## 2 Related Work
### Homomorphic Encryption Approaches  
To overcome the limitations of traditional schemes of encryption and introduce an alternative to the aforementioned approaches, such as biometric cryptosystems and cancellable biometrics, homomorphic encryption algorithms represent a promising option for protecting biometric templates through encryption while allowing computations directly on encrypted data without the need for decryption for highly accurate identity verification. Comprehensive research and detailed analysis regarding the state-of-the-art homomorphic encryption (HE) algorithms in the context of biometrics were provided in [33], such as the evolution of HE algorithms, possible attacks that can be initiated against HE on biometrics, various HE-based approaches to the security of the main biometric user features: iris, face, voice, fingerprint, and also focused on the presentation of the main benefits of integrating HE with other technologies for biometric security. Several research papers in the specialized literature have used homomorphic encryption for template protection in biometric recognition systems. Initially, the application of Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE) for enhancing security for biometric traits was investigated in [34; 35; 36; 37; 38]. These schemes allow performing a limited type of arithmetic operations such as addition and multiplication in the encryption process. Moreover, in [39], an authentication scheme that combines three components is designed: classic user authentication (based on username, password, and a message with a code using short message service (SMS)), biometric authentication, and a searchable encryption scheme that uses the Rivest-Shamir-Adleman (RSA) cryptosystem. In [40], an encoding method that incorporates the Paillier homomorphic algorithm into the inner product protocol applied on the FaceNet dataset achieved 98.78% recognition accuracy. Fully Homomorphic Encryption (FHE) was introduced because these systems proved to be vulnerable to quantum attacks. FHE systems based on integers and polynomial rings support an unlimited number of addition and multiplication operations in the encrypted domain over the facial biometric templates. In the surveyed literature, different and relevant approaches are given as follows. In [41], a privacy-preserving face verification scheme based on fully homomorphic encryption and a garbled circuit is proposed. In [42], a hybrid scheme for the protection of biometric templates, which combines cancellable biometrics methods and homomorphic encryption using different state-of-the-art face recognition models (ArcFace, ElasticFace, and FaceNet) is developed. Moreover, in [43], an efficient and improved use of coefficient packing for homomorphically protected biometric templates tested on public datasets is presented. Other secure and privacy-preserving methods for biometric template protection using fully homomorphic encryption evaluated on public datasets, that proved to be computationally efficient and practically feasible with no loss in recognition accuracy, are described in [44; 45; 46; 47]. Table 1 presents a comparison of the proposed mechanism of authentication with other various existing methods of authentication that combine different biometric templates with encryption algorithms presented in the specialized literature. The major difference between the authentication scheme proposed in this research paper and the other works consists of the implementation level as we can see in Table 1. Our mechanism of authentication is developed at the hardware level, which is considered superior to software implementation in terms of security, and tested on real user faces, compared with the other methods developed and tested on facial datasets available online.