# CNT-PUFs: Highly Robust and Heat-Tolerant Carbon-Nanotube-Based Physical Unclonable Functions +
## 2 Related Work  
In this section, we provide a brief overview of some of the most-important works on carbon-nanotube-based PUFs and comment on their relevance to our work. In 2014, [PERSON] et al. [25] examined the ability of two series of CNT-FETs to be used for the creation of PUFs through the comparison of their output currents. This work provided only simulation results for the temperature range between \(-20\,\mathrm{\SIUnitSymbolCelsius}\) and \(80\,\mathrm{\SIUnitSymbolCelsius}\) and reported an average intra-device Hamming distance of 1.9%, which is similar to the average Hamming distance value that our work achieved for different temperatures. In 2016, [PERSON] et al. [26] investigated the ability of self-assembled CNTs arranged in a \(64\times 40\) crossbar structure to serve as either a binary or a ternary PUF. For both cases, a mean intra-device Hamming distance of \(\approx\)3% was reported, which is higher than the 2% value reported in our work, which concerns temperature variations between \(23\,\mathrm{\SIUnitSymbolCelsius}\) and \(120\,\mathrm{\SIUnitSymbolCelsius}\). Additionally, the work of [PERSON] et al. only examined the stability of the relevant CNTs through measurements at \(25\,\mathrm{\SIUnitSymbolCelsius}\) and at \(85\,\mathrm{\SIUnitSymbolCelsius}\). In 2017, [PERSON] et al. [27] proposed novel CNT-based PUF types utilising either the voltage or the current output of CNT-FETs. This work provided simulation results for the temperature range between \(0\,\mathrm{\SIUnitSymbolCelsius}\) and \(100\,\mathrm{\SIUnitSymbolCelsius}\), demonstrating reliability values that would correspond to intra-device Hamming distances of at least 3.33%. In comparison, our work can achieve an intra-device Hamming distance of at most 2% in a temperature range of up to \(120\,\mathrm{\SIUnitSymbolCelsius}\). In 2018, [PERSON] et al. [28] discussed the combination of a CNT-FET crossbar structure with the Lorenz chaotic system in order to provide PUFs that would be resistant to machine learning attacks. Again, only simulation results were provided. Furthermore, this work focused on the uniqueness, randomness, and unpredictability of the PUF responses, with no results being reported regarding the stability of these responses. Also in 2018, [PERSON] et al. [29] proposed the use of multi-gate CNT-FETs for the creation of PUFs, in order to increase the number of bits that each CNT-FET could produce and, in this way, enhance the entropy of the overall PUF response, potentially resulting not only in ternary responses, but also up to base-17 PUF responses. However, this work focused on the uniqueness and the entropy of the produced responses and did not provide any results relevant to their robustness. Moreover, while individual CNT-FETs seem to have been fabricated for the purposes of this work, the relevant CNT-FET networks seem to have been only simulated. A work by [PERSON] et al. regarding PUFs produced by all-printed CNT networks that was published in 2019 [30] demonstrated no significant changes (only an overall 1.0% difference) regarding the reliability of the fabricated CNTs over 10,000 measurement cycles and 14 days. However, the relevant resistance characteristic of individual CNTs was reported to have changed up to 16.7%, and the results for temperature variations between \(25\,\mathrm{\SIUnitSymbolCelsius}\) and \(80\,\mathrm{\SIUnitSymbolCelsius}\) exhibited an average difference of up to 30%. In comparison, our work reports a very low number of unstable CNT cells for temperature variations between \(23\,\mathrm{\SIUnitSymbolCelsius}\) and \(120\,\mathrm{\SIUnitSymbolCelsius}\), around 2% of the overall structure examined. Additionally, the thin-film PUF architecture of the PUF proposed in [30] requires a much higher area per bit cell compared to our CNT-PUF. Also, in 2019, [PERSON] et al. [31] examined the ability of single-walled carbon nanotubes to be used for the creation of PUFs.