Face recognition technology has demonstrated tremendous progress over the past few years, thanks to advances in representation learning. As we witness the widespread adoption of these systems, it is imperative to consider the security of face representations. In this paper, we propose a data encryption based framework to secure databases of face representations, with the goal of preventing information leakage and preserving the privacy of users, while maintaining it’s utility. Specifically, we explore the possibility of using a fully homomorphic encryption based scheme for matching face representations directly in the encrypted domain along with a dimensionality reduction scheme to trade-off face matching accuracy and computational complexity. Experiments on benchmark face datasets (LFW, IJB-A, IJB-B, CASIA) indicate that secure face matching is practically feasible (0.01 sec per match pair for 512-dimensional features from SphereFace) while exhibiting minimal loss in matching performance.