This paper introduces a novel protocol for privacy-preserving biometric identification, named Monchi, that combines the use of homomorphic encryption for the computation of the identification score with function secret sharing to obliviously compare this score with a given threshold and finally output the binary result. Given the cost of homomorphic encryption, BFV in this solution, we study and evaluate the integration of two packing solutions that enable the regrouping of multiple templates in one ciphertext to improve efficiency meaningfully. We propose an end-to-end protocol, prove it secure and implement it. Our experimental results attest to Monchi’s applicability to the real-life use case of an airplane boarding scenario with 1000 passengers, taking less than one second to authorize/deny access to the plane to each passenger via biometric identification while maintaining the privacy of all passengers.