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 4. ${\rm P}$-value test results (NIST-800-22) for chaotic series ${u}_{1}\left(t\right),$ at different values of $\alpha .$

S. No Test Name $\alpha $ = 1 $\alpha $ = 0.99 $\alpha $ = 0.92 Results 1 Mono bitFrequency Test 0.665 006 0.484 806 0.317 884 Successful 2 Block Frequency Test 0.678 612 0.985 867 0.518 35 Successful 3 Runs Test 0.707 856 0.193 446 0.360 131 Successful 4 Longest Runs Ones 10 000 0.235 903 0.556 629 0.063 0856 Successful 5 Binary Matrix Rank Test 0.443 084 0.298 222 0.045 5016 Successful 6 Spectral Test 0.474 456 1. 0.458 246 Successful 7 Non-Overlapping Template Matching 0.529 55 0.840 569 0.488 286 Successful 8 Overlaping Template Matching 0.544 82 0.981 736 0.375 187 Successful 9 Maurers universal Statistic Test 0.463 56 0.183 854 0.385 959 Successful 10 Linear Complexity Test 0.701 088 0.515 697 0.503 53 Successful 11 Serial Test {0.259 896,0.713 345} {0.326 326,0.718 48} {0.760 873,0.839 907} Successful 12 Approximate Entropy Test 0.344 719 0.223 394 0.141 817 Successful 13 Cumulative Sums Test 0.638 251 0.825 325 0.593 75 Successful 14 Random Excursions Test 0.296 283 0.194 65 0.123 997 Successful 15 Random Excursions Variant Test 1 0.245 779 0.863 832 Successful 16 Cumulative Sums Test Reverse 0.976 076 0.822 779 0.593 75 Successful