## 4 Experimental Results  
Experiments were conducted to evaluate the performance of the confidence-interval-based fuzzy vault scheme. To assess its effectiveness in a bio-cryptographic system, we used faces [51] and implemented them in MATLAB R2023a on a computer with a 3.40 GHz CPU (i7-3770), 8 GB RAM, and 64-bit Windows. For these experiments, the proposed scheme assumed that the confidence interval set for each of the 50 subjects was generated from qualifying face images. There are originally five face images in the database per subject, three to four of which were used to generate a confidence interval set. Qualifying faces underwent PCA, the most basic preprocessing method for dimension reduction and feature extraction in recognition schemes [52; 53]. The threshold value for classifying a face as qualified is a recognition rate of 50% by PCA and our previous works based on the confidence interval [50; 53]. The set of confidence intervals is organized by the generation algorithm of the \(t\)-test-based prediction scheme shown in [50]. The confidence interval set has cardinality equal to the number of features and is saved in a secure token or database on the client and a server through a secure channel. This set calculates \(x_{i}\), generating the genuine points to share the secret key. The genuine points in the proposed scheme result from calculating the difference between the upper and lower bounds of the saved confidence intervals. Before this calculation, this scheme has to check whether each PCA-based feature from an acquired face is under the upper bound and over the lower bound. Suppose the including rate is over the threshold, a system parameter for decision by \(ID(F)>th\) in the encoding and decoding algorithms. In that case, access to the confidence interval is allowed for calculating the genuine points. Otherwise, it is not permitted, and we cannot calculate them. The confidence interval is stable information and equal data on the encoding and decoding side. And so, the genuine points generated by this confidence interval set in encoding are also completely the same as with the genuine points in decoding. In this proposed system, the confidence interval set is the key to solving the previous problems. The genuine points based on it can increase chaff points without decreasing the recognition rate, encoding and decoding time, and increasing the risk of correlation attacks. Figure 4 shows an example confidence interval set marked on the bar graph, with features from acquired faces marked with a circle for 20 principal components. Using more principle components is also possible because the face is a high-dimension trait for extracting enough features. In our previous work, we tested the number of principal components with AR Face DB for quality assessment [51] and used 20 principle components. The bar graph consists of upper and lower bounds. The \(i\)-th bar represents the confidence interval of the \(i\)-th feature in several qualified faces for confidence interval registration, such that \(1\leq i\leq 20\). In the example, non-satisfied features, which are under the lower bound or over the upper bound, are the 2 nd, 3 rd, 5 th, 7 th, 9 th, 11 th, and 14 th bars, respectively. In decoding, the satisfaction rate of the acquired face is 65% (13/20) and allows the use of the confidence interval set if the threshold is 50%. Figure 5 shows an example of the difference from the confidence interval set. The values are calculated regarding the difference between the upper and lower bounds by \(\mathit{dif}_{i}\leftarrow\mathit{abs}(u_{i}-v_{i})  
To investigate the distribution of vaults by using difference values, the normalized difference, marked with circles shown in Figure 7, is made by the representation of the difference shown in Figure 6. Here, the \(X\)-axis is for difference values before normalization, and the \(Y\)-axis is for normalized different values. The genuine points are generated with these normalized difference values.