## 4 Privacy Preservation  
To ensure privacy preservation by securely storing and processing fingerprint data, we implement a masking encryption technique to protect sensitive biometric information during transmission and storage. Apply anonymization or tokenization methods to dissociate user identities from raw fingerprint data while maintaining the ability to perform validation. The biometrics cryptosystem masking algorithm uses a crypto key to obfuscate the details of the fingerprint during the transmission and storage in the database within the edge network server. An unmasking procedure can be performed on a queried Finger: ID from within the database to enable user validation. \[F1(a,b,c)=A.K.allow(f1,f2,f3,\ldots fn) \tag{4}\]  
The privacy protection technique adopts an algorithm, similar to the Paillier cryptosystem algorithm [11] for the generation of private and public twin tokens (\(N\), g) and (\(\lambda\),\(\mu\)) that are used for the masking and unmasking of finger ID [23]. This process is shown in Figure 6. The edge server produces random integer \(z\), \(q\), where \(z-1\), and \(q-1\) are prime numbers (set of bits more than 1024). To allow parameters in Equation (4) to have protection parameters Pr, substituting Equation (9) into the protection equation, we have as follows: For a token generation, let \(p\) and \(q=\) two large prime numbers. These primes are used to generate the modulus n for the cryptosystem [23; 24]. Let lambda (\(\lambda\)): The Carmichael function, also known as the least common multiple of \(p-1\) and \(q-1\). It is used in various calculations within the Paillier cryptosystem [23], particularly for generating public and private tokens. \[\lambda=LCM(z-1,q-1) \tag{5}\]  
Let the plaintext message \(x\) be transformed using \(L(x)\) before being masked, set  
\[L(x)=\frac{(x-1)}{N},where,N=zq \tag{6}\]  
To obfuscate the matched fingerprint, select a token  
\[g\in(Z*N^{2}) \tag{7}\]Then, let \(g=\) LIG, the learning integer generator  
Let the public and private pair token  
\[(N,g)\text{ and }(\lambda,\mu) \tag{8}\]  
Choose a random integer r from the set of invertible elements modulo \(N\), denoted as \(Z*N\), such that gcd(r,N) = 1. Let Pr = mask  
\[Pr=LIG^{n}*r^{N}modN+F1(r^{N}modN)+F1(r^{N}modN)+F3(r^{N}modN). \tag{9}\]  
where \(\Delta=r^{N}\bmod N\). Let the sum of all random values and modulus = 1  
\[Pr=LIG(F1,2,3)*\sum_{1}^{i}(r^{N}modN)(F1,2,3)F1,2,3=\Delta a,b,c*LIG(F_{1},2,3 \ldots n)) \tag{10}\]  
Then the ciphertext mask is calculated as follows:  
\[\Pr(a,b,c)=\Delta(a,b,c)\cdot\text{LIG}\big{(}F((a,b,c))\big{)} \tag{11}\]  
Summarily, token generation involves selecting two large primes and computing public and private keys using a generator g. Masking consists of selecting a random value r and masking the message with the public token (N, g). The experiment setup is made up of a biometric sensor, AccesSensor, used as a fingerprint input device for users of the industrial Metaverse system. A display device, a laptop of specification processor: Intel Core i7-1165G7 Processor, memory: 16 GB DDR4 2666 Mhz Memory, storage: 1 TB PCIe NVMe M.2 SSD solid state drive internal storage, with connectivity to a wireless network and the server/database for validation, classification, matching and storage of FingerID, based on the deep learning classification of minutiae points for feature vector. The process for user validation includes the User Biometric entry phase and the User validation phase as displayed in Figure 3. The outcome of the timely validation process of User fingerID is Unmatched (Reject) or matched (Accept), for which user access to the Metaverse platform is declined or granted, respectively. In conducting extensive testing and evaluation of the algorithm using benchmark fingerprints from the database and real-world scenarios, and displaying the masked user interface, as shown in Figure 6.0  
Figure 6.1 Masking Procedure. We evaluate performance metrics such as efficiency, precision, recall, and processing time under varying conditions.