## 2 Related Preliminary Basics
### Biometric Authenticated Secret Key  
A fingerprint can be used as a biometric property to extract digital data using a variety of methods, such as a block-based approach to create a feature vector [62]. With the help of this feature vector, code words can be created that are sufficiently random and large to be employed. The procedure includes the following steps: feature extraction, straight line attribute calculation, straight line attribute obfuscation, and production of a biometric binary string. Then, from the fingerprint image, we extract the minute points, core points, and delta points. If P is a collection of minute points, then \(p(x,y)\) stands for a minute point's coordinate. A collection of minor points is denoted by the notation point \(p=\{p_{1}(x_{1},y_{1}),p_{2}(x_{2},y_{2}),\ldots,p_{k}(x_{k},y_{k})\}\). Miniscule points are represented by \(p_{i}(x_{i},y_{i})\), \(i=1,2,\ldots k\). The core point is then represented as \(Cp(x_{c},y_{c})\), where \(x_{c}\) is the x-coordinate and \(y_{c}\) is the y-coordinate of the discovered core point \"\(Cp\)\"from the input fingerprint picture. Finally, when a delta point is found in a fingerprint picture, it is represented as \(D_{p}(x_{d},y_{d})\), where \(x_{d}\) is the discovered delta point's x-coordinate and \(y_{d}\) is its y-coordinate. Divide the image into small blocks and compute the straight-line properties between the points in the set 'P'. The fingerprint image I' will be divided into a number of tiny blocks, each measuring \(m\times m\) pixels, with \(l=p\times q\) of all blocks.  
Using all the blocks, we determine the straight-line properties when computing all straight lines from a block's minutiae point (\(p_{k}\)), which stands for the block in the \(i^{th}\) row and \(j^{th}\) column of \(I_{ij}\) as a reference block for all other blocks' minutiae points. Compute the length and angle of each straight line, using the Euclidean distance for length (li) and the \(x\)-axis for angle \((a_{i})\). Let \(F_{B}\) represent a collection of straight-line lengths and angles for all blocks, \(F_{B}=\{(1_{1},a_{1}),(1_{2},a_{2}),\ldots,(1 zb,azb)\}\). Find the block \(I_{lm}\) that contains the core point (\(C_{P}\)), compute all straight lines that connect the core point (\(C_{P}\)) to all other minutiae points of neighboring blocks, and then extract the core and delta points from image I. Let \(F_{C}\) denote a set of lengths and angles of straight lines, where the size of the \(F_{B}\) is \(z^{b}\). Finally, the extracted minutiae attributes contain three fields per minutiae: the x-coordinate([1, 511]), y- coordinate ([1, 511]) and orientation \(\theta\) ([0, 359]); the three parameters \((x.y.\theta)\) are used as a biometric minutia [63; 64; 65]. In [64], a high-performance fingerprint scanner and a recognition engine are both included in the FS83 serial Fingerprint Authentication Module (FS83-sFAM), which is used in order to generate 2072 bytes from three samples of different fingerprints of one user. The resultant bits are represented in hexadecimal format, which is used in authenticated and secret key generation. The biometric fingerprint image is shown in Figure 1.