# On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation
## 4 Experimental Results
### Trng-Ro Experimental Results  
The bit-stream quality of the [PERSON] et al.'s TRNG [12] has been checked using two well-established NIST statistical test suites [5; 18]. To that end, 5 Mbit of data were collected for each accumulated dose. Figure 5 shows boxplots of the p-value distribution (NIST tests) for different accumulated doses. It can be appreciated that the quality of the output decreases with the accumulated dose. Please note that a random generator passes the NIST tests whether the obtained p-values are uniformly distributed on the interval [0,1]. In our particular case, NIST tests are passed until 35 krad(Si) are reached. After this point, the quality of the TRNG output degrades rapidly. This phenomenon can be explained if we pay attention to the ratio of 0's/1's generated by the TRNG. In Figure 6 are depicted the percentages of 0's of each bit-stream. It can be seen that for an accumulated dose lower than 35 krad(Si), the distribution is almost ideal (50%). From this point to the end, the number of 0's in the bit-stream increases reaching a 59.3%. This bias can be explained because a lower oscillation frequency of the RO means that there are fewer events to sample in the jitter zone producing a higher number of deterministic bits. The lower oscillation frequency is induced by the accumulated dose as explained in Section 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **RO-TRNG** & **STR-TRNG** \\ \hline Frequency & 0.911413 & 0.253551 \\ Block Frequency & 0.804337 & 0.082177 \\ Cumulative Sums & 0.476471 & 0.215914 \\ Runs & 0.671779 & 0.804337 \\ Longest Run & 0.949602 & 0.991468 \\ Rank & 0.253551 & 0.862344 \\ FFT & 0.148094 & 0.739918 \\ Non-Overlapping Template & 0.462714 & 0.479021 \\ Overlapping Template & 0.534146 & 0.299251 \\ Universal & 0.253551 & 0.299251 \\ Approximate Entropy & 0.066882 & 0.082177 \\ Random Excursions & 0.633125 & 0.257812 \\ Random Excursions Variant & 0.508011 & 0.135850 \\ Serial & 0.789259 & 0.504774 \\ Linear Complexity & 0.213309 & 0.122325 \\ \hline \hline \end{tabular}
\end{table}
Table 1: NIST STS Results.  
Figure 4: FPGA current (A) vs Total Ionizing Dose [krad(Si)].  
Regarding the min-entropy of the entropy source, Table 2 summarizes the entropy per bit estimation of the tests included in SP 800-90B Entropy Estimation Suite [18]. The same trend than before (the degradation of the randomness quality is noticeable from 35 krad(Si)) can be appreciated due to the direct relation between the quality of the entropy source and the quality of the output. It is worth noting that the estimated min-entropy is set to the lowest value of the ten estimation methods computed. In our particular case, collision, t-Tuple and LSR tests determine the min-entropy value. The first one [25] gives a measure of the mean number of samples to the first collision in a dataset, where a collision is any repeated value. The t-Tuple estimation examines the frequency of pairs, triples, etc. in the bit-stream and produces an estimate of the entropy per sample based on these frequencies [18]. Finally, LSR checks the IID assumption using the length of the longest repeated substring. As the number of 0's increases with the total ionizing dose, it will be more likely to have a collision or a higher frequency of pairs and triples, and as consequence of this the min-entropy will be lower.  
Figure 5: [PERSON] et al. p-value distributions for different accumulated doses.  
Figure 6: [PERSON] et al. % 0’s for different accumulated doses.