# Challenge-Response Pair Mechanisms and Multi-Factor Authentication Schemes to Protect Private Keys
## 4 Experimental Section and Analysis
### Generation of Reference Tables from Biometric Images  
Using facial images as PUFs is a relatively novel concept, enabling the generation of cryptographically secure keys for authentication. While numerous methods for facial recognition have been researched, the use of facial images for cryptographic key verification offers heightened security and better protection of users' biometric data. Recent studies have introduced unique techniques, such as placing landmarks on facial images and calculating distances between random points and these landmarks. These distances are unique due to the individuality of facial structures influenced by factors such as age, ethnicity, and other biometric traits, ensuring that the placement of landmarks is specific to each individual. However, challenges such as the \"twin problem\" persist, as existing  
Figure 6: Kernel Density Estimation of “0”, “1”, and “X” for server and client reference table CT-T generated from tokenized PUF. We observe that the SRAM PUF contains more “1”s than “0”s, which is an asymmetry due to the component. This could eventually be resolved by using a different supplier of SRAM. The rate of “fuzzy” cells is at a perfect level of 28%. facial recognition techniques struggle to differentiate between identical twins [65]. In our proposed technique, the landmark placement relies on unique facial expressions during the enrollment session, ensuring the landmarks' positions are distinct to the user. Additionally, incorporating a user-defined unique password introduces random positions for calculating landmark distances, providing an extra layer of security and effectively mitigating the twin problem. The generation of a reference table from biometric images represents an innovative approach, with limited research available on this topic. Our work demonstrates promising results regarding the usability and security of reference tables generated using biometric data, following a methodology similar to that used for token-based PUFs. Experimental section: On the server side, multiple facial images of an individual are processed by applying landmarking techniques to each image and calculating the distances between random challenge points and landmarks. Figure 7 provides an example of the enrollment images. As we can see, there are 15 images where the user changed her angle, hair color, and style. We aimed to capture the natural movement of an individual during the enrollment phase. Although it may seem counterintuitive to change hair color during this phase, we included that image for authentication purposes, considering that the user might change their hair color later. Additionally, we observed that hair color does not impact the landmark placement technology and does not impact the verification of the user. The results from each image are compared to create a ternary representation, where \"0\" and \"1\" denote stable positions across all frames, and \"X\" represents flaky positions. The generation of ternary states using multiple facial images is an ongoing research endeavor, with results currently in the process of publication. In brief, our methodology calculates distances between 64 landmarks and 256 random challenge points on facial images. Each distance is converted into a 4-bit gray code representation, ultimately producing a 65,536-bit representation of the facial image. These representations are then compared across enrollment images to establish the ternary states. To ensure security, the reference table containing the ternary states is not stored on the server. Furthermore, since the challenge positions are entirely random, reconstructing the original facial image from the reference table is computationally infeasible. For experimentation, we utilized 6000 AI-generated facial images from 400 individuals, with each individual represented by  
Figure 7: Example of multiple enrollment images for the same individual to generate a bio-reference table. 15 images.