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TABLE IV.
RESULTS OF KEY SENSITIVITY AT DECRYPTION WITH SLIGHTLY MODIFIED KEYS
Modified secret keys by adding ? UACI (%)
38.3964
(d) of RSA algorithm 35.1154
35.0457
(x0) of Duffing map 34.8304
(a) of Duffing map 34.8787
35.0486
(a) of Lu¨ system 34.9767
(b) of Lu¨ system
(x0) of Lu¨ system
z0 of Lu¨ system
analyze the algorithm performance. The algorithm speed
relies upon the time needed for both ciphering/deciphering
operations. The required time for these two processes depends
on several parameters like operating system used and its con-
figuration, code optimization, and the utilized programing
language [32, 33]. The information about the utilized environ-
ment for experiential findings has been mentioned in Section
IV. The six test grayscale images with different sizes are uti-
lized for assessing the TIC speed performance. The ciphering
and deciphering time required for each image size are listed
in Table V. It is observed from Table V that the requisite time
for encryption and decryption stages is influenced by the im-
age size, which implies that big image requires longer time.
As an example, the proposed scheme needs 0.154946 s and
0.670657 s, respectively to cipher/decipher the Cameraman
test image with size 256 × 256, while this time is increased
to be 1.580442 s and 2.502797 s, respectively for the same
image with size 1024 × 1024. Also, the decryption time is
more than the encryption time for all test images. For in-
stance, the time needed to encrypt the Lena image of size
256 × 256 is 0.162288 s, whereas the time required to decrypt
the same image of same size is 0.643419 s. Based on the
computed encryption/decryption time outcomes in Table V,
it can be found that the ciphering time obtained by the pre-
sented work is considered very short for system having three
stages of encryption: zigzag shuffling, RSA and chaotic maps
with two phases: confusion and diffusion. Therefore, the
TIC is efficient and fast to be utilized in practical applications tacked by cutting parts of various sizes from it to produce the
to encrypt/decrypt images of various sizes throughout open
networks.
E. Robustness Analysis
1) Noise Attack Analysis:
Robustness of the ciphered image to noise is an essential re-
quirement for an efficient encryption scheme. Gaussian noise
is the most common noise that may impact on the encrypted
image during transmission [20]. This noise with different
levels is added at the simulation to the encrypted image Boat
for assessing the current algorithm performance. The cipher
Yousif, Hameed & Al-Zuhairi
NPCR (%) PSNR (dB) rxy
99.62 9.1753 0.0024
99.63 10.5947 -0.0068
99.60 10.6220 -0.0191
99.61 7.6114 -0.0104
99.59 7.6073 -0.0212
99.64 7.5778 -0.0064
99.57 7.5902 -0.0232
version of Boat is influenced by various densities of Gaus-
sian noise (0.1, 0.05, 0.02, 0.01 and 0.006, respectively), and
the obtained noisy decrypted images corresponding to the
attacked cipher images are presented in Fig. 8. Furthermore,
PSNR and correlation between the noisy restored images and
original image Boat against noise density are shown in Fig. 9
to test the deciphered image quality at the receiver. It can be
watched in these figures that the visual quality of the recon-
structed image increases progressively as the noise intensity
decreases, but the manifestation of the plain image can be
readily recognized from the retrieved image even at high level
of noise density in the ciphered image. Additionally, it is
evident from Fig. 9 that PSNR and correlation values increase
gradually with noise intensity decreasing, such that PSNR and
correlation change from 14.8482 dB to be 26.6204 dB, and
from 0.6977 to be 0.9242, respectively when the noise inten-
sity varies from 0.1 to 0.006. It can be manifested from the
above simulation outcomes that in the existence of noise, the
deciphered image is shown visibly in spite of the high degree
of noise density. Hence, the TIC can successfully resist the
noise attack.
2) Cropping Attack Analysis:
Cropping attack analysis intends to evaluate the robustness
of cryptosystem against cutting parts of the encrypted image
through transmission [47]. The cipher image Peppers is at-
attacked cipher images as exhibited in Figs. (10a-10e). Then,
the attacked cipher images are deciphered to get the restored
outcomes as revealed in Figs. (10f-10j), whereas the results
of PSNR and correlation between the input and deciphered
images for Peppers test image are tabulated in Table VI. It is
obvious in these figures that when the cropping size is large
(for example, 1/2 of the cipher image), the visible quality of
deciphered image decreased; this quality is enhanced as the
cropping size becomes small (for example, 1/8 of the cipher
image). In addition, PSNR and correlation values in Table
VI increase with the decreasing of crop size, such that these
values vary from 10.0189 dB and 0.3957 to be 18.9409 dB