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encrypted images are susceptible to attacks in practical appli- image encryption scheme based on a novel fusion applica-
cations.
In 2020, Kumar et al. [14] demonstrated the 2D multiple pa-
rameters fractional discrete cosine transform (2D-MPFrDCT)
and the 3D-chaotic logistic map (3D-LCM) to present a new
encryption and decryption method for optical and digital dou-
ble color images. A random phase mask (RPM) produced by
3D-LCM was multiplied by the second scrambled image.
In 2021, Man et al. [15] proposed a double grayscale im-
age encryption algorithm based on dynamic adaptive diffu-
sion, five-dimensional (5D) chaos, and CNN. The algorithm
used a two-channel (optical channel/digital channel) encryp-
tion method supported by a novel image bit-level split-fusion
scheme, which depends on the amount of information it holds.
Further, a chaotic sequence was employed as a convolution
kernel of CNN to generate a plaintext-related chaotic pointer
to control the scrambling operation of two images. The optical
encryption channel used DRPE scheme.
In 2021, Liao et al. [22] introduced a two-step DL strategy
for ciphertext image-only attacks (COA) on a classical DRPE
system. In particular, they built a virtual DRPE system to
collect the training data. In Addition, the inverse problem
in COA was split into two more specific inverse problems.
Two deep neural networks (DNNs) were used after training to
respectively learn the removal of speckle noise in the autocor- 2)
relation domain and the de-correlation operation to retrieve
the plaintext image.
In 2021, Ni et al. [23] suggested a multiple image encryption
approach based on CS and DL in the optical gyrator trans-
form (GT) domains. Various measurements were obtained
after compression of the images using CS, then the pixels of
each measure were scrambled using a chaotic system. The
scrambled measurements were combined into a matrix and
diffused by XOR operation with a chaotic matrix. Later, the
diffused matrix was encoded with an RPM and an optical
gyrator transform to obtain a complex-valued matrix, which
was taken as the ciphertext.
In 2022, Abuturab et al. [17] investigated using CS, chaotic-
biometric keys, and optical FrFT for multiple-color image
fusion, compression, and encryption. The original four-color
images were split into four sub bands in the proposed cryp-
tosystem. Four sub bands were merged to create a single
image separated into R, G, and B channels, where CS com-
presses each channel. The measurement matrix was a circulant
matrix based on a logistic map’s random sequence. The com-
pressed R and G channels produce the first chaotic-biometric
phase mask (CBPM), while the compact B channel produces
the second CBPM. The resulting complex image is modulated
by a second CBPM, then FrFT. The final encrypted image was
a phase- and amplitude-truncated.
In 2022, Zhang et al. [24] proposed a secure double grayscale
Muttashar & Fyath
tion of CS and DRPE optical transformation technology. The
method not only realizes the compression and encryption of
two images into one image but also realizes image authentica-
tion.
In 2022, Zhang et al. [25] evaluated the use of DL to create a
single-exposure phase-only optical image encryption and hid-
ing (POIEH) technique. The original image and correspond-
ing encrypted hidden interferogram acquired with POIEH
were used to train an end-to-end designed U-net. Once the
relationship between the encrypted hidden interferogram and
the reconstructed image was learned, only a single-frame
encrypted hidden interferogram was needed to reconstruct
POIEH.
The main conclusions drawn from this survey as related to
double and multiple image encryption are
1)
The maximum dimension of the used chaotic system is 5D.
It is expected that going to higher-dimensional chaos will
increase the level of encryption security and open new space
keys to support further the quality measures of the encryption
process.
The optical transform (such as Fourier transform (FT), FrFT,
and GT)-based encryption methods used a double random
phase encoding approach. It is interesting to investigate these
optical transform-based methods using double chaotic (or
hybrid chaotic/random) phase-encoding approaches.
3)
The use of DL to enhance double and multiple-image optical
inception is limited in the open literature. This issue needs
further investigation to enhance the optical encryption capa-
bility.
This paper aims to design a high-secure optical scheme for
multiple color image encryption incorporating deep learning
techniques for performance enhancement. This aim may be
achieved through the following steps
A.
Proposing a chaotic-based HDOE scheme to make use of
the advantages behind both digital and optical encryption
algorithms.
B.
Using a high-order chaotic system such as a 9D system to
enhance the security level and robustness of the proposed
HDOE algorithm.