CHAOTIC COMMUNICATION – AN
OVERVIEW
Rupak Kharel
NCRLab, Northumbria University
Supervisors
Dr. Krishna Busawon, Prof. Z. Ghassemlooy
OUTLINE OF THE PRESENTATION

Chaos –




Chaos Synchronization



Introduction
Examples
Application to cryptography & secure communication
Why/How (??)
Different Types/Methods
Secure communication using chaos
Different methods, problems(!!!)
 Different attack methods

Methods proposed, results and analysis
 Future works

2
CHAOS – INTRODUCTION

Deterministic system


Aperiodic long term behaviour


system has no random or noisy inputs or
parameters. The irregular behaviour arises from the
system’s nonlinearity rather than from the noisy
driving forces.
trajectories that do not settle down to fixed points,
periodic orbits or quasiperiodic orbits as t →∞.
Sensitive dependence on initial conditions &
parameters

nearby trajectories separate exponentially fast - the
system has positive Lyapunov exponent.
3
CHAOS – EXAMPLE
The Lorenz system
30
20
10
y(t)

0
-10
-20
-30
20
10
50
40
0
x(t)
30
-10
-20
10
0
20 z(t)
4
CHAOS – EXAMPLE
The Chua System
f(x) is a 3-segment piecewise linear function.
1
0.5
y(t)

0
-0.5
-1
5
4
2
0
0
z(t)
-5
-2
-4
x(t)
5
CHAOS – EXAMPLE
The Duffing system
15
10
5
x2(t)

0
-5
-10
-15
-5
0 x (t)
1
5
6
CHAOS – APPLICATION TO SECURE
COMMUNICATION
has a broadband spectrum – message does not
change the properties of transmitted signal.
 Constant output power even when the message is
included
 Little affect by multi-path fading


cheaper alternative solution to traditional spread
spectrum systems.
Aperiodic - limited predictability.
 High security at physical level.

7
CHAOTIC SYNCHRONIZATION WHY/HOW(??)

Essential in communication systems
Chaotic systems are very sensitive:
 to initial conditions and initial parameters - slight
different initial condition leads to totally different
trajectories
 Even the smallest error between Tx and Rx can be
expected to grow exponentially.
Q1: How can one achieve synchronization?

Q2: Can sensitive chaotic systems be used in
communications?


Pecora & Carroll1: showed that it is possible to
synchronize two chaotic system if they are coupled
with common signals
Cuomo & Oppenheim2: practically utilized chaotic
synchronization for transmitting message signal
8
1) L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett., 64, pp. 821-824, 1990
2) K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to
communications,” Phy. Rev. Lett., 71, pp. 65-68, 1993.
CHAOTIC SYNCHRONIZATION – TYPES
One or more driving signals is required to be
transmitted sent from source (driving/master) chaotic
system to the chaotic system (slave)







Complete Synchronization
Generalized Synchronization
Projective Synchronization
Phase Synchronization
Lag Synchronization
Impulsive Synchronization
Adaptive Synchronization
––In
trajectories
slave
special
slave
Synchronization
thissystem
system
case,
caseofdriving
of
trajectory
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master
generalized,
is converges
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signal
and
converges
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slave
from
where
this
tosystems
master
masters
to
is
to
one-to-one
important
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masters
system
converges
but trajectory
their
mapping
trajectory
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is not
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to be
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f(x)=ax.
exactly
may
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time
well.
not
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the
be same.
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This
but
same.
is special
as
impulses
case of complete
determined
synchronization.
by a fixed or time
varying interval τ.
9
CHAOTIC SYNCHRONIZATION – METHODS
Drive-Response Principle
 Active Passive Decomposition
 Observer Based Synchronization
 Extended Kalman Filtering Method
 etc.
Driving signal is always transmitted from master
to the slave chaotic oscillator for synchronization.
Does this means communication??

10
OBSERVER BASED SYNCHRONIZATION
Concept borrowed from the control theory
 Chaotic oscillator defined as:


An observer can be defined as:

Therefore, if the error is

, then
Therefore, if Kp is chosen such that eigen value
of (A- KpC) is negative, then error converges to
zero thus achieving synchronization.
11
P & PI-OBSERVERS
Performance comparison of proportional (P) and
proportional-integral (PI) observer under noisy
environment.
 P-observer will amplify the noise with the value
of gain values chosen.
 PI-observer will add degree of freedom to the
system.

12
RESULTS
Duffing system used as chaotic oscillator
 Additive white Gaussian noise (AWGN) channel
with signal-to-noise ratio (SNR) of 25 dB

5
150
100
x1h
x1h
50
0
0
-50
-100
-150
-150
-100
-50
0
x1
50
100
150
Synchronization using P-observer
-5
-5
0
5
x1
Synchronization using PI-observer
My opinion: Secure communication is related with how message is
mixed with chaotic carrier but not the method used for synchronization.
13
CHAOTIC COMMUNICATION – METHODS

Chaotic Masking Technique

Chaotic Parameter Modulation Technique

Message Inclusion Technique

Chaotic Shift Keying (CSK)
Almost all other methods falls into one or more of these categories.
14
CHAOTIC MASKING TECHNIQUE
Message spectrum is hidden in the broad chaos
spectrum
 Observer should show robustness even if it is
driven by message + chaotic carrier

15
PARAMETER MODULATION TECHNIQUE
Message is used to vary the parameters of the
chaotic system
 Care should be taken so that change in
parameters do not affect the chaotic nature of the
system

16
CHAOTIC SHIFT KEYING (CSK)



Used for transmitting digital message signal.
Two statistically similar chaotic attractor are
respectively used to encode bit ‘1’ or ‘0’.
Two attractors are generated by two chaotic systems
having the same structure but slightly different
parameters.
17
MESSAGE INCLUSION TECHNIQUE
Rather than changing the chaotic parameter, the
message is included in one of the states of the
chaotic oscillator. By doing this, we are directly
changing the chaotic attractor at phase space.
 A transmitted signal will be different than the
state where the message will be included.
 Encryption rule can also be applied.

18
PROBLEMS
Masking, parametric modulation technique and
CSK has been proved to be insecure1,2,3.
 Breaking methods were based on forecasting and
predicting the carrier values, which when
subtracted revealed the spectrum of message.
 Inclusion method can be secure, however presents
a problem of left invertibility.
 Hence, the need to improve the security of the
above techniques.

1)
K. M. Short, "Steps toward unmasking secure communications," International Journal of Bifurcation and
Chaos, vol. 4, pp. 959-977, 1994.
2)
G. Alvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking parameter modulated chaotic secure
communication systems," Chaos Solitons & Fractals, vol. 21, pp. 783-787, 2004.
3)
T. Yang, L. B. Yang, and C. M. Yang, "Application of neural networks to unmasking chaotic secure
communication," Physica D, vol. 124, pp. 248-257, 1998.
19
OUR PROPOSED SOLUTIONS


Cascaded Chaotic Masking
Two chaotic signal of similar powers are added
together to create of carrier of sufficient
complexity, where the message is masked.
20
CASCADED CHAOTIC MASKING – RESULTS

Lorenz system was employed for both oscillators
and drive response principle as used for
achieving synchronization.
Fig. 1: Output ym after first level of masking
Fig. 2: Output yt after second level of
masking (transmitted signal)
21
RESULTS (CONTD...)

Input and output waveforms
22
YANG’S METHOD BASED ON CRYPTOGRAPHY
T. Yang et. al proposed a chaotic communication
system based on cryptography where they
extended the method of masking1.
 One chaotic signal was chosen as carrier where
an encrypted message signal is masked.
 Encryption is performed by using a chaotic key
stream different from chaotic carrier.
 Method was resistant for various attacks
including Short’s method.

23
1) T. Yang, C. W. Wu, and L. O. Chua, "Cryptography based on chaotic systems," IEEE Transactions on
Circuits and Systems-I: Fundamental Theory and Applications, vol. 44, pp. 469-472, 1997.
SO WHAT IS THE PROBLEM?
Later, work done by Parker & Short showed that
it is still possible to generate the keystream from
transmitted chaotic carrier1.
 The fact that the dynamics of chaotic keystream
was in the transmitted chaotic signal, it was
possible to estimate the keystream.
 After seeing all these methods to be insecure,
does this mean, it is pessimistic to think that
chaotic signals after all cannot be used for secure
communication???
 My answer will be NO.

1) A. T. Parker and K. M. Short, "Reconstructing the keystream from a chaotic encryption," IEEE Transaction
on Circuit and Systems-I: Fundamental Theory And Applications, vol. 48, pp. 624-630, 2001.
24
OUR PROPOSED CHAOTIC CRYPTOSYSTEM

Chaotic keystream is generated which is not part of
the chaotic dynamics of the transmitter oscillator.
Separate chaotic oscillator is used
 Encryption of message signal using this key



Resulting encrypted message signal is masked with
chaotic carrier from the chaotic transmitter.
At receiver side, chaotic synchronization is performed
and encrypted signal is recovered where same chaotic
keystream is applied to decrypt the message signal
back.
Q: How to generate same keystream in Tx and
Rx???
25
PROPOSED CHAOTIC CRYPTOSYSTEM
Chaotic
Transmitter (T)
y1(t)
y2 (t)
Chaotic Key
Generator (A)
yt (t)
+
e(m(t))
k(t)
Encryption
Rule e(.)
y't (t)
Channel
Chaotic
Receiver (R)
y2 (t)r
Chaotic Key
Generator (B)
y1 (t)r
e(m (t))r
kr(t)
Decryption
Rule d(.)
m(t)
mr(t)
Fig. Block diagram of the proposed chaotic communication based on cryptography.


Non-coupled synchronization is obtained between two
chaotic key generator oscillators where both are driven by
equivalent chaotic carriers.
No dynamics of the chaotic keystream is present on the
transmitted chaotic carrier, hence impossible to estimate
the keystream and decrypt the message signal back.
26
RESULTS
27
Ideal Channel
AWGN Channel with SNR = 40dB
GENERAL ISSUES

The channel through which the signal is
transmitted will not be ideal ― most of the
researcher tend to assume ideal channel when
proposing a new method.


Therefore, the method might not be feasible when
implemented practically.
Also, significant development has already been
made on digital communication where channel
equalization, error correction methods, etc are
well developed.


Therefore, parallel development of these techniques
on chaotic communication is impractical.
Chaotic communication should therefore complement
existing digital communication.
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DIGITIZATION OF CHAOTIC SIGNALS
ŋt
mt
Chaotic
Oscillator
yt
x1
x1r
LPF
A/D
Chaotic
Observer
Yi
ytr
Digital
Encoder
D/A
rt
Channel
h(t)
Yir
zt
Threshold
Detector
Matched
Filter
Sampler
mr
Fig. Block diagram of proposed chaotic communication system using digitization




Chaotic signal is converted to digital format with uniform sampling
and encoding.
Simple baseband modulation technique on-off keying with 100% duty
cycle is used.
We study the performance of this system with respect to bit error rate
(BER).
Once optimum BER is set, error control coding can be applied to
improve the BER performance.
29
DIGITIZATION OF CHAOTIC SIGNALS...


The message recovery is good up to BER>10-4
AWGN channel was considered here, but dispersion in
dispersive channels can easily be compensated using
equalizers such as linear equalizer or Wavelet and ANN
based equalizers.
30
CONCLUSIONS
Chaotic property of a system has a lot of potential
in secure communication
 Lots of methods has been proposed, but most of
them are broken by one method or other
 We proposed few methods for realizing potential
secure communication links
 Digitization concept was implemented on chaotic
signals, where already made developments on
digital communication is readily available

31
FUTURE WORKS
Hardware realization of the proposed encryption
method
 Security analysis of the proposed method under
various attack methods
 Hardware realization of the proposed digitization
of chaotic signal, may be by using a DSP board
 Implement channel equalization and error
control codes

32
PUBLICATION LIST
Journal

Kharel, R., Busawon, K. and Ghassemlooy, Z.: "A chaos-based communication scheme using
proportional and proportional-integral observers", Iranian Journal of Electrical & Electronic
Engineering, Vol. 4, No. 4, pp. 127-139, 2008.
Conferences




Kharel, R., Rajbhandari, S., Busawon, K., and Ghassemlooy, Z.: “Digitization of chaotic signal for
reliable communication in non-ideal channels”, proceeding of International Conference on
Transparent Optical Networks’’, Mediterranean Winter’’ 2008 (ICTON-MW'08), ISBN: 978-1-42443485-5, pp. Sa1.2 (1-6), Marrakech, Morocco, 11-13 Dec., 2008. Invited Plenary Paper.
Kharel, R., Busawon, K. and Ghassemlooy, Z.: “Novel cascaded chaotic masking for secure
communication “, The 9th annual Postgraduate Symposium on the convergence of
Telecommunications , Networking & Broadcasting (PGNET 2008), ISBN 978-1-902560-19-9,
Liverpool, UK, pp 295-298, June 2008.
Busawon, K., Kharel, R., and Ghassemlooy, Z.: “A new chaos-based communication scheme using
observers”, proceeding of the 6th Symposium on Communication Systems, Networks and Digital
Signal Processing 2008 (CSNDSP 2008), ISBN: 978-1-4244-1876-3, pp. 16-20, Graz, Austria, July
2008.
Kharel, R., Busawon, K. and Ghassemlooy, Z.: “A Novel Chaotic Encryption Technique for Secure
Communication”, Submitted.
33
ACKNOWLEDGEMENT
Northumbria University for providing
studentship to carry out my Ph.D research work.
 My supervisors Dr. Krishna Busawon & Prof.
Fary Ghassemlooy for their support and
invaluable guidance.
 All my colleagues in NCRLab.

34
Thank You.
 Any Questions !!!

35