## 3 The Proposed PRNG  
Considering the approaches necessary to increase the complexity and to avoid the insecurity conditions of the PRNGs based on single chaotic maps, and assuming that the proposed PRNG is implemented in a computer, we use the highest finite precision [47,58], cascading chaotic maps [47,59,60,61], combining chaotic maps by using modular operation [62,63], and using a function composition from chaotic maps [64,65,66]. It is worth noting that, considering recent technological advances, it would be interesting to address the possibility that the PRNGs based on chaotic maps can be implemented in microfluidic lab-on-a-chip devices [76,77,78,79]. The microfluidic technology is characterized by its advantages of miniaturization, integration and automation. It has enabled the development  
Figure 9: (**a**) Sensitivity level for the STM, considering 100 randomly selected initial conditions; (**b**) Sensitivity level for the FC, considering 100 randomly selected initial conditions; (**c**) Sensitivity index for the STM and (**d**) Sensitivity index for the FC. In all cases we consider \(k\in[1,15]\), \(x_{0}=0.1\), \(\mu=1.0\), \(\alpha=2.0\), and \(n\in[1,5000]\). of universal computing based on two-phase microfluidics, and it is named _bubble logic_ because the bubbles in a microfluidic device can carry process control information similar to what happens in a microprocessor, while performing chemical reactions [80; 81; 82]. Resuming the strategies mentioned to increase the complexity and to avoid the insecurity conditions of the PRNGs based on single chaotic maps, the cryptanalysis will be more difficult for the proposed PRNG, since the output sequences will be determined by many different mixed chaotic orbits. We emphasize that all mathematical operations included in the proposed PRNG have been performed considering double precision arithmetic and floating-point representation for the real numbers. In addition, we do not apply scaling or discretization processes to the functions used, rather we use them in their original form by using double precision arithmetic for the calculations. Thus, the final output of the proposed PRNG converted to 8-bit, 16-bit, and 32-bit integers, depending on the configuration used. It is worth noting that with a computer and any arithmetic, we can not produce chaos; the use of a computer leads to the degradation of the chaotic dynamics [83]. Thus, the proposed PRNG includes three chaotic maps produced by the function composition from the sine function and the skew tent map. It consists of three blocks: (i) **RCMb**- Block of the robust chaotic maps, which includes three FCs, each one using different values for \(\mu\), \(\alpha\) and \(x_{0}\). **RCMb** receives the key \(K\) of the PRNG as input, and it produces three output sequences; in this case, \(K\) is a word constituted by the concatenation of \(\mu_{i}\) and \(\alpha_{i}\) with \(i=1\), 2 and 3, and the values for the initial conditions \(x_{0}\), \(y_{0}\), and \(z_{0}\); and each one of the three output sequences is a chaotic sequence of real numbers produced by each chaotic map. (ii) **Tb**- Block to translate real number sequences into integer number sequences, and it includes three functions with a single input and a single output. Finally, (iii) **MSb**- Block sum module \(2^{bits}\), which has three inputs and a single output that represents the output of the proposed PRNG, where \(bits\) can be 8, 16 or 32. As previously expressed, and considering Figure 10, we define the following steps to generate a pseudorandom number sequence with uniform distribution and good statistical properties. 1. Assuming that **RCMb** includes three FCs, from \(k\), we produce three pseudorandom sequences of real numbers: \(\hat{x}=\{\hat{x}_{j}\}\), \(\hat{y}=\{\hat{y}_{j}\}\) and \(\hat{z}{=}\{\hat{z}_{j}\}\), with \(j=1\), 2, 3,...