# FeRHA: Fuzzy-Extractor-Based RF and Hardware Fingerprinting Two-Factor Authentication
## 6 Results and Performance Analysis
### Performance Results  
During the operation phase, an eavesdropper may attempt to intercept communication between entities, e.g., \(\delta_{x}\) and \(\delta_{y}\), to obtain a significant number of CRPs. These data can then be used to mimic the PUF and impersonate the legitimate node \(\delta_{x}\). In order to prevent such an attack, FeRHA pursues a two-factor authentication protocol that effectively obfuscates exchanged response bits \"R\". To evaluate the efficacy of FeRHA, we conducted two distinct attack scenarios based on the attack model discussed earlier in Section 4. These scenarios were designed to model the behavior of \(PUF_{x}\) and impersonate \(\delta_{x}\). In the first scenario, an attacker intercepts the transmission of a single communication link between a verifier, \(\delta_{y}\), and a prover, \(\delta_{x}\), with the goal of modeling the PUF of \(\delta_{x}\). In the second scenario, an attacker eavesdrops on links between a prover, \(\delta_{x}\), and multiple verifiers, and uses the intercepted packets, i.e., the exchanged CRPs to model the PUF of \(\delta_{x}\). The results for these attack scenarios are discussed in detail below. * Single-link attack: in this scenario, we focus on the authentication of a prover, \(\delta_{x}\), by a verifier, \(\delta_{y}\), where an adversary may intercept transmissions between them. It is important to note that the adversary's primary objective is to capture as many CRPs as possible for \(PUF_{x}\) during the operation phase of FeRHA. Specifically, the adversary aims to obtain the maximum number of CRPs for the prover's \(PUF_{x}\). Recall, FeRHA utilizes two primitives, PUFs and RFF, to generate an authentication token. Notably, the PUF response, \(R\), is not included in the verifier's request. Instead, the obfuscation function, \(\Phi\), is applied to produce an authentication token, \(Token^{y}_{x,i^{\prime}}\) for every challenge bit-string, \(C_{x,i}\), where \(\Phi\) factors in the pairwise link between \(\delta_{x}\) and \(\delta_{y}\). Thus, an adversary will record the exchanged \(Token^{y}_{x,i}\) as the PUF response and, consequently, will use these tokens as input to the machine learning model, with the aim of mapping the challenge bits to the corresponding token. The results of the modeling attack under FeRHA are depicted in Figure 7. We performed the modeling attack using the ML models applied earlier in Figure 6 to model the PUF with the  
Figure 6: Accuracy of modeling 64-bit arbiter-PUF using NN and XGBoost for various training set sizes (CRP count). application of FeRHA. As demonstrated by the results, an adversary cannot achieve an accuracy of more than 53% and 56% using CNN and XGBoost, respectively. Such an accuracy is equivalent to a random guess, given the binary nature of the PUF response. The effectiveness of FeRHA in preventing modeling attacks is clearly evident from the comparison of the results in Figure 7 with those in Figure 6.
* Multi-link attack: in this scenario, we assume that an adversary is actively eavesdropping on all links that the prover, \(\delta_{x}\), has with other nodes. The adversary's primary objective is to collect as many CRPs of \(PUF_{x}\) as possible, with the ultimate goal of modeling \(PUF_{x}\) and impersonating \(\delta_{x}\). It is worth noting that, in contrast to the single-link scenario, the adversary will intercept the exchanged packets between \(\delta_{x}\) and multiple verifiers, such as \(\delta_{y}\), \(\delta_{z}\), \(\delta_{w}\), and so on. Hence, the applied function, \(\Phi\), will be varied among the intercepted packet (since \(\mathcal{L}_{xy}\
eq\mathcal{L}_{xz}\
eq\mathcal{L}_{xw}\)). Despite the adversary's ability to capture more data, the semantic of such data is not coherent since the tokens are derived from the PUF response differently for the various verifiers. The results depicted in Figure 8 illustrate the outcomes of utilizing CNN and XGBoost models in conjunction with a 64-bit PUF integrated into \(\delta_{x}\).