Page 11 - 2024-Vol20-Issue2

7| Yousif, Hameed & Al-Zuhairi

Algorithm 1: The proposed image encryption method.

// A: Input image of size (m, m).

// E2: Output image of size (m, m).

// k: Total blocks number (even value).

1: Divide A into 8 × 8 non-overlapping blocks from top to bottom.

2: Join the odd blocks of A to get M. % M of size (8 ×8 × k )
2
k
3: Join the even blocks of A to get N. % N of size (8 ×8 × 2 )

4: Set x0, y0, z0, a, b, c values of Lu¨ System.

5: Produce u, v, w according to (4). % u, v, w of size (m2)

6: Quantize v, w to obtain ' , ' . ' ' (vi' ,wi' ).

v w v w

7: Choose the first k elements of , to form the pair of % i = 1, 2, . . . , k

8: Select the starting pixel position (row, column) according to (vi' ,wi' ).
'
9: Apply zigzag scan (Fig. 1b) according to w2i-1' ) on each block of M to get Y1. % Y1 of size ( 64 k
(v2i-1 , 2)
'
10: Apply zigzag scan (Fig. 1c) according to w2i' ) on each block of N to get Y2 . % Y2 of size ( 64 k
(v2i , 2)
11: Concatenate Y1 and Y2 to get Y ' . %Y ' of size ( 64k)
Reshape Y ' to get Y1' . %Y1' of
12: Apply RSA according to (5) size (m, m) F.
13: on Y1' to gain

14: Set x0, y0, a, b values of Duffing map.

15: Produce x, y according to (3). % x, y of size (m2)

16: Reshape x, y to gain x1, y1. % x1, y1of size (m, m)

17: Sort x1, y1in ascending order according to (6) to obtain (L1, d1) and (L2, d2).
18: Scramble F via (L1, d1) to get E1(confusion) according to (7).
19: Quantize and reshape u to gain u' . % u' of size (m, m)
20: Diffuse E1 via u' to get E2(diffusion) according to (8). % E2of size (m, m)

CPU. For the performance assessment, six different stan- usually utilized for measuring the cryptosystem performance.
dard grayscale images are used as test images, each of size In general, an efficient ciphering system has a uniform his-
256 × 256. The images are chosen from USC-SIPI image togram [8]. The outcomes of histogram analysis achieved by
database (http://sipi.usc.edu/database/). The image files are: TIC are clarified in Fig. 5 . Figs. 5a and 5b represent the
Cameraman, Lena, Baboon, Barbara, Boat and Peppers, which histograms of the Cameraman grayscale plain image and its
are displayed in Fig. 3. The RSA secret parameters are: 33, 7 corresponding encrypted image, respectively. Fig. 5a reveals
and 3 for n, e and d, respectively. For duffing map, the values that the plain image pixels values are concentrated at some
of initial conditions and system parameters are: 0.11, -0.6, values, whereas the encrypted image, Fig. 5b, pixels values
2.75 and 0.15 for x0, y0, a and b, respectively. For Lu¨ system, are fairly uniform, flat and completely distinct from that of
the values of secret keys are: 0.4, -0.5, 0.7, 36, 3 and 13 the original image. Moreover, the histogram of the recovered
for x0, y0, z0, a, b and c, respectively. The ciphered version of image in Fig. 5c is similar to that of the plain text image.
Cameraman image produced via the presented image cryp- No helpful data about the original image can be assembled
tosystem is given in Fig. 4a, whereas the deciphered image by histogram analysis, which points that the TIC has enough
result using the assigned secret keys is shown in Fig. 4b. It is ability to endure the statistical attacks.
obvious that the ciphered image comprises no beneficial in-
formation in comparison with its corresponding original one; 2) Information Entropy Analysis:
it is meaningless and a noise-like. On the other hand, the de- Information entropy H(X) is a significant measure employed
ciphered and the plain images are identical, which manifests for measuring the randomness or uncertainty of information
that TIC can cipher and decipher images effectively. in the plain image [23]. This metric is calculated as:

A. Statistical Analysis L-1 (9)
1) Histogram Analysis:
Histogram is a kind of bar diagram that illustrates the pixel H(X) = - ? P(xi)log2P(xi)
values distribution of the image at particular intensity. It is i=0

where X symbolizes a random variable, and P(xi) is the oc-
currence probability of xi. For a random grayscale image