Table 12 Cryptographic Randomness Test of the Encrypted Image of Block of 4 × 4.
From: A design of multiple color image encryption scheme based on finite algebraic structures
Test | P-Value for RGB ciphering of encrypted image block \(4\times 4\) | Output | |||
|---|---|---|---|---|---|
Red Channel | Green Channel | Blue Channel | |||
Block frequency | 0.031601345 | 0.023547181 | 0.678442303 | \(\checkmark\) | |
Rank | 256 | 256 | 256 | \(\checkmark\) | |
Frequency | 0.710215435 | 0.387544670 | 0.334531182 | \(\checkmark\) | |
Overlapping templates | 0.636543561 | 0.776892154 | 0.943471243 | \(\checkmark\) | |
Spectral DFT | 0.656686199 | 0.257323376 | 0.177717108 | \(\checkmark\) | |
Runs (M=10000) | 0.213663762 | 0.876554652 | 0.854317934 | \(\checkmark\) | |
Long runs of ones | 0.837235124 | 0.647357428 | 0.7226 | \(\checkmark\) | |
Universal | 0.869316572 | 0.998123043 | 0.928324786 | \(\checkmark\) | |
No overlapping templates | 0.042963112 | 0.230435687 | 0.0106377855 | \(\checkmark\) | |
Serial | p = 1 | 0.3119731634 | 0.0930372163 | 0.55490829110 | \(\checkmark\) |
Serial | p = 2 | 0.488615843 | 0.312438731 | 0.655491012 | \(\checkmark\) |
Cumulative sums forward | 0.05270 | 0.231194834 | 0.145624575 | \(\checkmark\) | |
Cumulative sum reverse | 0.828767435 | 0.706364524 | 0.413216156 | \(\checkmark\) | |
Random excursions Variants | X=−5 | 0.955695873 | 0.412830332 | 0.791970877 | \(\checkmark\) |
X=−4 | 0.899741293 | 0.198542793 | 0.940400322 | \(\checkmark\) | |
X=−3 | 0.654720845 | 0.108319380 | 0.275241873 | \(\checkmark\) | |
X=−2 | 0.248213074 | 0.126630457 | 0.101634225 | \(\checkmark\) | |
X=−1 | 0.243345001 | 0.058781721 | 0.322628546 | \(\checkmark\) | |
X=1 | 0.867632334 | 0.108197247 | 0.597843376 | \(\checkmark\) | |
X=2 | 0.847389653 | 0.230062298 | 0.620669622 | \(\checkmark\) | |
X=3 | 0.765594483 | 0.374857142 | 0.637059371 | \(\checkmark\) | |
X=4 | 0.528733321 | 0.830324257 | 0.920591267 | \(\checkmark\) | |
X=5 | 0.697358343 | 1.0 | 0.725086072 | \(\checkmark\) | |
Random excursions | X=−4 | 0.034012610 | 0.731696895 | 0.529652156 | \(\checkmark\) |
X=−3 | 0.375415680 | 0.021163304 | 0.237713946 | \(\checkmark\) | |
X=−2 | 0.349226729 | 0.2875517263 | 0.2967982526 | \(\checkmark\) | |
X=−1 | 0.096484759 | 0.170562490 | 0.3333385721 | \(\checkmark\) | |
X=1 | 0.4578982272 | 0.017785387 | 0.721425208 | \(\checkmark\) | |
X=2 | 0.582643718 | 0.0428027573 | 0.936978326 | \(\checkmark\) | |
X=3 | 0.871938591 | 0.1908926105 | 0.890659214 | \(\checkmark\) | |
X=4 | 0.953445779 | 0.010566115 | 0.169515566 | \(\checkmark\) | |
