Page 15 - 2024-Vol20-Issue2

11 | Yousif, Hameed & Al-Zuhairi

TABLE II.
RESULTS OF INFORMATION ENTROPY, PSNR, MSE, UACI AND NPCR FOR THE TEST IMAGES

Image Plain entropy Cipher entropy UACI (%) NPCR (%) PSNR (dB) MSE
Cameraman 7.0097 7.9974 33.9472 99.61 6.3604 1.5033×104
Lena 7.4318 7.9971 33.3258 100 6.6813 1.3962×104
Baboon 7.2285 7.9970 33.2240 99.99 6.4303 1.4793×104
Barbara 7.3913 7.9974 33.7393 99.90 6.9521 1.3118×104
Boat 7.1583 7.9969 33.9939 99.86 5.8159 1.7041 ×104
Peppers 7.5647 7.9970 33.5428 99.74 6.4938 1.4578 ×104

TABLE III.
RESULTS OF CORRELATION COEFFICIENTS BETWEEN TWO NEIGHBORING PIXELS IN THE PLAIN AND ENCRYPTED

IMAGES OVER THREE DIRECTIONS FOR THE TEST IMAGES

Image Horizontal Vertical Diagonal

Cameraman Plain image Cipher image Plain image Cipher image Plain image Cipher image
Lena
Baboon 0.9289 -9.6603 × 10-5 0.9124 -3.9055 × 10-4 0.9113 3.9393 × 10-4
Barbara
Boat 0.9492 4.9266 × 10-4 0.9356 -3.6102 × 10-4 0.9126 2.6482 × 10-4
Peppers
0.8751 4.2133 × 10-5 0.7643 -9.5688 × 10-4 0.7780 -9.4679 × 10-4

0.9467 6.7268 × 10-4 0.9345 4.7278 × 10-4 0.9245 4.9117 × 10-4

0.9506 -4.0670 × 10-4 0.9140 1.7182 × 10-5 0.9145 -5.4659 × 10-4

0.9424 -8.4578 × 10-4 0.9122 -7.1571 × 10-4 0.8963 6.2330 × 10-4

C. Exhaustive Analysis Duffing map) with variation of ? = 10-14, while preserving
other keys values. This changed key is employed for deci-
1) Key Space Analysis: phering the encrypted image to analyze the key sensibility in
the decryption phase. The corresponding reconstructed im-
The most significant feature of any cryptography algorithm ages using these inaccurate keys are explained in Figs. 7c-7i,
is the key space. Ideal cryptosystem should possess a large whereas the decrypted image by employing the right keys is
key space in order to defeat the exhaustive attack. Broadly, displayed in Fig. 7b. It is explicit that the output decrypted
the key space size should be larger than 2100 [45–47]. The images in these figures are quite distorted and any helpful
key space includes all the secret keys that have been utilized information about the input image cannot be revealed even if
in the ciphering process. For the current method, the secret a slight error occurred in the secret keys. Moreover, the cryp-
keys of RSA algorithm are p, q and d. In the confusion stage, tosystem is validated by calculating the PSNR, UACI, NPCR
Duffing map is adopted with two initial values: x0, y0, and two and correlation coefficient between the input image Barbara
system parameters: a, b. In the diffusion stage, Lu¨ system is (Fig. 3d) and the other resultant decrypted images obtained
exploited with three initial values: x0, y0, z0, and three control from slightly altered keys (Figs. 7c- 7i) as listed in Table IV.
parameters: a, b, c. Hence, there are totally 13 secret keys. The UACI and NPCR values in this table demonstrate that
If the computational accuracy of each secret key is 10-14, the differences between the original image (Fig. 3d) and the
then the key space size is equal to: 1013 14 = 10182 ˜ 2605. retrieved images (Figs. 7c-r7i) are more than 99 %, which
So, this technique possesses an adequate large key space to means that almost all pixels are modulated as compared with
counter the exhaustive attacks. the plaintext image. Additionally, the values of PSNR and the
correlation are extremely small. From the results in Fig. 7 and
2) Key Sensitivity Analysis: Table IV, it can be disclosed that any trivial variation in the
decryption keys yields a noisy restored image, which proves
Ideal image cryptosystem should possess a high sensitivity to the algorithm sensibility to the decryption secret keys.
all of its secret keys used in both ciphering and deciphering
phases to withstand the brute force attacks. This implies that D. Computational Speed Analysis
a tenuous alteration in one of the utilized secret keys should
yield a great deformation in the decrypted images. To test the Ciphering and deciphering speeds of any cryptographic sys-
keys sensitivity, Barbra image is encrypted using the TIC and tem are significant criterion of security demands in order to
the resultant ciphered image is clarified in Fig. 7a. Then, one
secret key is changed (as example, the initial parameter (x0 of