## 2 State of the Art
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Methods** & **Modality, Dataset** & **Obtained Results** \\ \hline i-vector, x-vector [2] & Voice, NIST SRE 2016, & EER = 9.23\%, EER = 5.21\% \\ \hline
2D-CNN (MFCC) [3] & Voice, authors’ own archive & F1-score = 99.6\% \\ \hline ResNet (AM-Softmax, AAM-Softmax) [4] & Voice, VoxSRC 2020 & EER = 5.19\% \\ \hline Res2 Net [5] & Voice, VoxCeleb & EER = 0.83\% \\ \hline PLDA + x-vector [6] & Voice & EER = 13.35\% \\ \hline RecXi [7] & Voice, VoxCeleb, SITW & EER reduction by 9.56\% \\ \hline VGSR [8] & Voice + Face, CN-Celeb, & Reduce EER by 10–15\% \\ \hline Wavelet-based classification [9] & Voice, RedDots & EER = 4.85\% \\ \hline GMM (MAP + NAP) [10] & Voice, RedDots & EER = 2.6\% \\ \hline HMM + i-vector [11] & Voice, RedDots & EER = 1.52\% (men), 1.77\% (women) \\ \hline Homomorphic encryption [12] & Face & Matching time 2.38 ms, memory 32.8 KB \\ \hline Lattice-based fuzzy extractors [13] & Face & Entropy equal to 45 bits, high security \\ \hline Fuzzy vault + DTW [14] & Voice & Impossibility of template inversion \\ \hline RBOMP with i-vector and prime factorization [15] & Voice & EER = 3.43\%, ARM attack protection \\ \hline Hybrid method: homomorphic encryption + cancelable biometrics [16] & Face & Authentication time is about 7 s \\ \hline Hybrid scheme: cancelable biometrics + biocryptography [17] & Face, CVL, FEI, & Accuracy: CVL = 99.47\%, FEI = 98.10\%, FERET = 100\% \\ \hline Neural fuzzy extractor with correlation neurons [18] & Voice, RedDots & EER = 2.64\% \\ \hline Fusion of four systems and tandem features [19] & Voice, RedDots & EER = 1.96–2.28\% \\ \hline TD-SV based on GMM-UBM [20] & Voice, RedDots & EER = 3.06\% with 5 db noise, 2.7\% with 10 db noise \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of modern biometric authentication methods. Lattice-based fuzzy extractors are also proposed to be used to protect templates [13]. The goal of the study was to create a reliable system capable of restoring a cryptographic key in the presence of certain errors in biometric data. In the work, dense lattices such as E8 and Leech were used to create stable templates that could maintain accuracy even when changed. Experiments have shown that their method reduces the likelihood of data leaks and provides a high level of security with an entropy of 45 bits, applicable to modern face recognition systems, such as ArcFace. In [14], the authors propose a BTP approach based on generating cryptographic keys from a voice template using a fuzzy vault scheme. The main goal is to ensure that the template cannot be easily inverted and compromised. The system uses dynamic time warping (DTW) to align voice characteristics. The fuzzy vault stores the template by adding chaff points, which makes it computationally difficult for attackers to distinguish between genuine and fake points. In [15], the authors propose a new approach to voice BTP using Random Binary Orthogonal Matrices Projection (RBOMP). The system works with i-vectors that are transformed using orthogonal matrices to create hashes that prevent template inversion. As an additional protection, the prime factorization method was introduced, which provides higher privacy and protection against multiple-record attack (ARM). The test results showed that the proposed system maintains a high level of protection (EER = 3.43%) without significant performance losses. A hybrid method based on a combination of homomorphic encryption and cancelable biometrics can be used to protect biometric templates [16]. cancelable biometric methods used included BioHashing, MLP hashing, and IoM hashing. Testing was conducted on MOBIO and LFW samples using modern ArcFace, ElasticFace, and FaceNet face recognition models. The results show that the proposed method provides comparable performance to homomorphic encryption, while reducing computational costs by reducing the template size. This made it possible to achieve a duration of the authentication procedure equal to seven seconds.