The data security and privacy of enrolled subjects is a critical requirement expected from biometric systems. This paper addresses said topic in facial biometric identification. In order to fulfil the properties of unlinkability, irreversibility, and renewability of the templates required for biometric template protection schemes, homomorphic encryption is utilised. In addition to achieving the aforementioned objectives, the use of homomorphic encryption ensures that the biometric performance remains completely unaffected by the template protection scheme. The main contributions of this paper are: It proposes an architecture of a system capable of performing biometric identification in the encrypted domain, as well as provides and evaluates an implementation using two existing homomorphic encryption schemes. Furthermore, it discusses the pertinent technical considerations and challenges in this context.