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Fig. 2. Block Diagram of The Suggested Encryption Scheme
after determining the initial conditions/system parameters
values (x0, y0, a, b).
Step 12: Reshape x and y to the same size of matrix F to
generate the two matrices x1,y1, then x1 and y1 are sorted in
ascending order:
[L1, d1] = sort(x1), [L2, d2] = sort(y1) (6)
where d1, d2 represent the new sequences, and L1,L2 denote
the index values of d1 and d2, respectively.
Step 13: Choose (L1) combination for shuffling F to get the
confused image E1as:
E1(i, j) = F(L1(i, j)) (7)
Step 14: Choose u of Lu¨ chaotic sequence to perform the
diffusion process after reshaping it to the same size of matrix crypted image E2 and finishes up with the original image
E1 to generate u1 matrix. The diffused image E2 is generated
according to the formula:
E2(i, j) = E1(i, j) ? u1(i, j) (8)
where E2 represents the earned ciphered image. If the plain
image is a color image (RGB image), A(m, m, 3), then A is
divided into three layers: R(m, m),G(m, m) and B(m, m). Af-
ter this, the encryption Steps (1-14) are implemented on each
Yousif, Hameed & Al-Zuhairi
layer separately to get the three ciphered images. The ulti-
mate step is concatenating them to acquire the final encrypted
image E2(m, m, 3).
In addition, the proposed work is applied on images of equal
dimensions, A(m, m). But if the input image is not square,
A(m, n), then a particular technique (interpolation technique)
should be applied to avoid falling-off out of range during split-
ting the image into (8×8) non-overlapping blocks. Algorithm
1 illustrates the encryption steps of the proposed cryptosystem
with more details.
B. Decryption Procedure
The procedure of image decryption can be executed by apply-
ing the encryption stages in the inverted order. The receiver
gets the correct secret keys from the sender. The deciphered
image is gained according to contrary process of the above
explained steps. The decryption process begins from the en-
A.
IV. IMPLEMENTATION RESULTS AND
SECURITY ANALYSIS
The experiments of encryption-decryption operations of TIC
algorithm are implemented using MATLAB (R2013a), 64-bit
Windows 7, on HP personal Laptop computer with Proces-
sor Intel (CORE i3), 4 GB RAM memory, and 2.40GHz