OPTICAL SECURE COMMUNICATION SYSTEM BASED ON

CHAOS SYNCHRONIZATION

Alexander N. Pisarchik and Flavio R. Ruiz-Oliveras

Centro de Investigaciones en Optica, Loma del Bosque 115, Lomas del Campestre, Leon, Guanajuato, Mexico

Keywords:

Synchronization, Chaos, Secure communication.

Abstract:

We propose a secure optical communication system based on the principles of generalized and complete syn-

chronization of chaotic oscillations. Both a transmitter and a receiver are composed by two chaotic external-

cavity semiconductor lasers which are coupled in a master-slave conﬁguration to provide generalized syn-

chronization, while the master lasers in the transmitter and in the receiver are completely synchronized via an

optical ﬁber. A message is added to the slave laser in the transmitter and sent to the receiver to be compared

with the output of the receiver slave laser. The system is robust to a small mismatch of the laser parameters or

of the coupling between the master and slave lasers, unavoidable in a real system, and can even enable a good

communication up to a 5 Gb/s transmission rate using the chaos masking encryption, when the master lasers

in the transmitter and in the receiver are coupled bidirectionally.

1 INTRODUCTION

Due to their high relaxation oscillation frequen-

cies (10 GHz and beyond) and direct comparability

with existing optical ﬁber communication technology,

semiconductor lasers have attracted much attention

from researchers working in optical communications

(Shore et al., 2008), especially after successive exper-

iments with the Athens’ ﬁber networks (Argyris et al.,

2005). In these lasers, high dimensional chaotic sig-

nals with a large information entropy are generated

by means of delayed feedback (Mirasso et al., 1996;

Ruiz-Oliveras and Pisarchik, 2006). The system per-

formance largely depends on the quality of chaos syn-

chronization, i.e. the synchronization error should be

minimized. Depending on the particular application

of chaotic optical communication, different encoding

and decoding schemes, such as chaos masking, chaos

shift keying, and chaos modulationwere implemented

(Tang et al., 2006). The majority of these schemes are

based on complete synchronization (CS) and use only

a single channel for both the laser coupling and the

signal transmission. A drawback of such schemes is

that CS asks for identical systems, very easy to obtain

in theory but difﬁcult in practice.

A secure communication system based on

the concept of generalized synchronization (GS)

(Afraimovich et al., 1986) and its combination with

CS was originally suggested by Murali and Lakshma-

nan (Murali and Lakshmanan, 1998). Since they used

a single communication channel, the signal itself cre-

ated a synchronization error that reduced the commu-

nication quality. A different approach (Terry and Van-

Wiggeren, 2001) consisted of two identical pairs of

chaotic systems (master and slave); one pair in the

transmitter and the other pair in the receiver. A bi-

nary message was encrypted in the coupling strength

between master and slave in the transmitter and was

recovered by analyzing the error dynamics in the re-

ceiver; in fact, this method was a modiﬁcation of a

chaos shift keying with an important innovation, it

used two channels: one to provide CS between the

transmitter and the receiver master systems, and the

other channel to compare the two slave trajectories.

However, in the chaos shift keying schemes a binary

bit message inherently produces a synchronization er-

ror, hence limiting the communication rate with the

synchronization time because the transmitter and the

receiver are not continuously synchronized.

2 COMMUNICATION SCHEME

AND LASER MODEL

We propose a new two-channel optical secure com-

munication system shown in Figure 1, which utilizes

two pairs of unidirectionally coupled external cavity

149

N. Pisarchik A. and R. Ruiz-Oliveras F. (2010).

OPTICAL SECURE COMMUNICATION SYSTEM BASED ON CHAOS SYNCHRONIZATION.

In Proceedings of the International Conference on Data Communication Networking and Optical Communication Systems, pages 149-153

DOI: 10.5220/0002912001490153

 SciTePress

semiconductor lasers, one pair in the transmitter, and

the other in the receiver; each consisting of a mas-

ter laser (ML) and a slave laser (SL), not necessar-

ily identical, but coupled enough to exhibit GS, while

the master lasers in the transmitter and in the receiver

should be identical (or near identical) and completely

synchronized. This scheme is completely symmetric,

the optical paths between the master and slave lasers

in the transmitter and in the recorder are the same, this

provides close similarity between their GS functions.

Such a similarity cannot be obtained if only one mas-

ter laser is coupled with two slave lasers, one in the

transmitter and one in the receiver (Yamamoto et al.,

2007; Annovazzi-Lodiet al., 2008), giving difﬁculties

for long distance communication.

Figure 1: Two-channel optical chaotic communication us-

ing chaos masking encryption scheme. ML

, SL

and

, SL

are the master and slave lasers in the transmitter

and in the receiver, respectively, κ

and κ

are the coupling

strengths between the lasers in the transmitter and in the re-

ceiver, ε is the coupling strength between the master lasers,

and D are the photodetectors.

The external cavity semiconductor lasers can

be modeled by the following equations based on

the well-known Lang-Kobayashi approach (Mirasso

et al., 1996; Lang and Kobayashi, 1980):

T,R

(t) =

(1+ iα)



T,R

(t) −



T,R

(t)+

T,R

(t −τ

T,R

)exp(−iϕ

T,R

εE

R,T

(t)+

2βN

T,R

(t)ξ

T,R

(t), (1)

T,R

(t) =

(1+ iα)



T,R

(t) −



T,R

(t)+

T,R

(t −τ

T,R

)exp(−iϕ

T,R

(t)+

2βN

T,R

(t)ξ

T,R

(t), (2)

M,S

(t) =

−

M,S

(t)

−G

M,S

(t)



M,S

(t)



, (3)

M,S

(t) = g

M,S

(t) −N

1+ ρ



M,S

(t)



, (4)

where the subscripts M and S stand for ML and SL,

T and R stand for transmitter and receiver, E

M,S

(t)

is the slow varying electric complex ﬁeld (P

M,S

(t)|

being the laser output power), N

M,S

(t) is

the carrier density, α = 3 is the linewidth enhance-

ment factor, τ

= 2 ps and τ

= 2 ns are the pho-

ton and carrier lifetimes respectively, γ

M,S

is the feed-

back parameter (γ

T,R

= 25 ns

−1

and γ

T,R

= 20 ns

−1

M,S

is the external cavity round-trip time (τ

T,R

= 1

ns and τ

T,R

= 0.5 ns), ϕ

M,S

= ωτ

M,S

is the initial

phase, ω = 1.2×10

−1

is the angular frequency for

all lasers, β = 1.1 ps

−1

is the spontaneous emission

rate, ξ

M,S

(t) is Gaussian white noise of zero mean

and unity intensity (Heil et al., 2001), I = 29 mA is

the pump current, q = 1.602×10

−19

C is the elec-

tronic charge, g = 1.5×10

−8

−1

is the gain param-

eter, N

= 1.5 ×10

is the carrier density at trans-

parency, ρ = 10

−7

is the gain saturation coefﬁcient,

and χ = η

ext

√

1−R/(τ

√

R) is the coupling parame-

ter (χ = κ

, κ

, ε) (Mirasso, 2000) varied in the simu-

lations (R = 0.3 being the facet laser power reﬂectiv-

ity and τ

= 6.6 ps being the internal cavity round-trip

time, and η

ext

accounts for losses different than those

introduced by the laser facet). χ = 100 ns

−1

corre-

sponds to the case when approximately 42.8% of the

laser output power is injected into the other laser. For

the case of unidirectional coupling, ε appears only in

2.1 Chaos Synchronization and

Information Transmission

To quantitatively measure synchronization, we calcu-

late the normalized cross correlation C between the

output powers of two coupled lasers (i and j)

C(t) =



′

−t) −P



′

, (5)

where h...i stands for time average, P

, P

and σ

, σ

are the mean and standard deviations of the laser pow-

ers, respectively. Since in this paper we only take into

consideration isochronous synchronization, we only

calculate C(0). CS can be quantitatively character-

ized with the mean synchronization error

hei = P

−P

. (6)

Figure 2 shows C and h ei when Eqs. (5) and (6)

are used for our system; C

, he

i are calculated for

and ML

[Fig. 2(a)], C

, he

i for ML

and

, C

, he

i for ML

and SL

[Fig. 2(b)], and C

i for SL

and SL

[Figure 2(c)], as functions of

the coupling strengths for unidirectional and bidirec-

tional coupling between ML

and ML

. The quali-

tative behavior is similar in both cases, however for

bidirectional coupling a much smaller ε is required

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150

to obtain CS between the masters [Figure 2(a)] and

between the slave [Figure 2(c)] lasers. Another ad-

vantage of bidirectional coupling, very important for

security purposes, is that the transmitter has feedback

information about the receiver’s behavior, so that if

someone tried to enter the synchronization channel

in order to obtain part (or all) of the laser light, the

feedback signal would be modiﬁed. If a hacker was

able to connect with the synchronization channel, he

would use a part of the laser power to synchronize his

own laser, this would reduce the power entering to the

authorized receiver and hence the power returning to

the transmitter that could be easily identiﬁed.

Since ML and SL are not identical, we obtain GS

characterized by a relatively small cross-correlation

(C ≈ 0.8) and a high mean error (hei ≈ 0.4) for even

very strong coupling (κ = 100 ns

−1

) [Figure 2(b)].

These characteristics indicate a large difference be-

tween the laser dynamics preventing a non-authorized

person, even when he has access to both channels, to

read the message without knowing the function H.

The same curves were obtained for both the trans-

mitter and the receiver, since we supposed that their

ML and SL were coupled with the same coupling

strengths, i.e. κ

= κ

. From Figures 2(b) and 2(c),

one can see that CS between the master and slave

lasers is not needed to obtain CS between SL

and

, proved even a relatively small coupling strength

(κ ≈50 ns

−1

) allows for an excellent correlation.

One way to quantitatively characterize the perfor-

mance of a communication system is Q-factor, given

Q =

i−hP

+ σ

, (7)

where hP

i and hP

i are the average optical powers of

bits “1” and “0”, respectively, while σ

and σ

are the

corresponding standard deviations. We prove the ben-

eﬁts of our system with three encoding methods: (i)

chaos modulation, where the message is encrypted by

modulating the transmitter’s chaotic carrier according

to the expression (1 + m(t))E

exp(iφ

) resembling

the type of amplitude modulation (AM), (ii) chaos

shift keying, where the message is added to the pump

current of SL

in Eq. (2), I + m(t), inevitably pro-

ducing an error in synchronization between the slave

lasers, and (iii) chaos masking, where the message,

completely independent of the electric ﬁeld, is added

to the chaotic carrier as E

exp(iφ

) + m(t) exp(iφ

)

(φ

being the message phase). In all these methods,

the message amplitude is set to a 2% of the SL

am-

plitude and the length of the encoded message is a

random bit sequence. The decoded message is ﬁl-

tered with a 5th order Butterworth low-pass ﬁlter and

Figure 2: Cross-correlation (ﬁlled signs) and mean synchro-

nization error (clean signs) between (a) ML

and ML

, (b)

and SL

, and (c) SL

and SL

, when ML

and ML

are coupled unidirectionally (dots) (ε = 80 ns

−1

) and bidi-

rectionally (triangles) (ε = 16 ns

−1

) as functions of their

coupling parameter. All cross-correlations are calculated in

the absence of a message.

the eye diagrams from the extracted codes are con-

structed to evaluate the transmission quality.

For the chaos modulation method, a very low Q-

factor is obtained and hence the information transmis-

sion is hardly possible. In Figure 3 we plot the values

of the Q-factor as a function of the coupling parame-

ter κ = κ

= κ

for chaos shift keying [Figure 3(a)]

and chaos masking [Figure 3(b)]. We use ε = 80 ns

−1

for unidirectionally coupled and ε = 16 ns

−1

for bidi-

rectionally coupled ML

and ML

. Note, that 5 Gb/s

good signal transmission is only possible for chaos

masking in the case of bidirectional coupling.

Finally, we consider the case when the transmit-

ter and the receiver systems are not exactly identical,

i.e. either κ

6= κ

or laser parameters exhibit a small

mismatch. Therefore, SL

and SL

are partially syn-

chronized by a certain function. Now, GS between

ML and SL in the transmitter and in the receiver

is characterized by two different functional depen-

dences, that causes a small difference betweenC

and

, δC = C

−C

, and we are interested in how the

mismatch δC affects communication quality. Keep-

ing all laser parameters identical and κ

= 80 ns

−1

for which C

= 0.7781 [Figure 2(b)], we vary κ

(60

−1

≤κ

≤100 ns

−1

) giving as a result the variation

OPTICAL SECURE COMMUNICATION SYSTEM BASED ON CHAOS SYNCHRONIZATION

151

Figure 3: Q-factor as a function of coupling parameter be-

tween ML and SL for (a) chaos shift keying and (b) chaos

masking for 1 Gb/s (ﬁlled signs) and 5 Gb/s (open signs)

signal transmission when master lasers are coupled unidi-

rectionally (dots) and bidirectionally (squares) for (a) chaos

shift keying and (b) chaos masking. The communication

quality is good above the dashed line. For chaos shift key-

ing the 5 Gb/s transmission is not possible.

of C

(−0.04 ≤C

≤0.04). Figures 4(a-c) show he

(in %) and Q as functions of δC for 1 Gb/s and 5 Gb/s

transmission; Fig. 4(a) was obtained with chaos shift

keying and Figs. 4(b) with chaos masking for bidi-

rectionally coupled master lasers with ε = 16 ns

−1

The loss of synchronization between slaves due to the

chaos shift keying results in the displacement of the

maximum C and minimum he

i from δC = 0 in Fig-

ure 4(a). With the same ε Figure 4(c) represents the

results for chaos masking for unidirectional coupling,

clearly not as efﬁcient as bidirectional coupling. The

communication quality for chaos shift keying with

unidirectionalcoupling is not sufﬁcient (Q < 10) [Fig-

ure 3(a)]. Although chaos masking allows a 1 Gb/s

communication with unidirectional coupling, the er-

ror is relatively high (he

i > 15%) [Figure 4(c)].

We now also consider what happens when the

master lasers are not completely identical, keeping

= κ

. In this case, the most critical parameter for

synchronization is the injection current. Figures 4(d-

f) show how a small mismatch δI = I

−I

and

being the injection currents of the master lasers in

the transmitter and in the receiver) affects he

i and

Q. One can see that when the master lasers are cou-

pled bidirectionally, the system is more robust to a

parameter mismatch, i.e. the 1 Gb/s transmission can

be realized in a much larger region of δC or δI, and

even a 5 Gb/s rate can be obtained but only for chaotic

masking and only when the slave lasers and the mas-

ter lasers are completely synchronized, i.e. when the

identity conditions, δC ≈ 0 and δI ≈ 0, are fulﬁlled.

Figure 4(d) shows that chaos key shifting even for 1

Gb/s is not as efﬁcient as chaos masking.

Figure 4: Mean synchronization error (triangles) and Q-

factor (dots) as functions of mismatch of (a-c) correlations

δC and (e-f) injection currents δI of master lasers for chaos

shift keying (left-hand column) and chaos masking (middle

and right-hand columns) when the master lasers are cou-

pled either bidirectionally (left-hand and middle columns)

or unidirectionally (right-hand column). 1 Gb/s and 5 Gb/s

transmission are shown by the closed and open dots, respec-

tively. κ

= 80 ns

−1

, ε = 16 ns

−1

for bidirectionally and

ε = 80 ns

−1

for unidirectionally coupling, and I

= 29 mA.

The communication quality is good above the dashed lines.

3 CONCLUSIONS

We have introduced an efﬁcient optical chaotic com-

munication system which uses the combination of

complete and generalized synchronizations. The sys-

tem contains two channels, one for synchronization

and the other for information transmission, and con-

sists of two pairs of external cavity semiconductor

lasers each coupled in GS conﬁguration, while the

master lasers in the transmitter and in the receiver

are completely synchronized. The ability of this

system for high-quality communication is demon-

strated through numerical simulations with the Lang-

Kobayashi model. We have shown that bidirectional

coupling between the master lasers provides much

better communication quality (up to 5 Gb/s) than uni-

directional coupling and makes the system more ro-

bust to a mismatch between the ML parameters or the

coupling strengths between ML and SL. In the case

of bidirectional coupling, the two coupled lasers in-

ﬂuence to each other so that the identity requirements

for complete synchronization are not as strong as in

the case of unidirectional coupling that allows more

tolerances. The efﬁciency of this system is very clear

when the encryption method is chaos masking, it can

also be used for other methods although the results

are not so spectacular.

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152

ACKNOWLEDGEMENTS

This work was supported by Consejo Nacional de

Ciencia y Tecnologa of Mexico (project No. 100429).

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