. . A system - SCiFI, which implements a secure computation of the face identification protocol. . Experiments which show that the entire system can run in near real-time: The secure computation protocol performs a preprocessing of all public-key cryptographic operations. Its online performance therefore mainly depends on the speed of data communication, and our experiments show it to be extremely efficient.