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Random bit generation using an optically

injected semiconductor

laser in chaos with oversampling

Xiao-Zhou Li and Sze-Chun Chan*

Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

*Corresponding author: scchan@cityu.edu.hk

Received February 21, 2012; revised April 12, 2012; accepted April 20, 2012;

posted April 23, 2012 (Doc. ID 163393); published June 1, 2012

Random bit generation is experimentally demonstrated using a semiconductor laser driven into chaos by optical

injection. The laser is not subject to any feedback so that the chaotic waveform possesses very little autocorrelation.

Random bit generation is achieved at a sampling rate of 10 GHz even when only a fractional bandwidth of 1.5 GHz

within a much broader chaotic bandwidth is digitized. By retaining only 3 least significant bits per sample, an out-

put bit rate of 30 Gbps is attained. The approach requires no complicated postprocessing and has no stringent

requirement on the electronics bandwidth.© 2012 Optical Society of America

OCIS codes: 140.5960, 140.1540, 140.3520, 190.3100.

Random bit generation requires each output bit to be

associated with an unbiased probability for 0 and 1, in-

dependent of the rest of the bits. Applications of random

bit generators include stochastic modeling, encryption,

and secure communication, where a fast generation

speed often has positive impact on the performances.

The broad bandwidths offered by photonic devices

have recently been utilized for high-speed random bit

generation [1,2]. For instance, random bit generation

using quantum randomness in a pulsed laser was demon-

strated [3]. Randomness of spontaneous emissions from

incoherent light sources wasalso utilized [4,5]. Pioneered

by Uchida et al., chaotic dynamics of semiconductor

lasers continue to be important for fast random bit

generation [1]. In their work, chaotic intensities were

emitted from two lasers subject to optical feedback.

Upon detection by photodetectors, chaotic waveforms

with electronic bandwidths of about 3 GHz were

obtained. The waveforms were digitized at a sampling

rate of 1.7 GHz by analog-to-digital converters (ADCs)

of 1-bit resolution. The digitized signals were merged

using exclusive-or (XOR) so the resultant output bit rate

was 1.7 Gbps. Progress was made by further optically in-

jecting the chaotic waveforms into another laser, which

enhanced the bandwidths to attain increment of the out-

put bit rates [6]. Simulations on all-optical generation

were also conducted [7,8]. Additionally, by incorporating

high-resolution ADCs, more than 1 bit can be generated

in each sampling period so that the effective output bit

rate can be significantly increased. Kanter et al. demon-

strated generation of 15 random bits per sampling period

[2]. With an electronic detection bandwidth of 12 GHz

and a sampling rate of 20 GHz, an effective output rate

of 300 Gbps was achieved after much postprocessing.

High-order derivatives were computed to enhance small

fluctuations of the digitized signals in order to pass the

randomness tests. Simplifications by discarding the most

significant bits (MSBs) and retaining the least significant

bits (LSBs) were also reported [9].

Two features are common to the above approaches.

First, the chaotic waveforms were always generated

by optical feedback into the lasers, even if the waveforms

were further broadened by optical injection into or from

another laser. This often leads to residual autocorrelation

at the feedback round-trip time, which should be set in-

commensurate with the sampling period through careful

design [10,11]. Second, the chaotic waveforms were

always undersampled in which two times their electronic

bandwidths exceeded the respective sampling rates.

Undersampling violates the Nyquist criterion to cause

aliasing and flattening of the spectrum for random bit

generation. However, the chaotic waveforms, photode-

tectors, and front ends of the ADCs must have suffi-

ciently large bandwidths in order to support high

sampling rates.

In this Letter, we experimentally demonstrate random

bit generation using an optically injected laser and over-

sampling. A chaotic waveform is generated by the in-

jected semiconductor laser. The waveform is digitized

by an 8-bit ADC with a low front-end bandwidth of only

1.5 GHz, but is oversampled at a sampling rate of 10 GHz.

By retaining only the 3 LSBs and performing XOR on

consecutive samples, random bits are generated at an

output bit rate of 30 Gbps. Since the laser is not subject

to any feedback, there is no round-trip time for the

sampling period to avoid. The use of oversampling also

relaxes the requirements on the front-end bandwidth of

the ADC. The output bits are shown to pass the standard

test suite for random numbers from the National Institute

of Standards and Technology (NIST).

Figure 1 shows our experimental setup for random

bit generation. The master and slave lasers are both

Fig. 1.

SL, slave laser; VA, variable attenuator; CIR, circulator; OI,

optical isolator; PD, photodetector; A, amplifier; PSA, power

spectrum analyzer.

Schematic of the experimental setup. ML, master laser;

June 1, 2012 / Vol. 37, No. 11 / OPTICS LETTERS2163

0146-9592/12/112163-03$15.00/0© 2012 Optical Society of America

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single-mode

ML920T43S-01) emitting at about 1.55 μm. The slave

laser is biased above threshold at 40 mA and is tempera-

ture stabilized at 26.50 °C. It emits about 10 mW with a

relaxation resonance frequency of about 11 GHz. The

master laser is biased at 128.5 mA and is also temperature

stabilized. Its continuous-wave emission passes through

a variable attenuator, a free-space circulator, and im-

pinges on the slave laser facet with about 0.3 mW. The

optical frequency detuning of the master laser from

the slave laser is about 12.5 GHz. Such optical injection

drives the slave laser into chaotic oscillation [12,13].

Chaotic oscillations are capable of amplifying the effects

of intrinsic laser noise [14]. The emission from the

slave laser then passes the circulator and an isolator

so that about 0.5 mW enters a photodetector (Newport

AD-10ir) for optical-to-electrical conversion. The electri-

cal chaotic waveform is then amplified by 40 dB using a

microwave amplifier. For digitization, the electrical

chaotic waveform is monitored by an 8-bit ADC in an

oscilloscope (Agilent 90254A) for subsequent processing

in a computer. The front-end bandwidth of the ADC is

only 1.5 GHz, but the sampling rate is set at 10 GHz.

To ensure randomness, only the 3 LSBs are retained

for each sample. The bits of each sample are then com-

pared by an XOR to the respective bits of the previous

sample, which are stored in a buffer. The buffer is equiva-

lent to a delay of one sampling period. So the output from

the XOR is a bit stream at 30 Gbps.

The chaotic waveform is first characterized by con-

necting the output of the amplifier in Fig. 1 to a power

spectrum analyzer (Agilent N9010A) instead of the

ADC. The red curve in Fig. 2(a) shows the power spec-

trum of the chaotic waveform. The signal bandwidth is

about 10.27 GHz according to the convention of 80% con-

tainment of total power [15]. The gray curve in Fig. 2(a)

shows the noise spectrum measured when the master

laser is turned off and the slave laser is free-running.

It is clear that the chaos spectrum is stronger than and

different from the noise spectrum. The corresponding

autocorrelation trace of the chaotic waveform is shown

in Fig. 2(b). The autocorrelation quickly diminishes as

the delay time increases from zero. Its magnitude is lower

than 0.02 when the delay is longer than 2 ns. By contrast,

chaotic lasers under optical feedback are often asso-

ciated with stronger autocorrelation peaks at multiples

of the feedback round-trip time, which cause restric-

tions on the sampling frequency [10,16]. Therefore, the

distributed-feedbacklasers(Mitsubishi

absence of any feedback round-trip time is a unique ad-

vantage of optical injection over optical feedback.

The chaotic waveform after the amplifier is input to the

ADC in Fig. 1. The peak-to-peak amplitude of the input

waveform is about 0.2 V. The digitized signal obtained

at position a immediately after the ADC in Fig. 1 is shown

in Fig. 3(i). Each sampled data point is digitized into

8 bits corresponding to 256 digitization levels, as the cor-

responding inset shows. The front-end of the ADC has a

low-pass cutoff frequency of only 1.5 GHz, but the ADC

performs oversampling at a sampling frequency of

10 GHz. This resulted in the rather smooth digitized sig-

nal, which cannot be directly used as random bits.

However, Fig. 3(ii) shows a very irregular signal at

position b of Fig. 1. It is because the 5 MSBs of each data

point are discarded and only the 3 LSBs are selected.

Selecting the LSBs is equivalent to a modulo operation,

or a folding action, that scrambles the data points [17].

The final output at position c of Fig. 1 is then obtained

by comparing consecutive data points through bitwise

XOR operations, as shown in Fig. 3(iii). The XOR opera-

tions effectively reduce any small statistical bias of the

bits [10]. Overall, the output bits are generated at a

rate of 30 Gbps. They are verified to be random through

passing the NIST Special Publication 800-22 statistical

(a)(b)

Fig. 2.

amplifier. (a) Power spectrum of chaos (red) and noise (gray).

(b) Magnitude of autocorrelation of chaos.

(Color online) Measurements at the output of the

Fig.3.

(ii) position b, and (iii) position c of the experimental setup.

(Coloronline)Digitizedsignalsobtainedat(i) positiona,

Table 1. Results of the NIST Special Publication

800-22 Statistical Tests for Random Bits

Statistical TestP-value ProportionResult

Frequency

Block-frequency

Cumulative-sums

Runs

Longest-run

Rank

FFT

Nonperiodic-templates

Overlapping-templates

Universal

Approximate-entropy

Random-excursions

Random-excursions-variant 0.068219

Serial

Linear-complexity

Total

0.919131

0.735908

0.298282

0.643366

0.112047

0.030399

0.002058

0.007639

0.454053

0.052275

0.518106

0.299251

0.9890

0.9930

0.9870

0.9900

0.9920

0.9910

0.9910

0.9820

0.9920

0.9940

0.9890

0.9842

0.9826

0.9830

0.9890

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

Success

15

0.429923

0.618385

2164OPTICS LETTERS / Vol. 37, No. 11 / June 1, 2012

Page 3

tests, which are standard tests for randomness. A total of

1000 sequences, each of size 1 Mbit, are collected for test-

ing. At significance level α ? 0.01, the success proportion

should be in the range of 0.99 ? 0.0094392. The compo-

site P-value should be larger than 0.0001 to ensure uni-

formity. The testing results are summarized in Table 1,

where the worst case is shown for tests producing multi-

ple P-values and proportions. Besides, when the master

laseris switchedoff,

running slave laser and the electronics is responsible

for generating the output bits. Because the correspond-

ing noise spectrum in Fig. 2(a) is very weak, the output

bits are found to fail the randomness tests even if 7 MSBs

are discarded in retaining only 1 LSB. This shows that

the chaotic waveforms are essential to random bit

generation in the experiment.

Random bits can be generated from the oversampled

signal because the signal bandwidth is significantly broa-

dened when the MSBs are discarded. Figure 4 shows

the spectra of the digitized signals at positions a, b,

and c of the setup in Fig. 1, which are Fourier transforms

of the digitized signals in Figs. 3(i), 3(ii), and 3(iii),

respectively. The full frequency-span of 5 GHz at half

the sampling frequency is presented. The red curve

shows the signal at position a. Limited by the front-

end bandwidth of the ADC, the signal drops quickly

at 1.5 GHz and is thus not suitable for random bit genera-

tion. However, the gray curve obtained at position b

shows a much broadened and nearly white spectrum.

This is because the MSBs are discarded in selecting

the LSBs, which is a very nonlinear operation that causes

significant frequency mixing. Experimentations show

that at least 5 MSBs have to be discarded in order to

ensure sufficient frequency mixing for passing the

randomness tests. The final output at position c has a

featureless white spectrum as shown by the black curve,

which is an essential indicator that the output bits are

random.

noisefromthe free-

In summary, random bit generation is demonstrated

using a chaotic laser driven by optical injection

alone. Because of the absence of optical feedback, the

autocorrelation of the chaotic waveform is free from

any problematic side peaks. Also, in spite of oversam-

pling, random bit generation is enabled by selecting only

the LSBs to effectively broaden the spectrum during

postprocessing. This relaxes the electronic bandwidth re-

quirements of the ADC front end. Utilizing only 1.5 GHz

of a much broader chaos spectrum, random bit genera-

tion at 30 Gbps is successfully demonstrated.

The work described in this paper was fully supported

by a grant from the Research Grants Council of Hong

Kong, China (Project No. CityU 111210).

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Fig. 4.

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(Color online) Spectra of the digitized signals obtained

June 1, 2012 / Vol. 37, No. 11 / OPTICS LETTERS 2165