76 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 2, JANUARY 15, 2007
Message Encryption by Phase Modulation of a
Chaotic Optical Carrier
Valerio Annovazzi-Lodi, Senior Member, IEEE, Mauro Benedetti, Member, IEEE,
Sabina Merlo, Senior Member, IEEE, Toni Perez, Pere Colet, and Claudio R. Mirasso
Abstract—We present a numerical and experimental evaluation
of message encryption by phase modulation, using a chaotic optical
carrier generated by a laser subject to delayed optical feedback.
This method offers better security than the conventional amplitude
masking, where the signal is simply added to the chaotic waveform.
Index Terms—Chaos, communication systems, cryptography,
phase modulation.
I. INTRODUCTION
O
PTICAL chaotic cryptography is a hardware technique for
secure transmission which makes use of a couple of lasers
operating in the chaotic regime [1]–[9]. Chaos-based encryp-
tion uses a chaotic laser [“master” laser (ML)] at the transmitter
side to hide the information to be transmitted (the message);
another laser [“slave” laser (SL)], at the receiver, allows for
message recovery. The extraction of the hidden message from
chaos is based on synchronization between ML and SL, i.e., on
the generation of the same chaotic waveform at both ends of
the channel. Synchronization can be only obtained under suit-
able conditions, by injecting part of the ML output into the SL,
and relies on two lasers being closely matched, which ensures
security. The cryptographic key consists in the set of parame-
ters of the two matched lasers. In the basic scheme (“chaotic
masking”), chaos is simply added to the message [1], [2], [4],
[6], and transmission of real signals has been recently demon-
strated [4].
Another approach, first proposed in [5], exploits the strong
dependence of synchronization on the relative phase between
the external cavities of ML and SL. Indeed, a phase variation
of the ML external cavity, which is small enough to be unde-
tectable by observation of the chaotic waveform or of its spec-
trum, can substantially affect the correlation between the two
laser outputs [8]. Thus, if the ML phase is modulated by a mes-
sage, the latter can be extracted by transferring the induced
Manuscript received July 6, 2006; revised November 9, 2006. This work was
supported in part by MIUR (COFIN 2005), in part by the Spanish MCyT and
Feder under Projects TEC2005-07799-C02-01 and FIS2004-00953, and in part
by EU Project PICASSO IST-2005-34551.
V. Annovazzi-Lodi, M. Benedetti, and S. Merlo are with the Dipartimento
di Elettronica, Universita' di Pavia, I-27100 Pavia, Italy (e-mail: valerio.
annovazzi@unipv.it).
T. Pérez, P. Colet, and C. R. Mirasso are with the Departament de Física,
Universitat de les Illes Balears and Instituto Mediterráneo de Estudios Avan-
zados, CSIC-UIB, Campus UIB 07122 Palma de Mallorca, Spain (e-mail:
claudio@galiota.uib.es).
Digital Object Identifier 10.1109/LPT.2006.888968
variation of the correlation coefficient into amplitude modula-
tion. This can be easily done by taking the difference between
the phase-modulated (PM) chaotic waveform coming from the
transmitter and the chaotic waveform from the receiver, as in
the standard masking scheme [3], [4]. Moreover, the system
must operate at a suitable bias point, which, for analog signal
transmission, is halfway between maximum and minimum cor-
relation level for best linearity. An important characteristic of
this method is that it requires a “closed loop” scheme for detec-
tion, i.e., the SL must be routed to chaos by an external cavity
identical to that of the master. On the other hand, with chaos
masking, the message can be extracted (with a lower signal-to-
noise (S/N) ratio) also by the less critical “open loop” scheme,
where the SL has no feedback and can be less strictly matched
to the ML [2].
Though phase modulation cryptography has been already
studied theoretically, it has been demonstrated experimentally
only in the quasi-static regime [5]. One problem in working
with real signals is that signal detection by waveform difference
results in a relatively complex setup, which is more critical to
align than in the case of standard masking; an accurate delay
compensation is required between the ML and SL chaotic
waveforms to get the true difference [3]. To that purpose, an
RF delay line may be used on either ML or SL photodetected
signal, as in [3] and [4]. In this letter we show, however,
that under suitable operating conditions, the message can be
detected simply by direct observation of the output of the
SL, by using a single photodetector and RF amplifier, which
requires neither delay trimming or matching of amplifiers
and RF lines. With this more manageable scheme, secure
transmission of a frequency-modulated (FM) carrier has been
demonstrated.
II. N
UMERICAL ANALYSIS AND
EXPERIMENTS
The arrangement for the phase modulation experiment is
shown in Fig. 1, and consists of a typical master/slave config-
uration. Each laser is driven to chaos by back-reflection from
the fiber tip positioned in front of its launching lens [4], which
defines an external cavity of about 10 cm. This short-cavity
scheme is compact and mechanically stable, as required for low
phase drift. A LiTaO
crystal is included in the master cavity
and is used as a phase modulator to insert the message; the
crystal in the slave cavity only keeps symmetry, as required for
efficient synchronization. To simplify the numerical analysis,
the laser and external cavity parameters were taken to be
identical for both ML and SL. The equations for the complex
1041-1135/$20.00 © 2006 IEEE
ANNOVAZZI-LODI et al.: MESSAGE ENCRYPTION BY PHASE MODULATION 77
Fig. 1. Transmission setup.
slowly varying electric field of transmitter (ML) and
of receiver (SL) are [5]
(1)
(2)
Equations (1) and (2) describe the lasers by the linewidth en-
hancement factor
, the photon lifetime ps,
and the modal gain
, where
ps is the differential gain,
is the carrier concentration at transparency,
is the saturation parameter. The external cavities are modeled
by the second terms:
ps is the feedback delay time,
ns is the feedback strength, and is the optical
phase, which is constant (
for our partameter values)
for the SL while it is modulated (
) in the ML. The last term of
the SL equation models the injection from the ML:
, are the
propagation time and phase (
in the simulations,
as in a back-to-back experiment),
ns is the coupling
coefficient. The equation for carriers
can be found in [5].
Applied phase modulation had the general form
, where is a
carrier frequency and
is the message frequency, assumed
to be of sinusoidal form. As it was observed experimentally,
this FM-over-PM scheme is robust to additive noise, consisting
mainly of residual chaos at the slave output, which, instead,
strongly affects message detection when the chaotic carrier is
directly modulated in phase. Numerical results have shown the
viability of detection by direct observation of the slave output.
Indeed, we have found that, by selecting suitable values of
message and carrier amplitude, the FM signal can be efficiently
hidden in the ML spectrum, while it is clearly detectable at the
SL output.
Typical results obtained in optimized conditions are shown
in Figs. 2 and 3. Parameter
, MHz,
Hz, and kHz were selected to match
Fig. 2. Simulated master RF spectrum with hidden FM modulated carrier.
Fig. 3. Simulated slave RF spectrum with the recovered signal (zooming
around the carrier frequency is shown in the inset).
the experimental values (see below). In Fig. 2, the master RF
spectrum, with the hidden modulated carrier, shows no visible
signal. However, the carrier is evident in the SL spectrum of
Fig. 3, with its FM modulation (at 1 kHz) highlighted in the
inset. The small second-harmonic component may be easily
filtered out.
Experiments were performed on the setup of Fig. 1. The
path between transmitter and receiver was
1.2 km of standard
telecommunication fiber and, besides splitters, couplers, and
joints, it included also a semiconductor optical amplifier, to
increase the maximum injection level from master into slave.
The optical isolator in Fig. 1 ensures unidirectional injection.
Polarizers in front of the lasers select, for both feedback and
injection, the same polarization as that of the laser emission.
Moreover, the polarizer in the slave was used, together with
the polarization controller, to trim the injection level. The laser
pair consisted of standard 1-mW distributed feedback telecom-
munication devices (
nm), which were selected
between first neighbors of the same wafer. Their difference of
threshold and differential efficiency were lower than 1%, and
their wavelengths were matched within 100 pm by temperature
tuning. The characteristics of the chaotic regime of the lasers
depend on the operating conditions, such as injection current
and feedback level.
Master/slave synchronization was obtained by adjusting the
injection current (
50% above threshold), the alignment, and
the temperature of both lasers, as well as the injection level,
78 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 2, JANUARY 15, 2007
Fig. 4. RF chaos spectra: ML with hidden carrier (black) and SL with extracted
carrier (gray). The traces have been separated by a 3-dB attenuator for a better
comparison of their shape.
which was of the same order of the feedback level (
of the laser output power). The two external cavities were also
carefully matched. The regimes of the two lasers were compared
by observing the outputs of photodiodes PD1 and PD2 by an
RF spectrum analyzer. The synchronization level was checked,
as explained in [3], by observing (with no delay compensation)
the spectrum of the difference of ML (at PD3) and SL (at PD2)
outputs.
When the setup was aligned at best, the correlation coefficient
between master and slave outputs was
0.9, in the absence
of modulation. The chaos bandwidth was
5 GHz, limited by
the photodiode and amplifier speeds. Transmission experiments
were performed by modulating the input voltage of the master
LiTaO
crystal, giving rise to a 100-MHz carrier, modulated on
its turn by a 1-kHz message. At the slave output, the carrier was
fed to an FM receiver to get the message.
In Fig. 4, the master and slave RF spectra are shown. The FM
carrier is not visible in ML spectrum (black line) since it is em-
bedded in chaos; after proper alignment of the setup, however,
the recovered carrier becomes clearly visible in the SL spectrum
(gray line). In the figure, synchronization was optimized in the
0- to 200-MHz working range and the two traces were separated
for easier comparison.
In Fig. 5, the message without encryption (a) can be compared
with the recovered message (d) obtained with both ML and SL
switched
ON, and with the setup properly aligned. Fig. 5(b) (ML
and SL
OFF) represents the channel noise; Fig. 5(c) (ML ON and
SL
OFF) is the message as it would be detected by an eaves-
dropper tapping the fiber. The carrier and the message ampli-
tude were adjusted to reach a compromise between low signal
distortion and good S/N ratio; the maximum phase modulation
was a small variation
around the phase bias , which
was also trimmed for the best quality of the recovered message.
Fig. 5. (a) Sinusoidal message modulating the carrier of Fig. 4; (b) system
output with ML and SL
OFF; (c) system output with ML
ON
and SL
OFF; (d) re-
covered message with both ML and SL
ON and aligned.
As expected [5], the optimum value of
gave partial chaos
correlation with no carrier, while trimming for both maximum
and minimum chaos correlation resulted into message fading.
In conclusion, we have shown that phase modulation of a
chaotic carrier is a viable method for secure transmission in the
RF range. Message detection by direct observation of the slave
output results in a much more manageable experimental setup.
Both the carrier and the modulation frequency of our experi-
ments were determined by the availability of suitable modula-
tors and receivers. Further investigations will be devoted to the
evaluation of the intrinsic speed limit (which is expected to be
related to the synchronization delay), as well as to the extension
of this method to higher frequency signals (including digital sig-
nals in baseband).
R
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