# A Power-Gated 8-Transistor Physically Unclonable Function Accelerates Evaluation Speeds
## 4 8-Transistor PUF Performance Measurements
### Robustness: Intra-Distance and BER  
For an ideal PUF cell, the _Respouses_ to the same _Challenge_ should always be the same. However, the existence of unstable cells makes this impossible. Thus, the intra-distance, which is the Hamming distance between bit strings of the _Respouses_ from repeated measurements of the same PUF, is used to evaluate the PUF robustness. To minimise the area overheads for error correction in the key regeneration phase, the intra-distance is expected to be close to zero. By comparing every pair of two _Response_ bit strings and adding up the total numbers of different bits, the intra-distances are calculated. The average intra-distance of all the simulated 8T PUF groups is 1.45%.  
Under nominal conditions, the average percentage of total unstable bits in 20 groups of 2048 8T PUF cells is 7.71%; the raw BER is 1.17%. The corresponding BER of the worst corner is 12.21%. Most of the unstable readings can be fixed by the Data Processing block using TMV, which can be visualised in the golden bitmap generated in the key enrolment phase. For example, in the golden bitmap shown in Figure 9, squares with different colours represent the statistical results of the PUF stability, i.e., white indicates stable '0', black squares show stable '1' and different grey shades present the degree of bias of the cells. Most impressively, the worst corner BER can be decreased to 0% with Dark-bit  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Measurement** & \multicolumn{4}{c}{**CMOS**} & \multicolumn{2}{c}{**Chip-Based**} & \multicolumn{4}{c}{**Simulation-Based**} \\ \hline  & **ISSCC** & **ISSCC** & **ISSCC** & **ISSCC** & **JSSCC** & **ISSCC** & **Electronics** & **IJCTA** & **This** \\  & **2014 [s]** & **2015 [s]** & **2016 [59]** & **2017 [9]** & **2020 [44]** & **2022 [60]** & **2023 [61]** & **2017 [62]** & **Work** \\ \hline
**Technology** & 22 nm & 65 nm & 45 nm & 14 nm & 130 nm & 180 nm & 130 nm & 65 nm & 65 nm \\
**Bitcell Area (\(\upmu^{\tt{2}}\))** & 4.66 & 25.35 & 5.3 & 1.84 & 6.3 & 223 & 72.03 & - & 4.19 \\
**Bitcell Area (\(\upmu^{\tt{2}}\))** & 9632 & 6000 & 2613 & 9388 & 373 & 7222 & 4262.13 & - & 992 \\
**Unstable Bits** & 30\% & 1.73\% & - & 26.37\% & 2.14\% & 0.61\% & 0.586\% & 0.32\% \({}^{\tt{A}}\) & 7.71\% \\
**Naive BER** & - & - & 0.1\% & 5.76\% & 0.21\% & 0.13\% & 0.49\% & - & 1.17\% \\
**Worst BER** & 6\% & 4.56\% \({}^{\star}\) & 2.84\% & 6.78\% & 0.34\% & 1.1\% & 3.125\% & - & 12.21\% \\
**Stabilised BER** & 0.97\% & 1.73\% & 0.21\% & 1.46\% & 0\% & 0.13\% & - & - & 0\% \\
**Intra-distance** & 2.58\% & 0.92\% & - & 3.4\% & 0.3\% & 0.16\% & 0.491\% & 2.25\% \({}^{\tt{A}}\) & 1.45\% \\
**Inter-distance** & 49\% & 50.14\% & 49.8\% & 48.6\% & 49.23\% & 49.3\% & 50.12\% & - & 50.67\% \\
**Mask Ratio** & 11\% & - & 18.5\% & 20\% & 31.2-75\% & 0.61\% & 0\% & - & 21.78\% \\
**ACF @95\%. c.1\({}^{\dagger}\)** & 0.01 & 0.0363 & 0.017 & - & 0.0228 & 0.0472 & 0.025 & - & 0.0315 \\
**Energy/bit (f)** & 13 & 15 & - & 4 & 128 & - & 5.36 & - & 6.15 \\ \hline \hline \end{tabular}  
* The worst unstable bit rate. \({}^{\dagger}\) Auto-correlation Function at 95% confidence level. \({}^{\tt{A}}\) M\({}_{VOUT}\) = 1 mV.  
\end{table}
Table 2: PUF performance comparison.  
masking coordinated with TMV in the worst voltage and temperature corners and in the field. The mask ratio is 21.78%. As a result, the hardware penalty for error correction is minimised.