# The Eye-Opening Arbiter-PUF FPGA Implementation with Auto Error Detection
## 5 PUF Stability Evaluation and Automatic Detection of Unstable Bits
### Stability Against Temperature Variations  
Environmental influences are a well-known non-ideality for all ICs and FPGA designs and can change the extracted PUF responses. Therefore, the influence of temperature changes on the EoA PUF is investigated. Please note that the used ZYBO allows no direct control of the FPGA power supply; thus, voltage variations are not investigated. Four FPGAs were evaluated at varying temperatures from \(-20\)\({}^{\circ}\)C to \(60\)\({}^{\circ}\)C in steps of \(10\)\({}^{\circ}\)C. This range was chosen to not damage the other components on the used ZYBO. The deadzone configuration was set to the maximum value of 20 bits, which corresponds to an expected deadzone of \(20\cdot 2\cdot 7\) ps = 280 ps and results in maximum stable bits. The midpoint of the evaluated temperature range was taken as a reference temperature at \(20\)\({}^{\circ}\)C. At every temperature step, an arbiter tuning (see Section 3.2) was conducted at start-up. Thereafter, all PUFs were evaluated 250 times and the resulting responses compared to the golden response at the reference temperature using Equation (4). The resulting HD\({}_{\text{intra}}\) is plotted in Figure 15 as green line for the EoA PUF. For the sake of comparability, a conventional SotA RO-PUF is implemented and evaluated on the same FPGAs. This is completed by disabling the arbitration signal and enabling the ROs for 1 ms evaluation time; this value was extrapolated from the results of [17], who used the same type of FPGA for RO-PUFs. By comparing the amount of oscillations of both ROs, a response bit was derived. This bit was compared to the median of all responses. The resulting HD\({}_{\text{intra}}\) for this RO PUF is plotted as blue line in Figure 15. The general profile over temperature is similar, but the RO-PUF shows a distinct shift to worse stability when compared to the EoA-configuration. As the same hardware setup was used for both configurations, platform-dependent reasons for this shift can be excluded. Further investigations showed that some RO pairs just differed in a few oscillations after the evaluation time of 1 ms and therefore are sensitive to noise. Since a pure RO-PUF implementation does not have an in-built detection of unstable bits, these bits cannot be blanked at runtime but have to be determined in a post-processing step. For further comparison of temperature dependency, results reported in the SotA for other FPGA designs are also considered. Even though the authors in [10] presented a PDL-based arbiter-PUF on an FPGA and reported their error rate over the temperature range from \(-10\) to 75 \({}^{\circ}\)C as up to 15%, no detailed data was provided and thus no graph was plotted. In [35], a TERO-PUF was implemented on FPGA. The TERO-PUF consists of two ROs connected in one chain, running until a stable state is reached. The best-case error rate over temperature provided in [35] is plotted as orange line in Figure 15, which shows a 2.5% higher error rate at reference temperature than the presented EoA implementation of this work. In addition, the slope of the error rate is two times higher for negative temperature changes. For positive temperature changes, the slope seems to decrease. As the authors of [35] did not address this behavior, it might also be a board-specific second-order effect, making further elaboration or comparison difficult. In [9], the authors evaluated a short RO-PUF, consisting of three LUTs, for temperature variations from 5 to 55 \({}^{\circ}\)C. From their data, the authors used a linear approximation of the error variation with temperature and stated 3.5% for a change of 60 \({}^{\circ}\)C. As the authors did not state an error rate at reference temperature, but only a change, no overall comparison can be made. Nevertheless, it can be stated that the slope of \(HD_{intra}\) of the EoA PUF and the approximation from [9] are quite similar for small temperature changes but diverge for larger temperature changes.