Biometric cryptosystems such as fuzzy vaults represent one of the most popular approaches for secret and biometric template protection. However, they are solely designed for biometric verification, where the user is required to input both identity credentials and biometrics. Several practical questions related to the implementation of biometric cryptosystems remain open, especially in regard to biometric template protection. In this article, we propose a face cryptosystem for identification (FCI) in which only biometric input is needed. Our FCI is composed of a one-to-N search subsystem for template protection and a one-to-one match chaff-less fuzzy vault (CFV) subsystem for secret protection. The first subsystem stores N facial features, which are protected by index-of-maximum (IoM) hashing, enhanced by a fusion module for search accuracy. When a face image of the user is presented, the subsystem returns the top k matching scores and activates the corresponding vaults in the CFV subsystem. Then, one-to-one matching is applied to the k vaults based on the probe face, and the identifier or secret associated with the user is retrieved from the correct matched vault. We demonstrate that coupling between the IoM hashing and the CFV resolves several practical issues related to fuzzy vault schemes. The FCI system is evaluated on three large-scale public unconstrained face datasets (LFW, VGG2, and IJB-C) in terms of its accuracy, computation cost, template protection criteria, and security.