Behavioral effects of a four-wing attractor with circuit realization: a cryptographic perspective on immersion

Najeeb Alam Khan,Muhammad Ali Qureshi,Tooba Hameed,Saeed Akbar,Saif Ullah

Table 5. ${\rm P}$-value test results (NIST-800-22) for chaotic series ${u}_{2}\left(t\right),$ at different values of $\alpha .$

S. No Test Name $\alpha $ = 1 $\alpha $ = 0.99 $\alpha $ = 0.92 Results 1 Mono bitFrequency Test 0.716 059 0.953 96 0.367 766 Successful 2 Block Frequency Test 0.638 647 0.474 88 0.617 961 Successful 3 Runs Test 0.004 748 35 0.567 602 0.784 317 Successful 4 Longest Runs Ones 10 000 0.692 827 0.933 756 0.377 388 Successful 5 Binary Matrix Rank Test 0.332 02 0.180 156 0.903 766 Successful 6 Spectral Test 0.289 315 0.524 923 0.542 336 Successful 7 Non-Overlapping Template Matching 0.873 754 0.329 533 0.137 408 Successful 8 Overlaping Template Matching 0.366 99 0.422 48 0.279 795 Successful 9 Maurers universal Statistic Test 0.336 621 0.535 156 0.844 607 Successful 10 Linear Complexity Test 0.229 947 0.969 042 0.224 795 Successful 11 Serial Test {0.235 703,0.593 431} {0.574 309,0.443 98} {0.864 631,0.918 161} Successful 12 Approximate Entropy Test 0.023 8884 0.586 246 0.249 462 Successful 13 Cumulative Sums Test 0.983 936 0.840 404 0.627 666 Successful 14 Random Excursions Test 0.769 331 0.804 348 0.316 433 Successful 15 Random Excursions Variant Test 0.947 793 0.388 667 0.331 918 Successful 16 Cumulative Sums Test Reverse 0.727 184 0.788 972 0.263 668 Successful