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 6. ${\rm P}$-value test results (NIST-800-22) for chaotic series ${u}_{3}\left(t\right),$ at different values of $\alpha .$

S. No Test Name $\alpha $ = 1 $\alpha $ = 0.99 $\alpha $ = 0.92 Results 1 Mono bitFrequency Test 0.981 575 0.623 605 0.724 701 Successful 2 Block Frequency Test 0.702 138 0.786 538 0.330 245 Successful 3 Runs Test 0.145 69 0.463 838 0.724 432 Successful 4 Longest Runs Ones 10 000 0.746 165 0.415 693 0.423 45 Successful 5 Binary Matrix Rank Test 0.685 773 0.574 195 0.570 329 Successful 6 Spectral Test 0.194 273 0.633 482 0.474 456 Successful 7 Non-Overlapping Template Matching 0.834 296 0.498 41 0.512 831 Successful 8 Overlaping Template Matching 0.219 927 0.664 717 0.230 988 Successful 9 Maurers universal Statistic Test 0.235 758 0.139 78 0.688 589 Successful 10 Linear Complexity Test 0.709 004 0.523 366 0.803 015 Successful 11 Serial Test {0.412 075,0.209 017} {0.197 128,0.442 195} {0.437 12,0.534 607} Successful 12 Approximate Entropy Test 0.734 978 0.135 837 0.845 66 Successful 13 Cumulative Sums Test 0.845 347 0.770 349 0.791 612 Successful 14 Random Excursions Test 0.654 05 0.281 157 0.428 759 Successful 15 Random Excursions Variant Test 0.262 747 0.326 878 0.391 404 Successful 16 Cumulative Sums Test Reverse 0.825 325 0.360 73 0.635 598 Successful