2021

[1]Harshil Bhatt

1]Department of Electronics and Communication Engineering, Manipal Institute
of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India

# Increasing Physical Layer Security through Hyperchaos in VLC Systems

Ashish Sharma<EMAIL_ADDRESS><EMAIL_ADDRESS>[

###### Abstract

Visible Light Communication (VLC) systems have relatively higher security
compared with traditional Radio Frequency (RF) channels due to line-of-sight
(LOS) propagation. However, they still are susceptible to eavesdropping. The
proposed solution of the papers have been built on existing work on
hyperchaos-based security measure to increase physical layer security from
eavesdroppers. A fourth-order Henon map is used to scramble the constellation
diagrams of the transmitted signals. The scramblers change the constellation
symbol of the system using a key. That key on the receiver side de-scrambles
the received data. The presented modulation scheme takes advantage of a higher
degree of the map to isolate the data transmission to a single dimension,
allowing for better scrambling and synchronization. A sliding mode controller
is used at the receiver in a master-slave configuration for projective
synchronization of the two Henon maps, which helps de-scramble the received
data. The data is only isolated for the users aware of the key for
synchronization, providing security against eavesdroppers. The proposed VLC
system is compared against various existing approaches based on various
metrics. An improved Bit Error Rate and a lower information leakage are
achieved for a variety of modulation schemes at an acceptable Signal-to-Noise
Ratio.

###### keywords:

visible light communication, sliding mode control, physical layer security,
chaos synchronization, constellation scrambling

###### pacs:

[

MSC Classification]94A60, 68P25

##  1 Introduction

Optical wireless communication is considered a promising technology for indoor
wireless communication due to the virtually unlimited and unlicensed spectrum
of visible light. Due to this, Visible Light Communication (VLC) has had
interest from researchers. In this form of wireless communication, an array of
white light-emitting diodes (LEDs) is used as a transmitter, while a
photodiode acts as a receiver. VLC has several promising features which
complement the traditional Radio Frequency (RF) wireless communication. VLC
systems are unaffected by the interference caused due to RF-based networks.
They can also supplement radio-based networks where RF signals are
significantly attenuated Blinowski2019SecuritySurvey . VLC systems have a
lower cost since the need for a carrier is eliminated as most indoor and
outdoor environments are well illuminated. VLC is considered a safer
technology compared to radio-based technology as it does not generate RF
multi-band interference Blinowski2019SecuritySurvey . Hence, VLC based
technology can be utilized in hazardous environments such as petroleum
refineries and applications where WiFi communication causes interference, such
as aircraft cabins.

Security requirements for VLC are similar to general security requirements for
all wireless communication. Due to noisy environments, signal superposition
may occur, leading to distortion and causing a drop in the authenticity and
integrity of the signal at the receiver end. Since a VLC transmitter
broadcasts data, shielding of the information from eavesdroppers is a
significant concern Lu2015High-SecurityShifting . The coherence of light
limits the throughput of VLC systems. The coherent length defines the minimum
distance from which meaningful phase information can be retrieved. This
coherence distance is  $\ignorespaces 20\mu$ m for LEDs, making phase
modulation inappropriate for VLC Classen2016OpportunitiesLayer .

Existing research lies in masking the transmitted data with a chaos map. This
is discussed in more detail in Section 2. We propose a novel hyperchaotic VLC
system to improve the system’s security from an eavesdropper. Chaotic systems
are highly sensitive to the initial value, never repeating and exhibit a non-
periodic long term behaviour. This provides an advantage while transmitting
data. We use a four-dimensional (4D) hyperchaotic Henon map to generate chaos
which is used to scramble the constellation of the transmitted data. A sliding
mode controller is used for chaos synchronization. The system is designed as a
DC Optical Orthogonal Frequency-Division Multiplexing (DCO-OFDM) modulation
using Intensity Modulated/Direct Detection (IM/DD).

The proposed solution utilizes a 4D Henon map to generate hyperchoas in the
transmitter providing users 4 dimensions of data, which can be used
independently to implement algorithms to improve physical layer security of
any given system. The paper contributes in presenting results of a multi-
dimensional hyperchaotic map in a VLC channel. It also presents a novel
approach of scrambling constellations of transmitted data and the effect of
multiple layers of scrambling on BER and information leakage of a system. We
achieve satisfactory BER and throughput, indicating increased physical layer
security in VLC against eavesdroppers.

The rest of the paper is organized as follows: Section 2 summarises relevant
work followed by Section 3 which describes the hyperchaotic map, the chaos
sequence generation and synchronization. Section 4 describes the proposed
system followed by the description of the communication channel in Section 5.
The simulation results are discussed in Section 6. Finally, the paper is
concluded with Section 7.

##  2 Literature Review

In recent years, Elgala2011 ; Elgala2009 ; Kumar2010  have been the first
papers to survey LED-based VLC systems with their applications Sevincer2013 .
brings attention to LEDs ability to provide smart-lighting and data
transmission simultaneously. Similarly, Wu2014  expands on the benefits and
challenges of VLC in the comparison of RF networks. The authors in
Karunatilaka2015  investigated various methods for enhancing the performance
of VLC, like modulation techniques and dimming control techniques. The authors
in Qiu2016  concentrated on different channel models for VLC, whereas
Sindhubala2016  inspected noise sources and noise mitigation methods for VLC.
In a recent comparative study between a user-centric and network-centric
design for VLC channels, various positioning and localization techniques were
reviewed for indoor and outdoor VLC applications Zhuang2018 . On the other
hand, a survey reported all the optimization techniques aimed to improve the
performance of VLC systems. The emphasis was given to new technologies like
Non-Orthogonal Multiple-Access (NOMA), Simultaneous Wireless Information and
Power Transfer (SWIPT), cooperative transmission and Space Division Multiple
Access (SDMA) Obeed2019 .

While VLC systems provide better security than RF-based technology, security
is still a significant concern due to the open nature of this technology.

Leung-Yan-Cheong et al. started the notion of secrecy capacity Parker . After
which, Oggier et al. derived the secrecy capacity expressions for wiretap
channels, assuming Both the legitimate user’s and eavesdropper’s Channel State
Information (CSI) is known Oggier2011 .

VLC based technologies work do not penetrate walls like RF, improving
security. Claasen et al. show eavesdropping is still possible, even from
outside the room, using door gaps, windows, keyholes or hiding eavesdropping
devices in the room Classen2015TheSN . Mostafa et al. propose a solution
establishing secure communication zones where eavesdropping is physically
impossible Wang2018Physical-layerAnalysis . However, this reduces the range of
the VLC transmitter. Lapodoth et al. formulate a theoretical rationale for
jamming VLC systems Lapidoth1998TheChannel . For a system at peak intensities,
a channel with limited capacity and sufficient transmitting power, the channel
will saturate and obscure the data source. This is also achievable with
multiple rogue low-power transmitters.

Chaos is defined as aperiodic, long-term behaviour in a deterministic system
that exhibits sensitive dependence on initial conditions. A chaotic system
needs to be aperiodic, unlike an unstable system where infinity works as a
fixed point the system is repelled towards. A dynamic system must be sensitive
to initial conditions, topologically transitive and have dense periodic orbits
to be classified as chaotic. Hyperchaos is defined by its characteristic of
having one or more positive Lyapunov exponent than chaos, providing greater
security in communication Strogatz2018 .

Although the infusion of chaos in Visible Light Communication is novel, it has
become more prevalent. There have been different approaches for gaining better
security, such as channel scrambling and modulated M-Quadrature Amplitude
Modulation (M-QAM) Mapper XiaogeWu2016 . A substantial drawback is the high
Bit Error Rate (BER) caused by adding chaos maps, making a VLC system
unsuitable for regular use.

Lee et al. analyze different chaos maps and propose a chaos map that has anti-
jamming characteristics Ryu2013 . Sadoudi et al. proposed a robust additive
hyperchaotic masking algorithm and implemented it on FPGAs Sadoudi2013 . A
significant drawback is that the system is only suitable for wired digital
communication. Fu et al. propose a hyperchaos based medical image protection
scheme. An extensive analysis is also carried out highlighting the security of
the approach Fu2015 . Hammami et al. present a third-order Henon map to
encrypt one-dimensional audio signals Hammami2016 . Yang et al. implement a
fractional-order hyperchaotic system and numerically simulate the
synchronization. The authors make use of adaptive control and fractional order
stability to implement an adaptive self-synchronization controller Yang2015 .

Gunawan et al. propose and implement a Colour-Shift Keying (CSK) OFDM, using
RGB LEDs, providing three channels for communication Gunawan2020 . Using three
channels instead of a single channel from a regular LED helps increase the
system’s data rate. Chen et al. improve this work by using a chaos-based
channel scrambling scheme capable of changing the communication channel
dynamically. This improves the security of the system Chen2016 . A notable
drawback of this proposal is the increased BER, which makes it unsuitable for
use at high data rates or regular use. Fang et al. propose a chaotic generator
based on the Gram-Schmidt Normalisation to reduce the BER using CSK Fang2017 .

Most research to increase VLC systems’ security involves masking the
transmitted data with a chaos map. Based on the analysis above, a novel system
in which a hyperchaos map is used to scramble the constellation diagrams of
the transmitted data is proposed. The transmitter and receiver have different
initial states for the hyperchaos generator, and a sliding mode controller is
used to synchronize them. Our approach builds upon existing research
summarised above, along with a novel approach of scrambling constellations to
increase security.

##  3 4D Hyperchaotic Henon Map

In the proposed system, a 4D Henon map is used to drive the hyperchaotic
transmitter. The transmitter and receiver are set at different initial values,
and a sliding mode controller is used to synchronize them. The hyperchaotic
map scrambles the transmitted data, providing security from eavesdroppers.

A Henon map is a discrete-time dynamic system that maps two points into
themselves. We use a 4D Henon map as described by the  $\ignorespaces 4^{th}$
order system of difference equation Richter2002TheChaos .

$\begin{gathered}x_{1}(k+1)=a-x_{3}^{2}(k)+-bx_{4}(k)\\\
x_{2}(k+1)=x_{1}(k)\\\ x_{3}(k+1)=x_{2}(k)\\\
x_{4}(k+1)=x_{3}(k)\end{gathered}$ (1)

Where,  $\ignorespaces x_{1}(k)$ ,  $\ignorespaces x_{2}(k)$ ,  $\ignorespaces
x_{3}(k)$ and  $\ignorespaces x_{4}(k)$ are the state variables and
$\ignorespaces a$ and  $\ignorespaces b$ are the system parameters.

Let  $\ignorespaces X_{c}=[x_{1},x_{2},x_{3},x_{4}]^{T}$ . Equation 1 exhibits
hyperchaotic behaviour when system parameters  $\ignorespaces a=1.76$ and
$\ignorespaces b=0.1$ AbdulRahman2019SecureSystems . The trajectories for the
4D Henon map with the aforementioned system parameters are plotted in Figure
LABEL:fig:trajectory_henon_map.

Figure 1: State trajectories of the 4D hyperchaotic Henon map

For a system to exhibit hyperchaos, it requires a minimum of four dimensions.
Due to this, we choose a 4D Henon map to scramble the transmitter data. A
higher-order Henon map can generate hyperchaos in the cascade of scramblers
without the need for generating newer maps. Hyperchaos occurs when a system
has two positive, one null and one negative Lyapunov exponents. Due to the
extra positive Lyapunov exponent, hyperchaotic systems exhibit more complex
dynamical characteristics than chaotic systems.

###  3.1 Chaotic Sequence Generator

The transmission and receiver system is defined by Equation 1 and 2
respectively.

$\begin{gathered}y_{1}(k+1)=a-y_{3}^{2}(k)+-by_{4}(k)\\\
y_{2}(k+1)=y_{1}(k)\\\ y_{3}(k+1)=y_{2}(k)\\\
y_{4}(k+1)=y_{3}(k)\end{gathered}$ (2)

Where,  $\ignorespaces y_{1}(k)$ ,  $\ignorespaces y_{2}(k)$ ,  $\ignorespaces
y_{3}(k)$ ,  $\ignorespaces y_{4}(k)$ are the state variable of the receiver
and  $\ignorespaces a$ ,  $\ignorespaces b$ are system parameters. Let
$\ignorespaces Y_{c}=[y_{1},y_{2},y_{3},y_{4}]^{T}$ .  $\ignorespaces u(k)$ is
defined as the sliding mode controller developed for projective
synchronization (PS) of the two systems.

The controller brings $\lim_{x\to\infty}$e(k) =0
$,where\begin{minipage}[t]{433.62pt}\rm\ignorespaces
\trivlist\par\trivlist@item@[]\hbox{\hbox{\hbox to0.0pt{\indent\hskip
0.0pt\hss}}\hskip
0.0pt\hbox{\hbox{}\hbox{\ignorespaces$\ignorespaces\alpha$}}}\par\endtrivlist\ignorespaces\end{minipage}isthescalingfactorforsynchronization.Theerrorismodeledaccordingtothefollowingequations.\begin{equation}e(k)=y(k)-\alpha(k)\end{equation}\par
TheerrorforeachdimensioniscalculatedasshowninEquation\ref{eq:error}.\par\begin{equation}\begin{gathered}e_{1}(k+1)=(1-\alpha)a+\alpha
x_{3}^{2}(k)-y_{3}^{2}(k)-be4(k)\\\ e_{2}(k+1)=e_{1}(k)\\\
e_{3}(k+1)=e_{2}(k)\\\ e_{4}(k+1)=e_{3}(k)\end{gathered}\end{equation}\par$

###  3.2 Synchronization of the 4D Henon Maps

The controller used for the synchronization is a sliding mode controller. A
sliding mode controller is used as it is highly scalable with increasing
dimensions, and the sliding surface is derived from the Lyapunov exponents of
the Henon maps. The sliding surface of the controller is defined by Equation
5. $S(k)=e_{1}(k)+c_{1}e_{2}(k)+c_{2}e_{3}(k)+c_{3}e_{4}(k)$ (5) Where,
$\ignorespaces c_{1}$ ,  $\ignorespaces c_{1}$ and  $\ignorespaces c_{1}$ are
the design parameters given by the root of  $\ignorespaces
P(s)=s^{3}+c_{1}s^{2}+c_{2}s+c2=0$ . From the sliding surface in Equation 5,
the controller is derived as AbdulRahman2019SecureSystems
$u(k)=(1-qT)S(k)-\epsilon_{1}(\lvert
S(k)\rvert)^{\beta}sgn(S(k))-\epsilon_{2}T(\lvert
S(k)\rvert)^{\gamma}sgn(S(k))\\\
-c_{1}e_{1}(k)-c_{2}e_{2}(k)-c_{3}e_{3}(k)+be_{4}(k)-\alpha
x_{3}^{2}(k)+y_{3}^{2}(k)-a+\alpha$ (6) Where  $\ignorespaces
T>0,\epsilon_{1}>0,\epsilon_{2}>0,q>0,(1-qT)>0,0<\beta<1$ and
$\ignorespaces\gamma>1$ . The controller ensures as $k\to+\infty$, the errors
in all the dimensions  $\ignorespaces e_{1},e_{2},e_{3},e_{4}$ will converge
to zero.

##  4 System Design

Figure 2: System schematics The system is designed to be a DCO-OFDM modulation
using IM/DD. A brief overview of the design of the model is presented in
Figure 2. The data is initially converted from serial to parallel and mapped
using the PSK/QAM sequence. The M-QAM mapped data is given by  $\ignorespaces
X=[X_{1},X_{2}...X_{m}]^{T}$ , which is then scrambled using the cascade of
scramblers with the help of the 4D Henon map generator. The data is then set
to hermitian symmetry  $\ignorespaces
X^{\prime}=[0,X^{\prime}_{1}...X^{\prime}_{m},0,X^{\prime}_{1}...X^{\prime}_{m}]^{T}$
. The data is transformed to hermitian symmetry to get real values when the
data goes through Inverse Fast Fourier Transform (IFFT), as LEDs cannot
transmit imaginary data. The data can be represented as
$S_{i,j}=\frac{1}{N_{d}}\sum\limits_{n=1}^{N_{d}}{{{{X^{\prime}}}}_{i,n}e^{\left({J\frac{2\pi}{N}(n\mathrm{-1)(}j\mathrm{-1)}}\right)}}$
(7) Where  $\ignorespaces S_{i,j}$ and  $\ignorespaces X_{i,j}$ , are the
$\ignorespaces j^{th}$ and  $\ignorespaces k^{th}$ samples of  $\ignorespaces
S_{i}$ and  $\ignorespaces X_{i}$ , respectively. The data is transformed from
parallel to serial, and a cyclic prefix (CP) is added. Then it is transformed
from analog to digital, and DC biasing is added, which is essential as LEDs
cannot transmit negative voltage. The data is finally converted from
electrical to an optical signal and transmitted via a visible light
communication channel described in Section 5. The incoming data is first
converted from an optical signal to an electrical signal using a photodiode.
This signal is then filtered at the receiver side, and gain is added before
converting it to a digital signal from analog. After the CP is removed, the
signal goes through a Fast Fourier Transform (FFT), and hermitian symmetry is
removed. We use the Least-Square Method for channel estimation. This then
works as an input to the sliding mode controller and gives the synchronization
constant,  $\ignorespaces u(k)$ . This synchronization constant is fed to the
receiver’s chaotic generator, which helps synchronize the two hyperchaotic
maps. The data is then de-scrambled using the synchronized 4D Henon map, and
the mapped data is finally converted from parallel to serial.

###  4.1 Constellation Scrambling

Scrambling is a common technique in encryption. There have been many
approaches to scrambling. We propose a technique for constellation symbol
scrambling using the 4D hyperchaotic Henon map. The scrambler is defined as
$\begin{gathered}X_{real}=real(X)*sign(x_{a})\\\
X_{imaginary}=imaginary(X)*sign(x_{b})\\\
X=X_{real}+X_{imaginary}\end{gathered}$ (8) Where  $\ignorespaces X$ is the
mapped constellation matrix of the system and  $\ignorespaces x_{a}$ ,
$\ignorespaces x_{b}$ are the dimensions of the Henon map. The hyperchaos
generator gives a random sequence of numbers of the range
$\ignorespaces(-2,2)$ . Thus, this scrambling system is entirely random
without the actual key to the synchronization sliding mode controller. Since
we use a 4D Henon map, we can improve the security by implementing a cascade
of scramblers. This provides more security than single-layered scramblers by
encoding the data into higher dimensions. With the given four dimensions of
the map, we can create a cascade of six scramblers using different mapping
dimensions.

###  4.2 Complexity

In the proposed method, most complexity is due to the chaotic generator, IFFT
and the channel scrambling. The IFFT requires
$\ignorespaces((N_{d})/2)\log_{2}N_{d}$ complex multiplication. The
computational complexity of the chaotic generating sequence with N is of the
order of O(N). The last part contributing to the system’s complexity is the
scrambling operations, which is of the order of O(N). In the proposed system
of 16QAM OFDM, we take the length of the scrambled digitally modulated symbol
sequence needed is  $\ignorespaces N/4$ . Thus the total complexity for six
scrambler in cascade can be written as. $O(N\log_{2}N)+O(N)+6*2*O(N/4)\\\ $
(9) And, total complexity for a single scrambler can be represented as
$O(N\log_{2}N)+O(N)+2*O(N/4)\\\ $ (10)

##  5 Communication Channel

###  5.1 LOS Impulse Response

The Line of Sight (LOS) impulse response, given an emitter E and receiver R
with distance  $\ignorespaces d_{0,R}$ as shown in Figure 3 is given by
Rodriguez2013  $h^{\left(0\right)}\left(t\mathchar
24635\relax\;E,R,\lambda\right)=\frac{1}{\left(d_{0,R}\right)^{2}}R_{E}\left(\varphi,n,\lambda\right)A_{\mathrm{eff}}\left(\psi\right)\delta\left(t-\frac{d_{0,R}}{c}\right)$
(11) where  $\ignorespaces R_{E}\left(\varphi,n,\lambda\right)$ represents the
generalized Lambertian model used to approximate the radiation pattern of the
emitter, c is the speed of light and  $\ignorespaces A_{eff}$ is the effective
signal-collection area of the receiver, which is given by
$A_{\mathrm{eff}}\left(\psi\right)=A_{R}\operatorname{cos}\left(\psi\right)\hskip
2.5pt\mathrm{rect}\left(\frac{\psi}{\mathrm{FOV}}\right)$ (12) The emitter is
generally modelled using a Lambertian radiation pattern for each wavelength
and has axial symmetry (independent of $\gamma$). Thus the receiving power can
be represented as
$\begin{array}[]{c}R_{E}\left(\varphi,n,\lambda\right)=\frac{n+1}{2\pi}P_{E}\left(\lambda\right)\operatorname{cos}^{n}\left(\varphi\right),\\\
\hskip 70.0001pt-\frac{\pi}{2}\leq\varphi\leq\frac{\pi}{2},\hskip
10.00002pt0\leq\gamma\leq 2\pi\end{array}$ (13) Where  $\ignorespaces n$ is
the mode number of the radiation lobe, which specifies the directionality of
the emitter, integrating  $\ignorespaces P_{E}(\lambda)$ over the emitter
wavelength interval yields the nominal power  $\ignorespaces P_{E}$ emitted by
the emitter. Figure 3: Geometry of emitter and receiver without reflectors

###  5.2 Noise Model

A Free-Space Optical (FSO) communication channel with the help of LEDs is
used. The received signal can be represented as $I_{p}(t)=RP_{t}(T)\otimes
h(t)+n(t)$ (14) Where  $\ignorespaces R$ is the photodiode responsivity,
$\ignorespaces P_{t}(t)$ the instantaneous transmitted power,  $\ignorespaces
h(t)$ is the channel impulse response, and  $\ignorespaces n(t)$ is the
variance of Total noise for the VLC System which is represented as the
variance of the sum of shot noise and thermal noise Komine2004 .
$N_{total}=\sqrt{N_{thermal}^{2}+N_{shot}^{2}}$ (15) Where,  $\ignorespaces
N_{total}$ is the total noise in the system,  $\ignorespaces N_{shot}$ is the
shot noise, and  $\ignorespaces N_{thermal}$ is the thermal noise. Shot noise
and Thermal noise is represented as
$\begin{split}N_{shot}^{2}=2q(P_{r}+P_{n})B\\\
N_{thermal}^{2}=\frac{4KT}{BR_{f}}\end{split}$ (16) Where  $\ignorespaces q$
is the charge on an electron,  $\ignorespaces P_{r}$ is the received noise
power,  $\ignorespaces P_{n}$ is the received optical power, and
$\ignorespaces B$ is the detector bandwidth. Moreover,  $\ignorespaces K$ s
the Boltzmann constant,  $\ignorespaces T$ is the absolute temperature and
$\ignorespaces R_{f}$ is the feedback resistance. Thus, the received signal
can be represented as $Y(t)=TX(t)*H_{loss}+N_{total}(t)$ (17) Where
$\ignorespaces Y(t)$ the received signal,  $\ignorespaces X(t)$ the
transmitted signal,  $\ignorespaces H_{loss}$ is the channel impulse response
which is taken as a constant as, during the results, the data rate has not
been changed.

###  5.3 Information Leakage

Assuming that 0 and 1 have equal probability of getting transmitted, the
mutual information between the transmitted data X and the data Y recovered by
eavesdroppers is. $I_{k}(Y\mathchar 24635\relax\;TX)=H_{k}(Y)-H_{k}(Y\textbar
TX)=1+p_{k}{\log_{2}p_{k}}+(1-p_{k}){\log_{2}(1-p_{k})}$ (18) Where
$\ignorespaces H_{k}(.)$ represents the entropy operation and  $\ignorespaces
p_{k}$ is the BER for each user of the proposed system.

##  6 Simulation

In this section, we evaluate the performance of the proposed system and
compare it against existing results. We use BER and Information Leakage to
represent the increased security of the system. The proposed VLC system is
simulated using Matlab and Simulink to show the performance achieved for
various modulation schemes. The simulation parameters are summarised in Table
1. Notation Definition Symbol Rate $\ignorespaces 1Gbps$ Room Size
$\ignorespaces 5*3*3\ m$ Transmitter Position $\ignorespaces(0,0,3)m$ Receiver
Position $\ignorespaces(2.5,2.5,0)m$ LED Power $\ignorespaces 3.2W$ Active
Area $\ignorespaces 1cm$ Half Angle FOV $\ignorespaces 85\degree$ Semi-angle
at half power $\ignorespaces 60\degree$ Optical Filter Gain $\ignorespaces
1.0$ Table 1: Simulation parameters of VLC Figure 4: Transmitted and received
photo for legitimate user and eavesdropper The initial condition for the two
4D Henon maps are given by  $\ignorespaces x_{1}(0)=0.1$ ,  $\ignorespaces
x_{2}(0)=-0.1$ ,  $\ignorespaces x_{3}(0)=0.1$ ,  $\ignorespaces x_{4}(0)=0.1$
,  $\ignorespaces y_{1}(0)=0.3$ ,  $\ignorespaces y_{2}(0)=-0.1$ ,
$\ignorespaces y_{3}(0)=0.2$ ,  $\ignorespaces y_{4}(0)=0.1$ , and parameters
for the sliding mode controller are given by  $\ignorespaces T=1$ ,
$\ignorespaces\epsilon_{1}=0.1$ ,  $\ignorespaces\epsilon_{2}=0.1$ ,
$\ignorespaces q=0.7$ ,  $\ignorespaces\alpha=0.8$ ,
$\ignorespaces\gamma=1.2$ ,  $\ignorespaces\beta=0.9$ ,  $\ignorespaces
c_{1}=0.001$ ,  $\ignorespaces c_{2}=0$ ,  $\ignorespaces c_{3}=0$ where the
scaling factor is  $\ignorespaces\alpha=0.8$ . Figure 5: BER vs SNR of
different modulation schemes for legitimate user and eavesdropper Figure 6:
Information Leakage vs SNR Figure 7: BER for single and cascading encryption
schemes The environment is set up as an empty room of size 5x5m and height 3m.
A  $\ignorespaces(5,5,3)m$ empty room is used as the simulation environment.
The transmitter is in the middle of the room on the ceiling
$\ignorespaces(0,0,3)m$ . The receiver is on the ground near the end of the
wall  $\ignorespaces(2.5,2.5,0)m$ . Figure 4 shows the transmitted image and
the received image for a legitimate user as well as for eavesdropper. A clear
image is shown for the legitimate users, whereas almost no information is
received for the eavesdropper. We achieve a very low information leakage for
the system of  $\ignorespaces 10^{-5}$ , indicating better results compared to
the existing system of around  $\ignorespaces 0.1$ Chen2016 . Figure 5
presents a relation between the BER and Signal-to-Noise Ratio (SNR) using
BPSK, QPSK and 8PSK modulation schemes for legitimate users and eavesdroppers
to represent the security of the system in case of no key. Without the key,
the BER of the system for all spatial modulation does not drop below
$\ignorespaces 0.49$ , exclaiming the capacity of security. On the other hand,
a relatively low BER can be seen for adequate SNR. We achieve a BER of
$\ignorespaces 10^{-6}$ , which is similar to existing results with decreased
complexity of the system, making it easier to implement on IoT devices
XiaogeWu2016 . Moreover, the increased BER of  $\ignorespaces 0.49$ indicates
better security than the present system.

(a) Histogram of transmitted image

(b) Histogram of Received Image for Legitimate user

(c) Histogram of Received Image for Eavesdropper

Figure 8: Histogram for transmitted and received image Figure 6 demonstrates
the Information Leakage of the proposed system at different SNR for the
previously mentioned spatial modulation schemes, with and without the key. The
graph indicates that the low-security leakage for eavesdroppers, not going
above  $\ignorespaces 0.1$ . Moreover, all legitimate user modulation schemes
go to one below  $\ignorespaces 25dB$ SNR. Figure 9: Information Leakage for
single and cascading encryption schemes Figure 7 compares the BER achieved by
the two encryption schemes proposed. The cascaded encryption consists of six
scramblers, where all the dimensions of the Henon map are used more
effectively to scramble the constellations than the single-layered encryption.
Cascaded systems provide more security than single-layered systems. However, a
higher BER is observed for both legitimate users and eavesdroppers than
single-layered systems. The complexity of a cascaded system is also relatively
higher. Figure 8 demonstrates the transmitted and the received histograms of
the image for the legitimate user and the eavesdropper. The histogram for the
legitimate users is near perfect to the transmitted image, whereas for the
eavesdropper, it is not recognizable. On testing the transmitted image and
received using the Two-sample Kolmogorov-Smirnov test, the  $\ignorespaces p$
-value for legitimate users came out to be one. On the other hand, it came out
to be  $\ignorespaces 1.5252e-14$ for an eavesdropper. The system was tested
for QPSK with cascade encryption and SNR  $\ignorespaces 25db$ .

##  7 Conclusion

A system design for increasing the physical layer security has been proposed
for visible light communication-based systems. The system gives a versatile
and less complex approach where one can choose the number of scramblers
depending on the SNR for optimal transmission. The BER was calculated for
different modulation schemes for legitimate users and eavesdroppers, and the
best results were obtained for 8PSK modulation. The system achieves a BER of
$\ignorespaces 10^{-6}$ for and SNR of  $\ignorespaces 25db$ for the 8PSK
modulation scheme, showing the system’s usability. Moreover, very low BER and
information leakage are seen for an eavesdropper, showing the security prowess
of the system. Future work will be addressed towards doing an experimental
analysis for the proposed system and finding new chaotic modulation schemes to
enhance the security and usability of the proposed system.

##  8 Statements and Declarations

All authors certify that they have no affiliations with or involvement in any
organization or entity with any financial interest or non-financial interest
in the subject matter or materials discussed in this manuscript.
Acknowledgments We thank our guide, Dr Ujjwal Verma, for his constant support
and guidance. We would also like to thank Mars Rover Manipal for providing us
with the necessary resources to complete the research.

## References

  *   * (1) Blinowski, G.: Security of Visible Light Communication systems—A survey. Physical Communication 34, 246–260 (2019). https://doi.org/10.1016/j.phycom.2019.04.003
  * (2) Lu, H., Zhang, L., Jiang, M., Wu, Z.: High-Security Chaotic Cognitive Radio System with Subcarrier Shifting. IEEE Communications Letters 19(10), 1726–1729 (2015). https://doi.org/10.1109/LCOMM.2015.2464214
  * (3) Classen, J., Steinmetzer, D., Hollick, M.: Opportunities and pitfalls in securing visible light communication on the physical layer, 19–24 (2016). https://doi.org/10.1145/2981548.2981551
  * (4) Elgala, H., Mesleh, R., Haas, H.: Indoor optical wireless communication: Potential and state-of-the-art. IEEE Communications Magazine 49 (2011). https://doi.org/%****␣sn-article.bbl␣Line␣100␣****10.1109/MCOM.2011.6011734
  * (5) Elgala, H., Mesleh, R., Haas, H.: Indoor broadcasting via white leds and ofdm. IEEE Transactions on Consumer Electronics 55 (2009). https://doi.org/10.1109/TCE.2009.5277966
  * (6) Kumar, N., Lourenço, N.R.: Led-based visible light communication system: A brief survey and investigation. Journal of Engineering and Applied Sciences 5 (2010). https://doi.org/10.3923/jeasci.2010.296.307
  * (7) Sevincer, A., Bhattarai, A., Bilgi, M., Yuksel, M., Pala, N.: Lightnets: Smart lighting and mobile optical wireless networks - a survey. IEEE Communications Surveys and Tutorials 15 (2013). https://doi.org/10.1109/SURV.2013.032713.00150
  * (8) Wu, S., Wang, H., Youn, C.H.: Visible light communications for 5g wireless networking systems: From fixed to mobile communications. IEEE Network 28 (2014). https://doi.org/10.1109/MNET.2014.6963803
  * (9) Karunatilaka, D., Zafar, F., Kalavally, V., Parthiban, R.: Led based indoor visible light communications: State of the art. IEEE Communications Surveys and Tutorials 17 (2015). https://doi.org/10.1109/COMST.2015.2417576
  * (10) Qiu, Y., Chen, H.H., Meng, W.X.: Channel modeling for visible light communications—a survey. Wireless Communications and Mobile Computing 16 (2016). https://doi.org/10.1002/wcm.2665
  * (11) Sindhubala, K., Vijayalakshmi, B.: Survey on noise sources and restrain techniques in visible-light communication. Light and Engineering 24 (2016)
  * (12) Zhuang, Y., Hua, L., Qi, L., Yang, J., Cao, P., Cao, Y., Wu, Y., Thompson, J., Haas, H.: A survey of positioning systems using visible led lights. IEEE Communications Surveys and Tutorials 20 (2018). https://doi.org/10.1109/COMST.2018.2806558
  * (13) Obeed, M., Salhab, A.M., Alouini, M.S., Zummo, S.A.: On optimizing vlc networks for downlink multi-user transmission: A survey. IEEE Communications Surveys and Tutorials 21 (2019). https://doi.org/10.1109/COMST.2019.2906225
  * (14) Leung-Yan-Cheong, S.K., Hellman, M.E.: The gaussian wire-tap channel. IEEE Transactions on Information Theory 24 (1978). https://doi.org/10.1109/TIT.1978.1055917
  * (15) Oggier, F., Hassibi, B.: The secrecy capacity of the mimo wiretap channel. IEEE Transactions on Information Theory 57 (2011). https://doi.org/10.1109/TIT.2011.2158487
  * (16) Classen, J., Chen, J., Steinmetzer, D., Hollick, M., Knightly, E.: The spy next door: Eavesdropping on high throughput visible light communications. Proceedings of the 2nd International Workshop on Visible Light Communications Systems (2015)
  * (17) Wang, J.Y., Liu, C., Wang, J.B., Wu, Y., Lin, M., Cheng, J.: Physical-layer security for indoor visible light communications: Secrecy capacity analysis. IEEE Transactions on Communications 66(12), 6423–6436 (2018). https://doi.org/10.1109/TCOMM.2018.2859943
  * (18) Lapidoth, A., Shitz, S.S.: The Poisson Multiple-Access Channel 44(2), 488–501 (1998)
  * (19) Strogatz, S.H.: Nonlinear Dynamics and Chaos. CRC Press, Boca Raton (2015). https://doi.org/10.1201/9780429492563
  * (20) Wu, X., Zhang, L.: A l-i-oscm mapping method for improving ber of chaotic cdma based vlc system. In: 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), pp. 1028–1032 (2016). https://doi.org/10.1109/IMCEC.2016.7867367
  * (21) Ryu, H.G., Lee, J.H.: High security wireless CDSK-based chaos communication with new chaos map. In: Proceedings - IEEE Military Communications Conference MILCOM, pp. 786–790 (2013). https://doi.org/10.1109/MILCOM.2013.139
  * (22) Sadoudi, S., Tanougast, C., Azzaz, M.S.: A new robust additive hyperchaos masking algorithm for secure digital communications. In: 2013 International Conference on Control, Decision and Information Technologies (CoDIT), pp. 501–504 (2013). https://doi.org/10.1109/CoDIT.2013.6689595
  * (23) Fu, C., Lin, Y., Jiang, H.-y., Ma, H.-f.: Medical image protection using hyperchaos-based encryption. In: 2015 9th International Symposium on Medical Information and Communication Technology (ISMICT), pp. 103–107 (2015). https://doi.org/10.1109/ISMICT.2015.7107507
  * (24) Hammami, S., Djemaï, M., Busawon, K.: Encrypted audio communication design using synchronized discrete-time hyperchaotic maps. In: 2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), pp. 1–6 (2016). https://doi.org/10.1109/CSNDSP.2016.7574015
  * (25) Yang, N., Wu, C., Liu, C., Liu, K.: Adaptive synchronization of a novel fractional-order hyperchaotic system with uncertain parameters. In: 2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pp. 248–252 (2015). https://doi.org/10.1109/ICCIS.2015.7274629
  * (26) Gunawan, W.H., Liu, Y., Yeh, C.H., Chow, C.W.: Color-shift-keying embedded direct-current optical-orthogonal-frequency-division-multiplexing (CSK-DCO-OFDM) for visible light communications (VLC). IEEE Photonics Journal 12(5) (2020). https://doi.org/10.1109/JPHOT.2020.3021032
  * (27) Chen, B., Zhang, L., Lu, H.: High Security Differential Chaos-Based Modulation With Channel Scrambling for WDM-Aided VLC System. IEEE Photonics Journal 8(5) (2016). https://doi.org/10.1109/JPHOT.2016.2607689
  * (28) Fang, F., Zhang, L., Rao, W., Chen, W.: Real-valued gram-schmidt transform-based non-coherent chaos shift keying scheme for visible light communication system. In: 2017 IEEE/CIC International Conference on Communications in China (ICCC), pp. 1–6 (2017). https://doi.org/10.1109/ICCChina.2017.8330401
  * (29) Richter, H.: The generalized Hénon maps: Examples for higher-dimensional chaos. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 12(6), 1371–1384 (2002). https://doi.org/10.1142/S0218127402005121
  * (30) Abdul Rahman, S., Zribi, M., Smaoui, N.: Secure communications based on the projective synchronization of four-dimensional hyperchaotic systems. Mathematical Problems in Engineering 2019 (2019). https://doi.org/10.1155/2019/2491850
  * (31) Rodríguez, S.P., Jiménez, R.P., Mendoza, B.R., Hernández, F.J.L., Alfonso, A.J.A.: Simulation of impulse response for indoor visible light communications using 3D CAD models. EURASIP Journal on Wireless Communications and Networking 2013(1) (2013). https://doi.org/10.1186/1687-1499-2013-7
  * (32) Komine, T., Nakagawa, M.: Fundamental analysis for visible-light communication system using LED lights. IEEE Transactions on Consumer Electronics 50(1) (2004). https://doi.org/10.1109/TCE.2004.1277847