Page 172 - 2024-Vol20-Issue2

168 | Muttashar & Fyath

Fig. 2. A simplified block diagram of the proposed
double-color image encryption scheme using hybrid
digital/optical algorithms.

C.
Using deep learning DnCNN to reduce the noise level of the
received encrypted images.

III. PROPOSED DOUBLE-COLOR IMAGE Fig. 3. Block diagram of the proposed DCI-HDOE scheme.
ENCRYPTION/DECRYPTION SCHEME
The chaotic dynamics is described by
This section describes a hybrid digital / optical encryption
/ decryption scheme for a double-color image (DCI). The C1 = s b1C1 -C2C4 + b4C42 + b3C3C5 - s b2C7
scheme is based on a 9D chaotic system and assisted by DL for
denoising the decrypted images. The proposed HDOE scheme C2 = -sC2 +C1C4 -C2C5 +C4C5 - sC9/2
uses a double chaotic phase encoding technique implemented
in the Fourier transform domain. The contribution behind the C3 = -s b1C3 +C2C4 + b4C22 - b3C1C5 + s b2C8
design of the process is also reported.
C4 = -sC4 -C2C3 -C2C5 +C4C5 + sC9/2
A. Proposed Encryption Scheme
The proposed DCI scheme is based on an HDOE algorithm C5 = -s b5C5 +C22/2 -C42/2 (1)
implemented with a 9D chaotic system. The scheme contains
several steps, as shown in the following subsections. A simple C6 = -b6C6 +C2C9 -C4C9
block diagram of the DCI-HDOE scheme is shown in Fig. 2,
and a detailed description of the system is given in Fig. 3. C7 = -b1C7 - rC1 + 2C5C8 -C4C9
The encryption scheme consists mainly of cascading a digital
encryption sub scheme (DEsS) controlled by three outputs of C8 = -b1C8 + rC3 - 2C5C7 +C2C9
the chaotic system (C1,C2, and C3) and an optical encryption
subscheme (OEsS) controlled by the rest six outputs of the C9 = -C9 - rC2 + rC4 - 2C2C6 + 2C4C6 +C4C7 -C2C8.
chaotic system (C4, ...,C9). The two-color images are first
applied to the DEsS to produce a single digital encrypted The control parameters s , r, b1, b2, b3, b4, b5 and b6 are time-
image IDEnc which then passes through the OEsS to yield the independent parameters used to control the chaotic dynamics.
final encrypted image IEnc.
The phase space projections of the 9D attractor is shown in
1) Nine-dimensional Chaotic System
In this work, two-color image encryption subschemes are Fig. 4, assuming s = 0.5, b1 = 10/3, b2 = 5/3, b3 = 6/5, b4
designed, one for the digital domain and the other for the = 1/5, b5 = 4/3, b6 = 8/3 and r = 24.00 . The used initial
optical domain. The 9D chaotic dynamical system adopted to conditions are C1(0) = 0.01, C2(0) = 0, C3(0) = 0.01, C4(0) =
control the two subschemes is based on reference [26]. This 0, C5(0) = 0, C6(0) = 0, C7(0) = 0, C8(0) = 0 and C9(0) = 0.1.
system has two Lyapunov exponent (LE), which indicates
the generation of hyper-chaotic dynamics. As a result, the 2) Digital Encryption Subscheme
system is suitable as the key generator of image encryption. Two-color images I1 and I2 each of size M×N is applied to
this subscheme to yield a single-color encrypted image IDE .
M and N are the numbers of rows and columns, respectively,
in each image’s R, G, and B channels. The algorithm of DEsS
consists of four steps: fusion process, image combining, XOR