Face recognition is a widely-used technique for identification or verification, where a verifier checks whether a face image matches anyone stored in a database. However, in scenarios where the database is held by a third party, such as a cloud server, both parties are concerned about data privacy. To address this concern, we propose CryptoMask, a privacy-preserving face recognition system that employs homomorphic encryption (HE) and secure multi-party computation (MPC). We design a new encoding strategy that leverages HE properties to reduce communication costs and enable efficient similarity checks between face images, without expensive homomorphic rotation. Additionally, CryptoMask leaks less information than existing state-of-the-art approaches. CryptoMask only reveals whether there is an image matching the query or not, whereas existing approaches additionally leak sensitive intermediate distance information. We conduct extensive experiments that demonstrate CryptoMask's superior performance in terms of computation and communication. For a database with 100 million 512-dimensional face vectors, CryptoMask offers ${\thicksim}5 \times$ and ${\thicksim}144 \times$ speed-ups in terms of computation and communication, respectively.
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