Page 12 - 2024-Vol20-Issue2

8| Yousif, Hameed & Al-Zuhairi

(a) (b) (c)

(d) (e) (f)
Fig. 3. The Test Images (a) Cameraman (b) Lena (c) Baboon (d) Barbara (e) Boat (f) Peppers

of 256 gray levels (L = 256), the maximum ideal value for the following mathematical equations [17]:
information entropy is 8. Usually, higher values of entropy
imply a more secure ciphering system. The computed results 1N
of information entropy for the six test original images and ?E(x) = xi
their corresponding ciphered images are given in Table II.
From the obtained values in this table, it is obvious that the N i=1
entropy values for all the ciphered images are extremely near
to the optimal value. This indicates that the encrypted images ?1 N (10)
produced by the TIC cryptosystem are so close to random
sources and therefore the suggested algorithm can withstand D(x) = (xi - E(xi))2
the entropy attack. N
i=1
3) Correlation Analysis:
cov(x, y) = 1 N
There is a strong correlation among adjoin pixels in the ordi- N
nary image along three directions due to the massive amount ?(xi - E(x))(yi - E(y))
of redundancy data. In contrary, less correlation between the
adjacent pixels in the encrypted image indicates a strong im- i=1
age cipher. Several couples of adjacent pixels are chosen to
compute the correlation coefficient value in a particular direc- cov(x, y)
tion. The correlation coefficient rxy is described according to rxy = D(x) × D(y)

where x and y are two adjoin pixels in the image, E(x), D(x)
and cov(x, y) indicate the mean, variance and covariance, re-
spectively. The range of rxy is in the interval [-1, 1]. If the
value of rxy is high, then the correlation between two neigh-
boring pixels is strong and vice versa. Any two couples of
adjoining pixels in the plain image commonly possess a potent
correlation. An effective ciphering technique should weaken
or break this correlation. In the TIC algorithm experiments,