Post-Quantum Biometric Authentication Based on Homomorphic Encryption and Classic McEliece

Abstract

Homomorphic encryption is a powerful mechanism that allows sensitive data, such as biometric data, to be compared in a protected way, revealing only the comparison result when the private key is known. This is very useful for non-device-centric authentication architectures with clients that provide protected data and external servers that authenticate them. While many reported solutions do not follow standards and are not resistant to quantum computer attacks, this work proposes a secure biometric authentication scheme that applies homomorphic encryption based on the Classic McEliece public-key encryption algorithm, which is a round 4 candidate of the NIST post-quantum standardization process. The scheme applies specific steps to transform the features extracted from biometric samples. Its use is proposed in a non-device-centric biometric authentication architecture that ensures user privacy. Irreversibility, revocability and unlinkability are satisfied and the scheme is robust to stolen-device, False-Acceptance Rate (FAR) and similarity-based attacks as well as to honest-but-curious servers. In addition to the security achieved by the McEliece system, which remains stable over 40 years of attacks, the proposal allows for very reduced storage and communication overheads as well as low computational cost. A practical implementation of a non-device-centric facial authentication system is illustrated based on the generation and comparison of protected FaceNet embeddings. Experimental results with public databases show that the proposed scheme improves the accuracy and the False-Acceptance Rate of the unprotected scheme, maintaining the False-Rejection Rate, allows real-time execution in clients and servers for Classic McEliece security parameter sets of 128 and 256 bits (mceliece348864 and mceliece6688128, respectively), and reduces storage requirements in more than 90.5% compared to the most reduced-size homomorphic encryption-based schemes with post-quantum security reported in the literature.