## 5 Comparison Results  
The efficiency of the proposed PRNG is compared with similar PRNGs based on chaotic maps. In this section, we focus on four tests: Correlation coefficient, Key sensitivity using correlation coefficient and variance ratio, key space and running speed. For this section three PRNGs were selected: (i) 32-bit PRNG proposed by Zhang et al. [91], (ii) 8-bit PRNG proposed by Huang et al. [40] and (iii) 8-bit PRNG proposed by Liu et al. [92]. We performed experiments on equal terms to the considered PRNGs for comparison with similar works. The comparison tests were developed using a C language compiler (MinGW) on an Intel Core i7-4800 MQ CPU-2.70 GHz and 24G RAM. Then, to determine the correlation coefficient we generate 6000 number sequences of 12000 numbers with different keys. The correlation coefficient obtained was within [\(-\)0.032, 0.029], while for the PRNG reported by Zhang et al. the correlation coefficient was within [\(-\)0.035, 0.035]. Regarding the key sensitivity, four sets of keys with a single bit difference between them were defined, then four number sequences of 12,000 numbers were generated. Finally, we obtain the difference between the sequences by applying the correlation coefficient and calculate the average to obtain the value shown in the Table 7. Note that the key sensitivity obtained for the proposed PRNG is slightly lower than the key sensitivity reported by Zhang et al. [91]. It is worth noting that the key space of the proposed PRNG considers double precision for 64-bit numbers, which is considered a great advantage over the PRNG developed by Zhang et al. [91]. Regarding the speed running test, Zhang et al. use an Intel Core i7-10710U CPU and 16 GB RAM. The algorithms were implemented in Visual Studio 2019 using C++, it can be observed that the PRNG proposed by Zhang et al. [91] has a high speed with respect to the proposed PRNG. However, the different architectures under which the tests were carried out could affect the measurements. In the second part of this section, the tests were performed when the proposed PRNG is set to 8-bit and only three tests are considered: key sensitivity, key space and running speed. Considering that the proposed PRNG has a high sensitivity to key changes, we performed the key sensitivity test using two different sequences generated by using two keys: \(K_{1}\) and \(K_{2}\), where \(|K_{1}-K_{2}|=1\times 10^{-15}\). Then, we calculated the variance ratio (\(D\)) [40,92] between the two binary sequences with size \(L=1,000,000\) resulting \(D=49.9872\%\), which \begin{table}
\begin{tabular}{c c} \hline \hline
**PRNG Configuration** & **Running Speed (MBytes/s)** \\ \hline
8-bit & 4.720276 \\
16-bit & 9.163551 \\
32-bit & 19.978822 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Execution time to generate 1,000,000 pseudorandom numbers by using the proposed PRNG considering the three configurations. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Microcontroller Architecture**} & \multirow{2}{*}{**8-Bit**} & \multicolumn{2}{c}{**PRNG Configuration**} & \multirow{2}{*}{**32-Bit**} \\  & & **16-Bit** & & \\
**Architecture** & & & & \\ \hline
8-bit & 141,645 & 132,920 & 25,139 \\
16-bit & 67,699 & 65,290 & 12,319 \\
32-bit & 33,206 & 30,605 & 5308 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Clock cycles consumed by the proposed PRNG when the 8, 16, or 32-bit configurations are used. is similar to results reported by Liu et al. [92] and Huang et al. [40]. On the other hand, the proposed PRNG has a key space larger than the PRNG proposed by Liu et al., but its key space is similar to the PRNG proposed by Huang et al. [40]. Finally, the running speed of the proposed PRNG is similar to running speed of the PRNG proposed by Zhang et al. [91]. It is worth noting that each author performs the tests with different equipment. For example, Liu et al. [92] used a computer with 3.3 GHz CPU and 4 GB RAM, but they do not indicate the used programming language. Huang et al.