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using a three-dimensional (3D) chaotic map and 2D-multiple
parameter fractional Fourier transform (FrFT) [14]. In 2021,
Faragallah et al. presented an OE algorithm for color images
using 2D logistic-based FrFT [5].
The main challenge facing researchers working in optical
image encryption is how to design efficient OE and HDOE
schemes incorporating the following issues (which have been
usually suggested as future work in their publications).
1)
Developing the existing designs or suggesting new designs to
support multiple color image encryption. Most of the related
work reported in the literature has been concerned mainly with
single-color image [16] and to less extent for double-color
image [15]. Very few works have been reported on multiple
color images [17].
Fig. 1. Block diagrams of different image encryption 2)
schemes (a) Digital encryption (b) Optical encryption (c) Incorporating advanced encryption-assisted techniques such
Cascaded hybrid digital/optical encryption (d) Hybrid image as deep learning (DL) and chaos. These two techniques
encryption using correlated digital and optical subschemes. have already been adopted in digital image encryption and
need to be modified for OE. Few publications have been ap-
techniques [5, 11]. In this case, the system is called a hybrid peared in the literature describing the design of DL-assisted
digital/optical encryption (HDOE) scheme. Fig. 1a-d briefly OE schemes, which concerned mainly with single-color im-
illustrate the main concepts of these different image encryp- ages [18,19]. Although chaotic dynamic systems have already
tion schemes using block diagram description. Note that the been adopted in OE, the dimension (order) of these dynamics
DE scheme needs an introductory stage where the image is does not exceed five. This is also true for DE counterparts. A
digitized before going to the DSP-based algorithms Fig. 1a. higher-order chaotic system is expected to play a key role in
In contrast, the OE scheme deals directly with the 2D image increasing the encryption level and robustness.
Fig. 1b. The hybrid encryption scheme is generally based on
cascaded DE and OE parts Fig. 1c. However more efficient II. RELATED WORK
hybrid encryption scheme has been proposed in the literature
where DE is used to control different parts of the OE scheme This section presents a brief literature survey on double and
Fig. 1d. multiple-image optical encryption methods. Due to the lim-
Recently, there has been increasing interest in using chaotic ited number of published articles using deep learning on this
dynamic systems in the design of image encryption/decryption topic, the survey is extended to cover deep learning-assisted
schemes to increase the level and robustness of security. The single-image optical encryption.
dynamic of a chaotic system is very sensitive to initial condi- In 2018, Huo et al. [20] suggested a double random phase
tions. To ensure a successful image decryption, two iden- encoding (DRPE) and compressive sensing (CS)-based mul-
tical chaotic sources with the same initial conditions are tiple image binary and grayscale optical encryption method.
used, one on the encryption side and the other on the autho- The multiple-image compressed sample data were integrated
rized user decryption side. Different chaotic-based algorithms and extracted using orthogonal encoding and used CS to sam-
have been proposed for DE [4, 12], OE [10, 13], and hybrid ple each plaintext image during the encryption process. The
HDOE [14, 15]. Increasing the dimension (i.e., order) of the results revealed that the hybrid multiple-image encryption ap-
chaotic system plays a key role to enhance the encryption proach minimizes key data while maintaining system security.
process’s efficiency. For example, Kumar et al. proposed in In 2019, Chen et al. [21] proposed a method to increase the
2020 an HDOE encryption algorithm for a double-color image robustness of 2D/3D optical image encryption using dilated
deep CNN. They adopted DRPE in the FrFT domain and in-
troduced the pixel position scrambling method to increase
the security of the encryption system. A fast and effective
denoising convolution neural network (DnCNN) based on
the DL concept was employed to overcome the problem that
