Emerging global privacy mandates enforce strict requirements for biometric data protection, requiring encrypted processing throughout storage and computation phases. While full homomorphic encryption (FHE)-based face recognition ensures security on platforms like Elastic Compute Service (ECS), three critical compliance gaps persist: 1) about 500 \(\times\) ciphertext expansion in high-dimensional facial features, exceeding practical deployment thresholds, 2) vulnerabilities in live verification scenarios documented by ENISA (83% failure rate in 2024 audits), and 3) absence of mechanisms satisfying IND-CPA and IND-CCA2 standards. These limitations collectively undermine both regulatory adherence and operational efficiency in practical biometric systems. To address these gaps, this paper proposes a Hybrid Encryption with Facial Data Integrity Verification(HEFDIVS) scheme, which combines dimensionality reduction and hybrid encryption algorithms. Specifically, the scheme first realizes facial feature similarity calculation in the ciphertext domain without decryption. Then, the ISOMAP algorithm is applied to reduce the dimensionality of the facial data, thus alleviating the computational complexity in the ciphertext domain. Finally, based on FHE, a hybrid encryption algorithm combining SM2 and SM4 is introduced to enhance the security of the scheme. Experimental validation on the LFW and Faces94 datasets demonstrates mean recognition accuracy rates of 95.45% and 96.98% respectively, with 89% faster ciphertext computation time (0.028s) compared to pure FHE implementations in the ciphertext domain. The proposed scheme surpasses existing methods in accuracy-efficiency tradeoff while complying with IND-CPA (NIST SP 800-57) and IND-CCA2 (ISO 19772) security standards through hybrid SM2-SM4 authentication mechanisms.
