## 6 Conclusions  
This work contributes to the design of PRNGs based on chaotic maps. In this case, we introduce a function composition (FC), which couples the sine function and the skew tent map to produce pseudorandom number sequences. We analyze the behavior of the chaotic maps by using the bifurcation diagram and Lyapunov exponent, and identifying the chaos annulling conditions and stability islands. In the FC, the Lyapunov exponent is positive when the control \(\mu\) is in \((0,\alpha)\) and then it can be used in the implementation of a PRNG. Using three FCs, the proposed PRNG has a large key space, it produces pseudorandom sequences with good statistical features and it has robust sensitivity to key changes. Ideally, the key space of the proposed PRNG is \(2^{576}\), and in a modest case it can be \(2^{384}\). Similarly, the strategy used to translate real numbers sequences into 8, 16 or 32-bit integer number sequences does not affect the behavior of the used chaotic maps. This does not exclude the possibility of having different behaviors due to precision errors in the representation of real numbers and arithmetic operations. Therefore, in this work we consider using the highest precision available when implemented on a computer or digital electronic device. In this regard, it would be interesting to research the possibility of implementing the proposed chaotic maps by using microfluidic-based processors and circuits. On the other hand, in this work, we prove that the proposed PRNG can produce uniformly distributed number sequences when the annulling chaos conditions are identified and avoided. Further, the number sequences generated by the proposed PRNG were evaluated by the following set of tests: correlation coefficient, key sensitivity, statistical analysis, entropy, linear complexity, and pseudorandomness. Additionally, we estimate the key space and the execution time when the proposed PRNG was programmed in C Language and electronically implemented on low-resources devices; notably, in all tests the proposed PRNG had a good performance. We especially emphasize that the proposed PRNG has a very high linear complexity when evaluated using the Berlekamp-Massey algorithm avoiding the problems presented by PRNGs based on a single chaotic map. Also, the proposed PRNG can be configured to generate pseudorandom 8, 16 or 32-bits numbers, so it can be implemented in microcontrollers of different architectures. Note that the proposed PRNG is two times faster than the algorithms proposed by Huang et al. and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Proposed PRNG** & **Zhang et al. [91]** & **Liu et al. [92]** & **Huang et al. [41]** \\ \hline Corr. Coeff. \({}^{b}\) & \([-0.032,0.029]\) & \([-0.035,0.035]\) & – & – \\ Key Sensit: Corr. Coeff \({}^{b}\) & 0.009278 & 0.007724 & – & – \\ Key Sensit: The variance & 49.9872\% & – & 49.9850\% & 49.9950\% \\ ratio (\(D\)) \({}^{a}\) & 2\({}^{576}\) & 2\({}^{136}\) & 2\({}^{184}\) & 2\({}^{448}\) \\ Running speed (MB/s) & 19.978822 \({}^{b}\) & 65.867475 \({}^{b}\) & – & – \\  & 4.720276 \({}^{a}\) & – & 2.729887 \({}^{a}\) & 2.688817 \({}^{a}\) \\ \hline \hline \end{tabular} \({}^{a}\) 8-bit generator and \({}^{b}\) 32-bit generator.  
\end{table} 
Table 7: Comparison analysis of the proposed PRNG against similar algorithms. Li et al., but is three times slower than the algorithm proposed by Zhang et al. when it is configured for 32 bits, since the algorithm proposed by Zhang et al. was computationally improved. In the key sensitivity test we considered two approaches: variance ration and correlation coefficient. Note that variance ratio is very close to 50%, which is similar to the results reported by Huang et al. and Li et al. Similarly, the correlation coefficient is very close to zero, which is similar to results reported by Zhang et al.