Page 178 - 2024-Vol20-Issue2

174 | Muttashar & Fyath

TABLE II.
THREE-DIRECTION CORRELATION COEFFICIENTS FOR

VARIOUS ORIGINAL COLOR IMAGES.

Images Channel VD HD DD
Lena Red 0.9477 0.9733 0.9259
Baboon Green 0.9474 0.9736 0.9270
Barbara Blue 0.9078 0.9486 0.8360
Airplane Red 0.8360 0.7723 0.7765
Sailboat Green 0.7523 0.6643 0.6604
Peppers Blue 0.8498 0.8007 0.7937
Red 0.9423 0.9736 0.9239
Green 0.9295 0.9681 0.9072
Blue 0.9417 0.9738 0.9234
Red 0.8906 0.8832 0.8180
Green 0.9099 0.9035 0.8497
Blue 0.8464 0.8237 0.7500
Red 0.8773 0.8654 0.8188
Green 0.9404 0.9379 0.9072
Blue 0.9426 0.9428 0.9137
Red 0.9350 0.9394 0.8987
Green 0.9642 0.9704 0.9425
Blue 0.9292 0.9381 0.8919

Fig. 18. Histograms of the decrypted images (a) Lena (b) H. DnCNN Results
baboon (c) Barbara (d) airplane (e) sailboat and (f) peppers. A four-layer DnCNN is designed in this work. Fig. 25 shows
the root mean square error (RMSE) and loss function curve
F. Key Sensitivity Analysis for training using a dataset of 931 images dataset. After 37240
The sensitivity of the encryption process to the initial condi- iterations, the RMSE decreases significantly and somewhat
tions of the chaotic parameters used to generate the chaotic settles between 1% and 2% RMSE values. While there is a
phase masks are examined here. Lena and baboon images are decrease in the curve of the loss function with respect to the
used as examples to test the sensitivity to the initial conditions number of iterations, which is about 0.4. This means that the
of the key. As depicted in Fig. 24 even if a tiny deviation proposed DnCNN structure does well despite the insufficient
is made for one of the deciphering key parameters (chaotic data set, and there is no overfitting in the training process.
initial condition), the decryption process fails. This indicates The PSNR measurement is used for the validation of this
that the key of the proposed technique is extremely sensitive. design. Table IV illustrates the PSNR values before and after
Investigation of the results also indicate that the maximum
allowable variation in the initial condition value to yield suc- TABLE III.
cessful decryption is 10-17. CORRELATION COEFFICIENTS IN THE THREE DIRECTIONS

G. Key Space Analysis FOR VARIOUS COLOR-ENCRYPTED IMAGES.
A key space analysis is performed to determine the number
of distinct keys that can be used in the encryption proce- Images Channels VD HD DD
dure. The proposed image encryption scheme assumes that BLaebnoao-n Red -0.0012 -0.0013 -0.0002
the transmitter and receiver share the secret keys and vari- Green 0.0018 -0.0004 0.0020
ables via a secure channel. seventeen keys are involved here: ABiarprblaanrae- Blue 0.0010 -0.0000 0.0005
a, r, b1, b2, b3, b4, b5, b6,C1,C2,C3,C4,C5,C6,C7,C8, and C9. Red 0.0032 0.0038 -0.0019
Because the calculation precision of the double precision num- PSeapiplbeorsat- Green -0.0052 0.0029 -0.0013
ber is 10-16, the key space of the algorithm will be more than Blue 0.0004 -0.0024 0.0047
(1016)17 = 2903 > 2100 which is sufficiently large to resist all Red -0.0041 0.0053 -0.0013
types of brute force attacks. Green 0.0004 -0.0013 -0.0000
Blue -0.0011 0.0093 -0.0017