## 6 Results
### Statistical Analysis  
The validation of the randomness has been executed by the test suite suggested by the NIST in the NIST 800-r1 document [41]. To perform the tests the hypothesis has been set up for all the tests as: \begin{table}
\begin{tabular}{l l l l} \hline  & **Propagation Criterion** & **Correlation Immunity** & **Algebraic Immunity** \\ \hline SRFG & \(\frac{n}{2}\) & 100\% & \(\frac{n}{2}\) \\ \hline [PERSON] et al. [18] & \(\sqrt{\frac{n}{2}}-1\) & 57.63\% & 0 \\ \hline [PERSON] et al. [26] & \(\frac{n}{4}\) & 87.50\% & 0 \\ \hline [PERSON] et al. [27] & \(\frac{n}{4}\) & 85.33\% & 0 \\ \hline [PERSON] [29] & log\(n\) & 76.67\% & 0 \\ \hline [PERSON] [31] & \(\frac{n}{2}\) & 92.30\% & \(\frac{n}{2}\) \\ \hline [PERSON] et al. [32] & log\(n\) & 76.67\% & 0 \\ \hline [PERSON] et al. [33] & \(\frac{n}{2}\) & 94.33\% & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparative feature analysis. Figure 5: Correlation Immunity. (**a**) Correlation immunity with varying bits and input variables; (**b**) Correlation immunity with varying bits and expression length%. **Hypothesis 1. ** (_null hypothesis): SRFG output sequences are significant for randomness._  
**Hypothesis 2. ** (_alternate hypothesis): SRFG output sequences are non-significant for randomness._  
For each of the applied tests, a choice or end is taken that acknowledges or dismisses the invalid theory which implies whether the SRFG is (or isn't) ready to deliver randomness features, in light of the grouping that was created. For each test, an applicable randomness measurement is chosen and used to decide the value of acceptance or rejection of the invalid speculation. A test measurement esteem (\(p\)-value) is figured on the information or arrangement of bits created by the SRFG. Practically, the explanation that factual theory testing works is that the reference appropriation and the basic worth are reliant on and created under a speculative suspicion of irregularity. In the event that the arbitrariness supposition that is, truth be told, valid for the current information, at that point the subsequent determined test measurement esteem on the information will have an extremely low likelihood (e.g., 0.01 ) of surpassing the basic worth. This estimation of 0.01 is likewise known as level of criticalness or level of significance. In the event that \(p\)-value is more noteworthy than the degree of noteworthiness, we can acknowledge the invalid theory. The outline of the \(p\)-values of the above said tests is given in Table 3. We can observe that in all the above tests, the \(p\)-values of the tests are greater than 0.01, the significance level of the tests. Therefore, the null hypothesis is accepted. This signifies that the SRFG has passed all the tests as per the recommendations by NIST test suite and the SRFG provides randomness in true significance. SRFG is quite an interesting random number generator that possess all the required features of being used for cryptographic derivations with randomness features. The statistical test suite also validates the same. It can also be considered to be a post processing method for any other random number generators to provide immunity and eliminating bias and correlations. Furthermore, to validate the tests proportion of sequences passing, a test and uniformity was evaluated as per the NIST standards [41]. The formula shown in the document to calculate the confidence interval level is used here. The confidence interval becomes:  
\[\hat{p}\pm 3\sqrt{\frac{\hat{p}(1-\hat{p})}{m}}=0.99\pm 3\sqrt{\frac{0.99(1-0.99 )}{800}}=0.99\pm 0.01055 \tag{25}\]  
where \(\hat{p}=1-\alpha\), \(\alpha\) is the significance level (0.01) and \(m\) is the number of samples of bit sequences which is 800 in the experimented process. The Equation (25) suggests that the proportion of the sequences under test should be more than 0.9794466. Out of 800 random