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Chaos Encrypted Optical Communication SystemV. Annovazzi-Lodi a; C. Antonelli b; G. Aromataris a; M. Benedetti a; M.Guglielmucci c; A. Mecozzi b; S. Merlo a; M. Santagiustina d; L. Ursini d

a Dipartimento di Elettronica, Universit di Pavia, Pavia, Italyb Dipartimento di Ingegneria Elettrica e dell'Informazione, Universit dell'Aquila,L'Aquila, Italyc Istituto Superiore delle Comunicazioni e delle Tecnologie dell'Informazione, Roma,Italyd Dipartimento di Ingegneria dell'Informazione, Universit di Padova, Padova, Italy

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To cite this Article: Annovazzi-Lodi, V., Antonelli, C., Aromataris, G., Benedetti,M., Guglielmucci, M., Mecozzi, A., Merlo, S., Santagiustina, M. and Ursini, L. (2008) 'Chaos Encrypted OpticalCommunication System', Fiber and Integrated Optics, 27:4, 308 — 316

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Fiber and Integrated Optics, 27:308–316, 2008

Copyright © Taylor & Francis Group, LLC

ISSN: 0146-8030 print/1096-4681 online

DOI: 10.1080/01468030802192625

Chaos Encrypted Optical Communication System

V. ANNOVAZZI-LODI,1 C. ANTONELLI,2

G. AROMATARIS,1 M. BENEDETTI,1 M. GUGLIELMUCCI,4

A. MECOZZI,2 S. MERLO,1 M. SANTAGIUSTINA,3

and L. URSINI3

1Università di Pavia, Dipartimento di Elettronica, Pavia, Italy2Università dell’Aquila, Dipartimento di Ingegneria Elettrica

e dell’Informazione, L’Aquila, Italy3Università di Padova, Dipartimento di Ingegneria dell’Informazione,

Padova, Italy4Istituto Superiore delle Comunicazioni e delle Tecnologie dell’Informazione,

Roma, Italy

Abstract In this article, we report on the research activity that has been recentlycarried out in Italy on secure transmission by using chaotic carriers in the framework

of a national and two international projects. Transmission of both analog and digital

signals has been demonstrated, as well as theoretically and numerically investigated.Close-loop digital transmission over 100 km distance has been achieved for the

first time.

Keywords chaos, cryptography, optical fibers, optical networks, steganography,transmission

1. Introduction

Security is one of the key aspects of modern communications. Today, transmission of

sensible data on networks is protected by suitable software techniques using algorithms

and numerical keys. Alternative promising approaches are based on hardware techniques.

Among them, quantum cryptography has a high level of theoretical security; however,

due to the low bit rates, it is suitable to transmit keys rather than full messages, and

it usually requires dedicated connections or networks. Another hardware technique is

optical chaotic cryptography [1, 2], which makes use of a pair of lasers routed to chaos,

usually by back-reflection from a remote mirror. A standard DFB telecommunication

laser routed to chaos exhibits a wide spectrum, typically in the order of 10–100 GHz; its

emission in the time domain shows a non-periodic and very complex, apparently random,

behavior, which, however, can be described on the basis of a deterministic model.

In the cryptographic schemes, two chaotic lasers are used: one (called “master”) at

the transmitter to hide the signal to be sent (the message) within the chaotic waveform,

and the other (called “slave”) at the receiver for message extraction. In most cases,

chaos is simply added to the message to strongly reduce its S/N ratio, implementing the

Received 25 April 2008; accepted 5 May 2008.Address correspondence to Marco Santagiustina, Università di Padova, Dipartimento di Ingeg-

neria dell’Informazione, via Gradenigo, 6/B, 35131, Padova, Italy. E-mail: marco.santagiustina@unipd.it

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Chaos Encrypted Optical Communication System 309

so-called “chaotic masking.” To this purpose, different solutions are possible [1, 2, 3]. If,

as shown in Figure 1, the message modulates a third laser, whose emission is combined

to that of the chaotic laser, the scheme is called “additive chaos masking” (ACM).

Extraction of the hidden message from chaos is based on the synchronization of

transmitter and receiver, i.e., on the generation of the same chaotic waveform at both

ends of the channel. Synchronization is obtained by injection of a part of the output

of the master laser into the slave laser, which, under suitable conditions, replicates the

chaotic regime of the master but does not replicate the message. Thus, message extraction

can be simply performed by making the difference between the signal coming from the

transmitter (message plus chaotic waveform) and the chaotic waveform replicated at the

receiver. However, (and this is the key point), it is very difficult for an eavesdropper to

synchronize the master by a system similar to that of the authorized addressee, since

synchronization relies on the two lasers being closely matched, and, typically, the two

devices must be selected from the same wafer. Two basic synchronization schemes are

possible: close-loop, where the slave is chaotic itself, and open-loop, where the slave has

no optical feedback and becomes chaotic because of injection from the master.

After initial investigations on basic principles, more recent work has been focused

on the application of chaotic cryptography to real networks. Digital transmission on

a metropolitan network [4] has been performed. Several basic functional blocks have

already been studied and experimentally demonstrated, such as the chaotic signal repeater

[5], modules for point-multipoint transmission [6], for two-channel transmission [7], for

wavelength multiplexing [8], and for wavelength conversion [9]. In the following, we

briefly report experimental results obtained with the close-loop setup of Figure 1, i.e.,

transmission of analog video signals [10] and transmission of digital signals on a long

(100-km) fiber span. We also present the evaluation of the system performances with

digital signals using a numerical model of the set-up of Figure 1. In particular, the

exploitation of the Manchester coding [11] to improve the performance of digital signal

transmission is explained and numerically investigated. An analysis of the dimension of

chaos in semiconductor lasers with delayed optical feedback is finally reported.

Figure 1. Experimental set-up for chaos generation and synchronization and for secure trans-

mission.

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2. Transmission of Analog Signals

Experiments have been performed on the ACM set-up of Figure 1. The lasers are driven

to chaos by back-reflection from the fiber tip positioned in front of its launching lens

[3, 10], which defines an external cavity of about 5 cm.

The fiber path between the transmitter and the receiver is about 1.2 km. The optical

isolator ensures one-way injection from master into slave. The injection level is trimmed

by using a birefringence controller and a polarizer in front of the slave. The laser pair has

been selected between first neighbors on the same wafer; their difference of threshold and

of differential efficiency is on the order of 1%, and their wavelengths have been matched

by temperature control. Master/slave synchronization is obtained by adjusting the working

point and the alignment of both lasers, as well as the injection level. The lengths of the

two external cavities must also be trimmed within a fraction of a wavelength. The regimes

of the two lasers are compared by viewing the output signals of photodiodes PD1, PD2,

by an RF spectrum analyzer. Since the slave receives the injected power from the master

with a delay, due to the different lengths of the propagation paths, a compensation delay

line has been introduced.

In Figure 2 (left), the RF spectra of the master and of the master/slave difference are

reported, showing chaos cancellation over a large bandwidth. A sinusoidal unmodulated

carrier (3 GHz) applied to the system input is also shown. The carrier is completely

hidden in the master spectrum; however, after master/slave synchronization, it becomes

visible in the difference at the system output.

Then the cryptographic set-up has been included in a transmission link connecting

a standard surveillance TV camera and its receiver. The TV camera output (a composite

TV signal at the carrier frequency of 2.4 GHz) has been sent to the system input. The

output of the cryptographic system is sent to the TV receiver connected to a monitor. In

Figure 2 (right), three photographs of the monitor display are shown when the camera

is aimed at a still picture. The first image is transmitted with no added chaos. The

second is hidden within chaos and represents the message, as it would be recovered by

an eavesdropper tapping the fiber. The third is the extracted message after master/slave

synchronization.

Figure 2. Left: Spectra of master and synchronized master/slave difference; a transmitted carrier

at 3 GHz is hidden in the master chaos, but becomes visible in the difference. Right: Video signal

transmission: (a) input signal, (b) signal hidden in chaos, and (c) recovered signal at the system

output.

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Chaos Encrypted Optical Communication System 311

3. Transmission of Digital Signals

Experimental measurements concerning digital signals were also performed. The close-

loop ACM set-up of Figure 1 was implemented and bit-error-rate (BER) and eye-diagram

measurements performed on NRZ, PRBS 231-1 bit-long sequences. The path between

the transmitter and the receiver was made of two fiber spans, 50 km long, of non-

zero dispersion-shifted fiber (NZDSF), each followed by an optical amplifier (EDFA or

SOA). The BER was measured in three different situations: (1) a unmasked transmission

without added chaos to fix reference values of the noise and distortion level due to the fiber

nonlinearities, chromatic dispersion, amplifiers spontaneous emission, and electrical noise

throughout the complete set-up; (2) with added chaos, before synchronization (masking

condition); and (3) after synchronization (recovering condition). In Figure 3a, an example

of the detected eye diagrams is presented with the corresponding measured BER, in order

to show the quality of message, masking, and recovering at a propagation distance of

100 km and at a bit rate (BR) of 1.25 Gb/s. At the top of the figure, the unmasked

transmission is presented, showing a BER D 10�9; this case demonstrates the good

quality of the propagating signal. The figure in the middle refers to the masking condition;

the message is hidden with a BER of about 10�3: for such a value, the eye diagram is

severely closed. At the bottom, the figure refers to the recovering condition, showing that

the message could be retrieved with a satisfying quality (the eye diagram is open); the fact

that the message is not perfectly recovered is due to small synchronization errors. The gap

between the masking and the recovering conditions is about 103; an optimum performance

(BER greater than 10�2 in masking condition and BER less than 10�9 in recovering

condition) is difficult to be attained, as shown also in previous experiments [4]. This is due

to the fact that achieving high-level performance is more difficult with baseband digital

signals. In fact, in this situation, the message is not very efficiently hidden because of

the weakness of the chaotic waveform at low frequencies. Moreover, the synchronization

process is also less effective at the frequencies around the DC component, degrading the

system performance. A better performing condition would be similar to that shown in

Figure 2 for analog signals, in which the information to be masked is shifted at higher

frequencies, where hiding and recovery from chaos are more efficient.

Figure 3. (a) Experimental eye diagrams at 100 km, BR D 1.25 Gb/s; (b) simulated Q-factor vs.

distance, BR D 1.5 Gb/s: NRZ (empty markers) and MC (full markers) comparison.

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4. Enhancing the Performances by Manchester Coding

According to the last remark, modulation formats that shift the information toward higher

frequency can be used in principle for improving the overall performance. An example

is provided by the Manchester coding (MC) [11, 12]. It entails a logic EXOR between

the NRZ signal and a clock signal twice the BR frequency; in this way, a “1” (“0”) is

coded as a high-to-low (low-to-high) transition at the half of each bit period (or vice

versa), and the power spectrum presents zeros at even BR multiples (including the DC

component) and relative maxima at odd multiples. So, the message spectrum is shifted to

higher frequencies with respect to the NRZ [11, 12]. At the receiver, the decoding process

entails the multiplication between the Manchester signal and a square wave at the BR

frequency, followed by a low-pass filter. In order to compare the performance of the NRZ

and MC, the ACM set-up of Figure 1 was numerically simulated. The performance is

evaluated in terms of Q-factor [13], instead of the BER. The two quantities are correlated

in the Gaussian noise approximation by BER D 0.5erfc(Q/21=2) [13]; in this case, this

approximation does not hold; however, the Q values for getting BER < 10�9 (Q >

15.6 dB) and BER > 10�2 (Q < 6 dB) are useful as reference values for defining a

well-open/closed eye diagram. The Q-factor, in hiding (label H) and recovering (label R)

condition, is plotted as a function of distance in Figure 3b, for both NRZ (empty markers)

and MC (full markers), at a BR of 1.5 Gb/s. An optimum message masking level is

achieved from 0 to 500 km for both MC and NRZ; this stems from the fact that, in

the simulations, the message amplitude is always chosen small with respect to the chaos

(1–7%) in order to provide a good synchronization. In the recovering condition, the

MC shows an evident improvement with respect to the NRZ: the MC ensures a good

recovering up to 500 km, while the NRZ only up to 250 km. This trend was verified

for various BR and message amplitudes. The improvement of performance is due to the

fact that MC shifts the NRZ signal spectrum from baseband to higher frequencies, where

it takes advantage of enhanced masking and better chaos suppression at the receiver

[14, 15].

5. Dimension of Chaos in Semiconductor Lasers

The theory of chaos [16] provides the framework for analyzing the nature of the chaotic

evolution of a dynamical system. Such a characterization could be based on several

criteria, including, for example, the computation of the Lyapunov exponents, the analysis

of bifurcation diagrams [17], and the study of the strange attractor of the system. The

chaotic nature of the field emitted by a semiconductor laser driven to chaos by external

feedback can be characterized by applying the above analysis to the dynamical variables

of the system. The number of dynamical variables of the system is infinite, because its

dynamics depends on the field emitted by the laser in a time interval equal to the delay

� of the external cavity. In this article, we will compute the Hausdorff dimension [16],

one of the most relevant quantities used for the study of strange attractors. Hausdorff

dimension coincides with the fractal dimension of the strange attractor of a system. For

a generic set S, it is defined as the value of f, such that the limit HS D lim"!0

infC."/

Pn ı

fn

is non-zero and finite, being C."/, a coverage of S made of balls with radius ıfn

smaller than ". The definition of the Hausdorff dimension prevents any practical direct

computation. Nonetheless, an estimate of f can be evaluated using a time series of the

system variables, the sampled complex envelope of the electric field, E.t/, in the time

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Chaos Encrypted Optical Communication System 313

interval Œt; t C�� and the carrier density N.t/. Let us denote by x�.t/ the vector containing

ŒfRefE.t 0/g; ImfE.t 0/g; t 0 D t; t C ıt; : : : ; t C �g; N.t/�, i.e., the samples of the electric

field acquired with step ıt in the interval Œt; t C ��, and the carrier density at time t.

The characterization of the strange attractor follows the two-step procedure proposed by

Grassberger and Procaccia [18]. The first step is the evaluation of the correlation function

C.r/ of the time series x�.t/, defined as the number of samples with Euclidean distance

smaller than a given value r :

C.r/ D1

N 2

X

i¤j

uŒr � jx�.i�t/ � x�.j�t/j�;

where u.�/ is the unit Heaviside step function, �t is the sampling interval, and N is

length of the time series. When evaluated over a chaotic system and for small values

of r, the correlation function exhibits the relevant property of being proportional to an

exponential function of r, C.r/ / exp.��r/, where � is the wanted estimate of the fractal

dimension f. The second step of the procedure is the evaluation of coefficient � out of a

bi-logarithmic plot of the correlation function versus r, where a sufficiently linear growth

appears. The described procedure has been applied to time series obtained by numerically

solving the equations for photon and carrier dynamics in a typical semiconductor laser

described by the Lang-Kobayashi equations [19]. The results are shown in Figure 4,

where the correlation function is plotted versus r corresponding to two different injection

strengths and external delay values. The first subfigure refers to a weak injection, which

drives the system to the regime of periodic oscillation. A 1.5-ns time series of the optical

power is shown in the corresponding inset. The slope of the curve in the linear region,

denoted as the tangent of angle ı1, can be estimated to be tan.ı1/ � 6. The second

subfigure refers to an injection strong enough to drive the system to chaos, as shown

by the corresponding inset reporting a time series of the optical power. In this case, the

slope of the curve is visibly higher and can be estimated to be tan.ı2/ � 10:5. The

third subfigure refers to the same system of the second, with shorter external delay. The

slope of the curve decreases to tan.ı3/ � 8. The presented analysis, while reporting

numerical results in agreement with those obtained in [20] through computation of the

Kolmogorov-Sinai entropy, shows the practical measurability of the Hausdorff dimension

using sampled strings of the system variables.

Figure 4. Correlation function of the time series of the sampled trajectories x� .t /, vs. distance r.

The first plot refers to the case of weak injection, the second to stronger injection, and the third to

shorter external delay. The insets show the corresponding time series of the optical intensity.

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6. Conclusions

In this article, a review of the state-of-the-art chaotic lasers toward secure communications

was presented, showing interesting possibilities in analog and digital transmission.

For digital transmission, the close-loop scheme was realized for the first time on

long distance (up to 100 km) and numerical simulations showed that the reach could be

extended by means of the Manchester coding of the NRZ sequence. The dimension of

chaos in semiconductor lasers was also investigated.

Acknowledgments

This work was supported by MIUR (PRIN 2005-091255) and by the EU (PICASSO

IST-2005-34551). This research was also held in the frame of the agreement between the

University of Padua and ISCOM (Rome).

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Biographies

Valerio Annovazzi-Lodi received the degree in Electronic Engineering from the

University of Pavia, Italy, in 1979. In 2001 he became a full professor at the same

institution. His main research interests include injection phenomena and chaos in oscil-

lators and lasers, electrical fiber sensors, the fiber gyroscope, passive fiber components

for telecommunications and sensing, optical amplifiers, transmission via diffused infrared

radiation, micromechanical systems. He is the author of more than 100 papers and holds

four patents.

Cristian Antonelli received the Master’s degree in Electronic Engineering and Ph.D.

in Electrical and Information Engineering from the University of L’Aquila in 2002 and

2006. In 2006 he was a post-doctoral fellow at the Research Laboratory of Electronics at

MIT. He is currently a post-doc at the Electrical and Information Engineering Department

of the University of L’Aquila. His research interests include optical communications,

PMD, and mode-locked lasers.

Giuseppe Aromataris received the degree in Physics in 2006 from the University

of Milan, Italy. He is currently working toward his Ph.D. in Electronics Engineering with

the Optoelectronics Group of the University of Pavia, Italy. His research interests include

non-linear dynamics on optically injected semiconductor lasers, with regard in particular

to numerical analysis on optical chaos synchronization and cryptographic communications

systems.

Mauro Benedetti received the degree in Micro-Electronics Engineering in 2002 and

the Ph.D. in Electronics Engineering in 2006 from the University of Pavia, Italy. He is

currently working as a post-doctoral researcher with the Optoelectronics Group of the

University of Pavia. His main research interests include non-linear dynamics in optically

injected semiconductor lasers, with regard in particular to optical chaos synchronization

and cryptography in fiber-optic communications, characterization of MEMS/MOEMS

devices, and photonic crystals.

Michele Guglielmucci received the degree in Electrical Engineering from the Uni-

versity of Naples and a post degree in Telecommunications at the Post Graduate School

of Italian Ministry of Communications, respectively, in 1978 and 1985. He has been

involved in studies carried out in the EU projects ACTS-ESTHER “Exploitation of Soliton

Transmission Highways for the European Ring” and IST ATLAS “All-Optical Terabit per

Second Lambda Shifted Transmission.” Currently, as head of Optical Communication

Research Department of Superior Institute of Communications and Information Tech-

nologies (ISCOM—Ministry of Communications), he is involved in activities regarding

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the Network of the Future and takes part in the researches carried out in the EU-funded

Projects e-Photon oneC (NoE), SARDANA (Strep), and BONE (NoE). He is author and

co-author of several papers concerning the telecommunication field.

Antonio Mecozzi is a professor with the Electrical and Information Engineering

Department of the University of L’Aquila, Italy. His areas of interest include studies

on soliton transmission, laser mode-locking, nonlinear propagation in fiber, polarization

mode dispersion, physics and applications of semiconductor optical amplifiers, and optical

amplification and noise. Professor Mecozzi is a Fellow of the Optical Society of America

and of the IEEE.

Sabina Merlo received the degree in Electronic Engineering from the University

of Pavia in 1987. In 1989 she received the M.S.E. Degree in Bioengineering from the

University of Washington. In 1991 she got her Ph.D. in Electronic Engineering from

the University of Pavia. In 2001 she became Associate Professor with the Department

of Electronics of the University of Pavia. Her main research interests include MEMS,

MOEMS, chaos in lasers, laser interferometry, fiber-optic passive components, and sen-

sors. She holds three patents and is the author of more than 60 papers.

Marco Santagiustina received the degree in Electronic Engineering and Ph.D.

in Telecommunication Engineering from the University of Padova, Italy, respectively,

in 1992 and 1996. Since 1999 he has been a research fellow at the same institution

(permanent from 2002). His research interests include fiber optic communications, non-

linear optics and fiber amplifiers, and chaotic signal transmission. He is the author or

co-author of more than 80 papers in international scientific journals and conference

proceedings.

Leonora Ursini received the degree (with honors) in Telecommunications Engi-

neering from the University of Padova, Italy, in 2005. She is working toward the Ph.D.

degree in Information Engineering with the Photonics and Electromagnetic Group (PEG)

of the University of Padova. Her research interests are the numerical analysis of optical

digital communication systems with particular regard to chaotic communications (for

cryptographic applications) and Raman amplification in birefringent and spun fibers.