Table 10 Chi-square test results.
From: Novel structures of chaos-based parallel multiple image encryption and FPGA implementation
\(\chi ^2\) of encrypted images in the exemplar simulation using Structure 1 in Fig. 1a | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(N_e\) | 1 | 2 | 3 | 4 | 5 | ||||||||||
Channel | R | G | B | R | G | B | R | G | B | R | G | B | R | G | B |
Baboon | 225.024 | 274.968 | 274.831 | 283.294 | 278.586 | 238.726 | 270.159 | 236.399 | 276.024 | 266.733 | 272.489 | 244.002 | 278.942 | 256.361 | 231.366 |
Flowers | 287.042 | 241.166 | 229.438 | 248.549 | 261.338 | 287.673 | 266.248 | 251.737 | 252.365 | 264.305 | 277.905 | 251.847 | 266.132 | 276.033 | 250.014 |
Peppers | 271.232 | 246.325 | 226.382 | 272.219 | 241.743 | 227.020 | 212.012 | 246.864 | 245.899 | 256.662 | 267.964 | 239.662 | 269.368 | 245.315 | 271.356 |
Goldhill | 256.172 | 223.146 | 269.022 | 255.493 | 268.755 | 258.332 | 225.218 | 269.318 | 278.298 | 227.722 | 253.505 | 252.721 | 241.462 | 284.386 | 258.382 |
Black | 258.190 | 275.968 | 266.930 | 242.293 | 266.213 | ||||||||||
Boats | 232.903 | 244.562 | 246.557 | 264.909 | 299.651 | ||||||||||
Clock | 237.016 | 251.578 | 260.742 | 272.211 | 270.281 | ||||||||||
White | 267.814 | 262.724 | 283.123 | 258.653 | 215.717 | ||||||||||
Average | 251.292 (Pass) | 259.785 (Pass) | 255.493 (Pass) | 257.099 (Pass) | 261.311 (Pass) | ||||||||||
\(\chi ^2\) of encrypted images in the exemplar simulation using Structure 2 in Fig. 1b | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(N_e\) | 1 | 2 | 3 | 4 | 5 | ||||||||||
Channel | R | G | B | R | G | B | R | G | B | R | G | B | R | G | B |
Baboon | 226.044 | 260.122 | 260.563 | 236.239 | 277.043 | 263.742 | 248.465 | 235.881 | 274.929 | 253.086 | 251.480 | 301.811 | 286.812 | 227.428 | 234.404 |
Flowers | 267.646 | 205.408 | 292.405 | 248.334 | 287.783 | 259.227 | 295.285 | 231.308 | 252.419 | 273.642 | 233.257 | 262.540 | 243.087 | 282.856 | 227.670 |
Peppers | 263.356 | 269.438 | 255.138 | 234.802 | 251.378 | 280.429 | 220.387 | 260.395 | 249.479 | 255.202 | 249.676 | 290.457 | 270.369 | 251.735 | 220.364 |
Goldhill | 266.360 | 269.895 | 268.893 | 280.378 | 249.177 | 232.245 | 280.120 | 252.197 | 253.164 | 273.825 | 235.658 | 294.107 | 304.127 | 255.396 | 238.926 |
Black | 241.076 | 251.418 | 276.914 | 230.526 | 216.151 | ||||||||||
Boats | 233.224 | 262.757 | 250.315 | 261.549 | 230.815 | ||||||||||
Clock | 240.406 | 222.055 | 244.469 | 255.430 | 273.727 | ||||||||||
White | 211.514 | 240.997 | 238.493 | 261.427 | 245.593 | ||||||||||
Average | 251.968 (Pass) | 254.875 (Pass) | 254.014 (Pass) | 261.480 (Pass) | 250.591 (Pass) | ||||||||||
\(\chi ^2\) of encrypted images in the exemplar simulation using Structure 3 in Fig. 1c | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(N_e\) | 1 | 2 | 3 | 4 | 5 | ||||||||||
Channel | R | G | B | R | G | B | R | G | B | R | G | B | R | G | B |
Baboon | 258.603 | 235.392 | 280.506 | 253.197 | 276.450 | 265.444 | 259.392 | 251.960 | 233.137 | 243.712 | 258.878 | 274.037 | 269.745 | 261.978 | 270.443 |
Flowers | 235.692 | 296.968 | 220.527 | 219.684 | 245.689 | 273.235 | 295.500 | 219.682 | 262.359 | 205.923 | 232.756 | 231.313 | 267.801 | 254.817 | 233.418 |
Peppers | 265.548 | 249.135 | 266.452 | 220.354 | 227.686 | 267.629 | 255.489 | 275.327 | 256.135 | 247.028 | 255.613 | 239.657 | 228.358 | 273.516 | 265.902 |
Goldhill | 231.418 | 249.874 | 218.995 | 222.326 | 247.528 | 237.083 | 267.491 | 278.048 | 203.367 | 241.728 | 271.877 | 219.586 | 245.952 | 265.682 | 253.891 |
Black | 203.720 | 245.266 | 267.113 | 266.415 | 256.545 | ||||||||||
Boats | 281.506 | 257.516 | 273.678 | 286.019 | 263.912 | ||||||||||
Clock | 237.133 | 255.656 | 218.313 | 186.922 | 234.008 | ||||||||||
White | 235.127 | 247.135 | 258.162 | 240.050 | 259.806 | ||||||||||
Average | 247.912 (Pass) | 247.617 (Pass) | 254.697 (Pass) | 243.845 (Pass) | 256.611 (Pass) | ||||||||||
