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Citation: Li, Y.; Wang, D.; Ding, H.; Li,
Z.; Wang, X. Physical Layer
Encryption for CO-OFDM Systems
Enabled by Camera Projection
Scrambler. Mathematics 2024,12, 1807.
https://doi.org/10.3390/math12121807
Academic Editor: Jonathan
Blackledge
Received: 14 May 2024
Revised: 4 June 2024
Accepted: 7 June 2024
Published: 11 June 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
mathematics
Article
Physical Layer Encryption for CO-OFDM Systems Enabled by
Camera Projection Scrambler
Yujin Li 1, Dongfei Wang 1,2,*, Haiyang Ding 1, Zhenzhen Li 1and Xiangqing Wang 3
1School of Information Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China
2School of Electronics and Information, Nanchang Institute of Technology, Nanchang 330044, China
3School of Physics and Electronic Engineering, Fuyang Normal University, Fuyang 236037, China
*Correspondence: wdfchina@126.com
Abstract: In this paper, we propose a camera projection approach to enhance the physical layer
security of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The
data are converted to the new location by the camera projection module in the encryption system,
where the 5D hyperchaotic system provides the keys for the camera projection module. The sim-
ulated 16QAM CO-OFDM security system over 80 km SSMF is shown to provide a key space of
about
9×1090
through the five-dimensional (5D) hyperchaotic system, making it impossible for
eavesdroppers to obtain valid information, and the peak-to-average power ratio (PAPR) is reduced
by about 0.8 dB.
Keywords: CO-OFDM; 5D hyperchaotic; camera projection; physical layer encryption
MSC: 37D05
1. Introduction
Coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems
are widely used in high-speed and long-distance transmission [
1
–
5
], and the importance of
solving security problems in the transmission process has emerged. The physical layer is
at the bottom of the open system interconnect (OSI) model, and to completely secure the
transmitted data, the advantages of research methods for encryption of the physical layer
are highlighted [6].
Various physical layer encryption methods, such as quantum key distribution (QKD) [
7
],
optical steganography [
8
], optical code division multiple access (OCDMA) [
9
], hardware
chaos encryption [
10
–
13
], and digital chaos encryption [
14
–
24
], etc., have all made signifi-
cant contributions to securing data. Zhang et al. used an implementation of high-speed
QKD in an SiP QKD encoder using a pass-block architecture and a dedicated SiP decoder
based on the polarization-based decoy state Bennett–Brassard 1984 protocol [
7
]. Su et al.
used a multi-user optical steganography transmission system based on filtered amplified
spontaneous emission (ASE) noise, in which stealth signals can be hidden in time and
frequency domains of a common channel to increase the capacity of the stealth chan-
nel [
8
]. Lu et al. used an electro-optical chaotic system with phase modules for time delay
signature elimination through deep learning to enhance nonlinearity. Long short-term
memory (LSTM) networks are trained with specially designed loss functions to enhance
the nonlinear effects [
10
]. Digital chaotic encryption with digital signal processing (DSP)
technology saves a lot of components and is easy to operate, and many researchers have
invested in the work. Zhang et al. enhanced the security of orthogonal frequency-division
multiple access passive optical network (OFDMA-PON) systems by deoxyribonucleic acid
(DNA) encoding and operational cryptographies through chaotic systems [
14
]. Liang et al.
used chaotic Hilbert motion encryption, and Hilbert motion on the key and used the hash
value generated from the encryption result as a digital signature to effectively secure the
Mathematics 2024,12, 1807. https://doi.org/10.3390/math12121807 https://www.mdpi.com/journal/mathematics
Mathematics 2024,12, 1807 2 of 8
OFDM-PON system [
15
]. Bai et al. used Chua’s circuit model to realize an OFDM-PON
security system with polarity-coded chaotic encryption [16].
In this paper, a scrambling method based on camera projection is proposed to offer a
low-complexity and novel design idea for enhancing the security of CO-OFDM systems.
The transmitted data are encrypted by the principle of camera projection mapping, in which
the camera projection matrix is controlled by keys generated by a five-dimensional (5D)
hyperchaotic system. Data in the subcarrier domain, symbol domain, and complex domain
of the three-domain coordinates are visualized in real-world three-dimensional space, and
the three-dimensional coordinates are projected through the camera to obtain homogeneous
coordinates so that the positional transformation of the coordinates reaches the role of data
perturbation. The feasibility and security of the encryption scheme are verified by running
back-to-back (BTB) and 80 km standard single-mode fiber (SSMF) computer simulations
of the CO-OFDM system. The results show that the encryption scheme has a decrease of
0.8 dB in peak-to-average power ratio (PAPR) and a key space size of about 9
×
10
90
and
the analysis of the bit error rate (BER) shows that the encryption scheme does not incur an
additional BER cost. These are good indications that the encryption scheme can effectively
secure the CO-OFDM system.
2. Proposed Algorithm
Figure 1demonstrates the physical layer encryption method to obtain the CO-OFDM
system employing camera projection. Firstly, the raw data are mapped into QAM symbols
after a serial-parallel (S/P) transformation such that the QAM symbols are arranged in
the subcarrier domain N = {1, 2,..., N}, the symbol domain S = {1, 2,..., S}, and the complex
number domain Q = {Re, Im}. Then, 5 keys are generated using the 5D hyperchaotic
system to participate in the encryption process. The projected homogeneous coordinates
are obtained by the method of camera projection of the three-dimensional coordinates
of the original data to realize the effect of data scrambling in the three domains. Finally,
encrypted data are passed through fast Fourier inverse transform (IFFT) and the cyclic
prefix (CP) is added to obtain the encrypted OFDM.
Mathematics 2024, 12, x FOR PEER REVIEW 2 of 8
deoxyribonucleic acid (DNA) encoding and operational cryptographies through chaotic
systems [14]. Liang et al. used chaotic Hilbert motion encryption, and Hilbert motion on
the key and used the hash value generated from the encryption result as a digital signature
to effectively secure the OFDM-PON system [15]. Bai et al. used Chua’s circuit model to
realize an OFDM-PON security system with polarity-coded chaotic encryption [16].
In this paper, a scrambling method based on camera projection is proposed to offer a
low-complexity and novel design idea for enhancing the security of CO-OFDM systems.
The transmied data are encrypted by the principle of camera projection mapping, in
which the camera projection matrix is controlled by keys generated by a five-dimensional
(5D) hyperchaotic system. Data in the subcarrier domain, symbol domain, and complex
domain of the three-domain coordinates are visualized in real-world three-dimensional
space, and the three-dimensional coordinates are projected through the camera to obtain
homogeneous coordinates so that the positional transformation of the coordinates reaches
the role of data perturbation. The feasibility and security of the encryption scheme are
verified by running back-to-back (BTB) and 80 km standard single-mode fiber (SSMF)
computer simulations of the CO-OFDM system. The results show that the encryption
scheme has a decrease of 0.8 dB in peak-to-average power ratio (PAPR) and a key space
size of about 90
910× and the analysis of the bit error rate (BER) shows that the encryp-
tion scheme does not incur an additional BER cost. These are good indications that the
encryption scheme can effectively secure the CO-OFDM system.
2. Proposed Algorithm
Figure 1 demonstrates the physical layer encryption method to obtain the CO-OFDM
system employing camera projection. Firstly, the raw data are mapped into QAM symbols
after a serial-parallel (S/P) transformation such that the QAM symbols are arranged in the
subcarrier domain N = {1, 2,..., N}, the symbol domain S = {1, 2,..., S}, and the complex
number domain Q = {Re, Im}. Then, 5 keys are generated using the 5D hyperchaotic sys-
tem to participate in the encryption process. The projected homogeneous coordinates are
obtained by the method of camera projection of the three-dimensional coordinates of the
original data to realize the effect of data scrambling in the three domains. Finally, en-
crypted data are passed through fast Fourier inverse transform (IFFT) and the cyclic prefix
(CP) is added to obtain the encrypted OFDM.
Figure 1. Physical layer encryption method based on camera projection for CO-OFDM system.
2.1. Camera Skewed Projection
The camera coordinate system is a three-dimensional coordinate system established
at the position of the aperture. The P point under the camera coordinate system is mapped
to the P’ point in the two-dimensional image plane and according to the principle of small-
hole imaging to aain (, ,)Pxyz=, then '( /, /)Pfxzfyz=, where
f
is the focal length.
The origin of the coordinate system of the pixel plane is at the lower left corner, while the
origin of the coordinate system of the image plane is at the center, and an offset of the
origin is required, i.e., '( / , / )
x
y
P
fx z c fy z c=+ +
. Since the image plane is measured in m
and the pixel plane is measured in pixels, the pixel-to-meter conversion quantities k and l
Figure 1. Physical layer encryption method based on camera projection for CO-OFDM system.
2.1. Camera Skewed Projection
The camera coordinate system is a three-dimensional coordinate system established at
the position of the aperture. The Ppoint under the camera coordinate system is mapped to
the P
′
point in the two-dimensional image plane and according to the principle of small-
hole imaging to attain
P= (x
,
y
,
z)
, then
P′= ( f x/z
,
f y/z)
, where
f
is the focal length.
The origin of the coordinate system of the pixel plane is at the lower left corner, while the
origin of the coordinate system of the image plane is at the center, and an offset of the
origin is required, i.e.,
P′= ( f x/z+cx
,
f y/z+cy)
. Since the image plane is measured
in m and the pixel plane is measured in pixels, the pixel-to-meter conversion quantities k
and l need to be decided on for the characteristics of the imaging components to obtain
P′= ( f kx/z+cx
,
f ly/z+cy)
. With
α=f k
,
β=f l
, and
α
,
β
as the camera parameters,
then the homogeneous coordinate is P′= (αx/z+cx,βy/z+cy).
Mathematics 2024,12, 1807 3 of 8
The pixel blocks in the real case are not square, but parallelograms. There will be
angles
θ
between the pixels, and then the mapping relation from the spatial point Punder
the camera coordinate system to the image point P′in the pixel coordinate system will be:
P′=
x′
y′
z′
=
α−αcot θcx0
0β/ sin θcy0
0 0 1 0
x
y
z
1
. (1)
The encryption method is to regard (N, S, Q) as (x,y,z) in the real space, and subse-
quently, the encrypted (x
′
,y
′
,z
′
), which is (N
′
, S
′
, Q
′
), is obtained by processing the camera
projection scrambler of Equation (1). The data scrambling encryption is realized by using
the positional changes on the coordinates of the equation.
2.2. Key Generation and Processing
To defend against strong attacks by eavesdroppers, a 5D hyperchaotic system is
introduced that allows the generation of unpredictable sequences, which is described as:
.
x1=a(x2−x1)
.
x2=cx1+dx2−x1x3+x5
.
x3=−bx3+x12
.
x4=ex2+f x4
.
x5=−rx1−kx5
, (2)
where
{x1−x5}
are state variables,
a>
0,
b>
0,
c
,
d
and fare constant parameters, e
is a coupling parameter, and rand kare two control parameters, where
d>−c
,
er =
0.
Fix
a=
10,
c=
28,
e=
10,
f=
0,
r=
10,
k=
0, and
b∈[
2, 11
]
. The system has two or
three positive Lyapunov exponents of hyperchaotic attractors [
25
]. The resulting
{x1−x5}
sequences are processed as Key1–Key5 by the following equation:
Key1=mod(ceil(abs(x1)), 10000)
Key2=mod(ceil(abs(x2)), 10000)
Key3=mod(ceil(abs(x3)), 10000)
Key4=mod(ceil(abs(x4)), 10000)
Key5=mod(ceil(abs(x5)), 10000)
, (3)
where Key1 and Key2 are the camera parameters
α
and
β
, respectively, Key3 is the skew
angle θ, and Key4 and Key5 are the coordinate offsets cxand cy.
3. Simulation Experiments and Results
The computer simulation experiment for encrypted transmission of camera projections
for 16QAM CO-OFDM is built according to Figure 2. A pseudo-random binary sequence
(PRBS) is generated at the transmitter side as the raw data, which has a length of 204,800 bits.
The original data are mapped into 16QAM symbols, and the signal is converted into a
symbol matrix of the number of subcarriers
×
the number of OFDM symbols by S/P con-
version, and the real and imaginary numbers are separated to obtain the three-dimensional
coordinates (N, S, Q). Next, the camera projection encryption technique obtains the coordi-
nates (N
′
, S
′
, Q
′
) after the perturbation, and the original data are placed according to the
coordinates to obtain the encrypted data. IFFT and added CP processing are performed to
obtain encrypted OFDM symbols, where the CP length is 1/16 of the length of an OFDM
symbol, a training sequence of 20 symbols, and 4 pilots. The encrypted OFDM symbols are
processed through an arbitrary waveform generator (AWG) to obtain an electrical signal.
An external cavity laser (ECL) with a center wavelength of 1550 nm is used as a light source
for an optical IQ modulator so that an encrypted electrical signal is modulated into an
encrypted optical signal by the IQ modulator. A 0 dBm optical signal is transmitted over
Mathematics 2024,12, 1807 4 of 8
80 km SSMF with fiber dispersion of dispersion factor 17
×
10
−27
s
2
/m and Gaussian white
noise. The total attenuation of the optical signal is 15 dB. Optical filtering and coherent
receiver detection are performed to convert the signal into an electrical signal. Where the
laser coherent detection power is a
−
6 dBm optical signal, the linewidth of the local laser is
less than 100 kHz and the frequency offset is ~300 kHz. Perform digital storage oscilloscope
(DSO) sampling. Compensate for IQ timing bias. Perform GSOP compensation for receiver
IQ mismatch [
26
,
27
]. Perform electronic dispersion compensation (EDC) for distortion gen-
erated by dispersion. Carry out frequency bias estimation and phase noise [
28
]. Suppress
narrow-band interference caused by clock leakage of the DAC in the 20 GHz band with an
adaptive trap filter [
29
], and other treatments. After synchronization and S/P conversion
to obtain the signal matrix, the signal is converted to the frequency domain by FFT and the
data are decrypted by camera projection. The decrypted signal is channel estimated and
balanced [
30
], and the remaining phase noise is estimated with the help of the pilots. The
signal is de-mapped to obtain the bit data.
Mathematics 2024, 12, x FOR PEER REVIEW 4 of 8
according to the coordinates to obtain the encrypted data. IFFT and added CP processing
are performed to obtain encrypted OFDM symbols, where the CP length is 1/16 of the
length of an OFDM symbol, a training sequence of 20 symbols, and 4 pilots. The encrypted
OFDM symbols are processed through an arbitrary waveform generator (AWG) to obtain
an electrical signal. An external cavity laser (ECL) with a center wavelength of 1550 nm is
used as a light source for an optical IQ modulator so that an encrypted electrical signal is
modulated into an encrypted optical signal by the IQ modulator. A 0 dBm optical signal
is transmied over 80 km SSMF with fiber dispersion of dispersion factor
27 2
17 10 s / m
−
×
and Gaussian white noise. The total aenuation of the optical signal is 15 dB. Optical fil-
tering and coherent receiver detection are performed to convert the signal into an electri-
cal signal. Where the laser coherent detection power is a -6 dBm optical signal, the lin-
ewidth of the local laser is less than 100 kHz and the frequency offset is ~300 kHz. Perform
digital storage oscilloscope (DSO) sampling. Compensate for IQ timing bias. Perform
GSOP compensation for receiver IQ mismatch [26,27]. Perform electronic dispersion com-
pensation (EDC) for distortion generated by dispersion. Carry out frequency bias estima-
tion and phase noise [28]. Suppress narrow-band interference caused by clock leakage of
the DAC in the 20 GHz band with an adaptive trap filter [29], and other treatments. After
synchronization and S/P conversion to obtain the signal matrix, the signal is converted to
the frequency domain by FFT and the data are decrypted by camera projection. The de-
crypted signal is channel estimated and balanced [30], and the remaining phase noise is
estimated with the help of the pilots. The signal is de-mapped to obtain the bit data.
Figure 2. Simulated experimental plot of a security enhanced 16QAM CO-OFDM system based on
camera projection for transmission over 80 km SSMF. EA: electrical amplifier; IQM: I/Q modulator;
EDFA: erbium-doped optical fiber amplifier; TOF: tunable optical filter; VOA: variable optical aen-
uator; ICR: integrated coherent receiver; FOE: frequency offset estimation; PN: phase noise.
The original and encrypted signals go through a transmission system of CO-OFDM
with BTB and 80 km SSMF, and the relationship between the optical signal noise ratio
(OSNR) and BER is observed in Figure 3. When data are passed through the camera pro-
jection encryption system, the BER of the data stolen by illegal users is about 0.5, which is
equivalent to invalid data. When the OSNR is greater than 21.5 dB, after the authorized
users use the key to decrypt the encrypted data transmied over the BTB and 80 km SSMF,
the data have a BER lower than the forward error correction (FEC), which is equivalent to
valid data. The curves of the original and encrypted signals are very close to each other,
which intuitively reflects that the encryption system has a negligible effect on the BER.
Figure 2. Simulated experimental plot of a security enhanced 16QAM CO-OFDM system based on
camera projection for transmission over 80 km SSMF. EA: electrical amplifier; IQM: I/Q modulator;
EDFA: erbium-doped optical fiber amplifier; TOF: tunable optical filter; VOA: variable optical
attenuator; ICR: integrated coherent receiver; FOE: frequency offset estimation; PN: phase noise.
The original and encrypted signals go through a transmission system of CO-OFDM
with BTB and 80 km SSMF, and the relationship between the optical signal noise ratio
(OSNR) and BER is observed in Figure 3. When data are passed through the camera
projection encryption system, the BER of the data stolen by illegal users is about 0.5, which
is equivalent to invalid data. When the OSNR is greater than 21.5 dB, after the authorized
users use the key to decrypt the encrypted data transmitted over the BTB and 80 km SSMF,
the data have a BER lower than the forward error correction (FEC), which is equivalent to
valid data. The curves of the original and encrypted signals are very close to each other,
which intuitively reflects that the encryption system has a negligible effect on the BER.
The OFDM signals generated by the superposition of multiple subcarriers will have
the same phase signal modulation when the subcarriers are in the same phase, resulting
in the generation of a large PAPR. However, OFDM signals with large PAPR easily cause
nonlinear distortion, which makes the system performance degraded [
1
]. Figure 4depicts
the complementary cumulative distribution function (CCDF) of the PAPR of the original
and encrypted signals in the CO-OFDM system. It is demonstrated that the encryption
scheme can optimize the PAPR performance of the CO-OFDM system by about 0.8 dB,
which in turn reduces the signal impairment.
Mathematics 2024,12, 1807 5 of 8
Mathematics 2024, 12, x FOR PEER REVIEW 5 of 8
Figure 3. Measured BER curves for CO-OFDM signals in different configurations.
The OFDM signals generated by the superposition of multiple subcarriers will have
the same phase signal modulation when the subcarriers are in the same phase, resulting
in the generation of a large PAPR. However, OFDM signals with large PAPR easily cause
nonlinear distortion, which makes the system performance degraded [1]. Figure 4 depicts
the complementary cumulative distribution function (CCDF) of the PAPR of the original
and encrypted signals in the CO-OFDM system. It is demonstrated that the encryption
scheme can optimize the PAPR performance of the CO-OFDM system by about 0.8 dB,
which in turn reduces the signal impairment.
Figure 4. Comparison of the CCDFs for the CO-OFDM signals with and without encryption.
Figure 5a shows a comparison of the sequence 1(400 : 600)x after 1000 iterations of
varying the initial value of 1
x
by a gap of 15
10− in the chaotic system, and Figure 5b
shows a comparison of the sequence 1(400 : 600)x after 1000 iterations of varying the var-
iable parameter b by a gap of 15
10− in the chaotic system. These two plots adequately
illustrate the sensitivity of the 5D hyperchaotic system to initial values and variable pa-
rameter b. Slight variations in the initial values and the parameters of the system make
the resulting sequences different, reflecting the unpredictability of the sequences
Figure 3. Measured BER curves for CO-OFDM signals in different configurations.
Mathematics 2024, 12, x FOR PEER REVIEW 5 of 8
Figure 3. Measured BER curves for CO-OFDM signals in different configurations.
The OFDM signals generated by the superposition of multiple subcarriers will have
the same phase signal modulation when the subcarriers are in the same phase, resulting
in the generation of a large PAPR. However, OFDM signals with large PAPR easily cause
nonlinear distortion, which makes the system performance degraded [1]. Figure 4 depicts
the complementary cumulative distribution function (CCDF) of the PAPR of the original
and encrypted signals in the CO-OFDM system. It is demonstrated that the encryption
scheme can optimize the PAPR performance of the CO-OFDM system by about 0.8 dB,
which in turn reduces the signal impairment.
Figure 4. Comparison of the CCDFs for the CO-OFDM signals with and without encryption.
Figure 5a shows a comparison of the sequence 1(400 : 600)x after 1000 iterations of
varying the initial value of 1
x
by a gap of 15
10− in the chaotic system, and Figure 5b
shows a comparison of the sequence 1(400 : 600)x after 1000 iterations of varying the var-
iable parameter b by a gap of 15
10− in the chaotic system. These two plots adequately
illustrate the sensitivity of the 5D hyperchaotic system to initial values and variable pa-
rameter b. Slight variations in the initial values and the parameters of the system make
the resulting sequences different, reflecting the unpredictability of the sequences
Figure 4. Comparison of the CCDFs for the CO-OFDM signals with and without encryption.
Figure 5a shows a comparison of the sequence
x1
(400:600) after 1000 iterations of
varying the initial value of
x1
by a gap of 10
−15
in the chaotic system, and Figure 5b shows
a comparison of the sequence
x1
(400:600) after 1000 iterations of varying the variable
parameter b by a gap of 10
−15
in the chaotic system. These two plots adequately illustrate
the sensitivity of the 5D hyperchaotic system to initial values and variable parameter b.
Slight variations in the initial values and the parameters of the system make the resulting
sequences different, reflecting the unpredictability of the sequences generated by the system.
The key space size of the camera projection encryption scheme is determined by the initial
values and parameters of the 5D hyperchaotic system, so the key space size provided by the
five initial values and variable parameters b is about (10
15
)
5×
(11
−
2)
×
10
15
= 9
×
10
90
,
which can effectively resist brute force attacks. Table 1shows the comparison of this paper
with some representative schemes in terms of key space. By comparison, it is concluded
that this scheme has superior key space size and low computational complexity compared
to most of the security schemes [
14
,
17
,
18
], some of which have large key space, but require
high computational complexity to achieve this effect [19].
Mathematics 2024,12, 1807 6 of 8
Mathematics 2024, 12, x FOR PEER REVIEW 6 of 8
generated by the system. The key space size of the camera projection encryption scheme
is determined by the initial values and parameters of the 5D hyperchaotic system, so the
key space size provided by the five initial values and variable parameters b is about
15 5 15 90
(10 ) (11 2) 1 0 9 10×−× =× , which can effectively resist brute force aacks. Table 1
shows the comparison of this paper with some representative schemes in terms of key
space. By comparison, it is concluded that this scheme has superior key space size and
low computational complexity compared to most of the security schemes [14,17,18], some
of which have large key space, but require high computational complexity to achieve this
effect [19].
(a) (b)
Figure 5. Sequence 1
x
of the 5D hyperchaotic system and (a) 1'
x
varying with the initial value 1
x
and (b) with the parameter b when n is between 400 and 600.
Table 1. Scheme key space comparison.
Schemes Key Space
DNA encoding [14] 89
2.25 10×
Digital optical polarization scrambling [17] 60
10
Key concealment and distribution based on carrier scrambling [18] 82
10
Chaos key enhanced based on the convolutional long short-term
memory neural network [19]
241
10
The proposed scheme 90
910×
Figure 6 is obtained by adding the analysis of the ability to resist statistical aacks,
where the horizontal coordinate is the constellation points of 16QAM and the vertical co-
ordinate is the percentage of constellation points to the total data. This figure shows that
the distribution of the ciphertext data is uniform and the aacker cannot obtain the infor-
mation by statistical aack.
Figure 5. Sequence
x1
of the 5D hyperchaotic system and (a)
x1′
varying with the initial value
x1
and
(b) with the parameter b when n is between 400 and 600.
Table 1. Scheme key space comparison.
Schemes Key Space
DNA encoding [14]2.25 ×1089
Digital optical polarization scrambling [17]1060
Key concealment and distribution based on carrier scrambling [18]1082
Chaos key enhanced based on the convolutional long short-term
memory neural network [19]10241
The proposed scheme 9×1090
Figure 6is obtained by adding the analysis of the ability to resist statistical attacks,
where the horizontal coordinate is the constellation points of 16QAM and the vertical
coordinate is the percentage of constellation points to the total data. This figure shows
that the distribution of the ciphertext data is uniform and the attacker cannot obtain the
information by statistical attack.
Mathematics 2024, 12, x FOR PEER REVIEW 7 of 8
Figure 6. Ver ification of encrypted signals against statistical aacks.
4. Conclusions
In this paper, we propose an approach that utilizes the idea of camera projection to
enhance the physical layer security and transmission performance of CO-OFDM systems.
The randomized keys obtained through the 5D hyperchaotic system control the camera
projection matrix and thus perturb the data. In the simulation experiments of the encryp-
tion scheme for a 16QAM CO-OFDM system over 80 km SSMF, the results show the fea-
sibility and security of the scheme, which provides a key space of about 90
910× . The
eavesdropper cannot obtain the valid data—only the authorized users can. Also, the PAPR
is reduced by about 0.8 dB.
Author Contributions: Conceptualization, Y.L. and D.W.; methodology, Y.L.; software, Y.L.; valida-
tion, Y.L., D.W. and X.W.; formal analysis, H.D.; resources, Z.L.; data curation, Y.L.; writing—origi-
nal draft preparation, Y.L.; writing—review and editing, D.W.; visualization, Y.L.; supervision, D.W.;
project administration, D.W.; funding acquisition, D.W. All authors have read and agreed to the
published version of the manuscript.
Funding: This work was supported by the R&D Program of Beijing Municipal Education Commis-
sion (KM202310015002), general research project of Beijing Association of Higher Education
(20240014), research project on digital education in Beijing (20240022), Jiangxi Provincial Natural
Science Foundation (20232BAB212006), Scientific Research Project of Fuyang Normal University
(2022KYQD0004), Anhui Education Department, University Natural Science Research Project of An-
hui Province (2022AH051338), Henan Key Laboratory of Visible Light Communications
(HKLVLC2023-B10), and the Youth Excellence Project of Beijing Institute of Graphic Communica-
tion (Ea202411).
Data Availability Statement: The original contributions presented in the study are included in the
article. Further inquiries can be directed to the corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.
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3. Wang, D.; Tang, X.; Xi, L.; Zhang, X.; Zhang, W.; Zhang, H. A scheme to generate 16QAM-OFDM vector mm-wave signal based
on a single MZM without optical filter and precoding. Opt. Commun. 2020, 475, 126227.
4. Agrawal, G.P. Fiber-Optic Communication Systems; John Wiley & Sons: Hoboken, NJ, USA, 2012.
5. Agrell, E.; Karlsson, M.; Chraplyvy, A.R.; Richardson, D.J.; Krummrich, P.M.; Winzer, P.; Roberts, K.; Fischer, J.K.; Savory, S.J.;
Eggleton, B.J.; et al. Roadmap of optical communications. J. Opt. 2016, 18, 063002.
6. Mitev, M.; Pham, T.M.; Chorti, A.; Barreto, A.N.; Feweis, G. Physical layer security-from theory to practice. IEEE BITS Inf.
Theory Mag. 2023, 1–12, doi:10.1109/MBITS.2023.3338569.
Figure 6. Verification of encrypted signals against statistical attacks.
4. Conclusions
In this paper, we propose an approach that utilizes the idea of camera projection to
enhance the physical layer security and transmission performance of CO-OFDM systems.
The randomized keys obtained through the 5D hyperchaotic system control the camera
projection matrix and thus perturb the data. In the simulation experiments of the encryption
Mathematics 2024,12, 1807 7 of 8
scheme for a 16QAM CO-OFDM system over 80 km SSMF, the results show the feasibility
and security of the scheme, which provides a key space of about 9
×
10
90
. The eavesdropper
cannot obtain the valid data—only the authorized users can. Also, the PAPR is reduced by
about 0.8 dB.
Author Contributions: Conceptualization, Y.L. and D.W.; methodology, Y.L.; software, Y.L.; valida-
tion, Y.L., D.W. and X.W.; formal analysis, H.D.; resources, Z.L.; data curation, Y.L.; writing—original
draft preparation, Y.L.; writing—review and editing, D.W.; visualization, Y.L.; supervision, D.W.;
project administration, D.W.; funding acquisition, D.W. All authors have read and agreed to the
published version of the manuscript.
Funding: This work was supported by the R&D Program of Beijing Municipal Education Commission
(KM202310015002), general research project of Beijing Association of Higher Education (20240014),
research project on digital education in Beijing (20240022), Jiangxi Provincial Natural Science Founda-
tion (20232BAB212006), Scientific Research Project of Fuyang Normal University (2022KYQD0004),
Anhui Education Department, University Natural Science Research Project of Anhui Province
(2022AH051338), Henan Key Laboratory of Visible Light Communications (HKLVLC2023-B10),
and the Youth Excellence Project of Beijing Institute of Graphic Communication (Ea202411).
Data Availability Statement: The original contributions presented in the study are included in the
article. Further inquiries can be directed to the corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.
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