The physical generation of true random numbers by uoh11382



The physical generation of true
random numbers
Zhiliang Yuan, James Dynes, and Andrew Shields

Ultra-secure quantum cryptography is realized through the wave func-
tion collapse of coherent photons.

The generation of high-quality random numbers is desirable for
a number of real world applications, most notably cryptogra-
phy. The strength of many cryptographic protocols relies upon
the quality of random numbers. Put simply, the higher the qual-        Figure 1. Two quantum RNG schemes based on the (a) particle-like or
ity of random numbers, the stronger the resulting cryptography         (b) wave-like nature of photons.
will be, and true random numbers are required for ultra-secure
quantum communication.1, 2                                             Post-processing has been required for all quantum RNGs except
   In practice, the generation of true random numbers is notori-       for the one we have designed, and it was not known, prior to our
ously difficult. By true, we mean that the random numbers must          work, whether a true quantum RNG could be purely physical.
be completely unpredictable and unreproducible. They must be              In our design, we avoid the photon detection rate imbalance
bias-free bits (‘0’ and ‘1’) generated with equal probabilities. At    by exploiting the wave-like nature of photons.3 A long-lasting
the same time, a random number produced earlier cannot re-             photon will collapse into a time window defined by measure-
liably be reproduced later, even by the same generator under           ment, and random wave function collapse is a source for true
exactly the same conditions.                                           randomness (provided that each measurement time window is
   These requirements dictate that a computer algorithm cannot         much smaller than the photon coherence time).
generate true random numbers because its output is always de-             As shown in Figure 1(b), a quantum RNG exploiting the
terministic and reproducible. A true random number generator           wave-like nature of photons can be constructed simply with a
(RNG) therefore has to be hardware based, making use of the            source and detector. We use a laser diode as the source with
intrinsically unpredictable outcomes of a physical process.            a coherence time of 1ms, while the detector is gated at 1GHz
   Quantum mechanical uncertainty is an ideal source of                with each detection window 1000 times smaller than the coher-
randomness in that it has the potential to offer the perfect ran-      ence time. Such a large disparity in time ensures an equal de-
domness guaranteed by the laws of quantum physics. As shown            tection probability between any two adjacent detection gates. By
in Figure 1(a), a quantum RNG can be realized by exploiting the        assigning a bit value ’0’ or ’1’ according to a detection event at
particle-like nature of photons. In this elegant scheme, the source    an even or odd clock cycle, a bias-free random number is readily
of randomness is the passive path selection of a photon hitting a      obtainable.
semitransparent beam splitter. In theory, it should produce per-          To realize this scheme, it is crucial for the detector to have
fectly random numbers.                                                 certain characteristics. Ideally, the detector should be operated
   However, random numbers obtained this way will be biased            in gated mode in order to allow unambiguous bit-value assign-
due to the inevitable imbalance in photon detection rates be-          ments. Moreover, to achieve high bit rates that are free of bias,
tween the two detectors. This bias, then, has to be removed            the detector must be able to handle high photon rates and pos-
through mathematical post-processing (which is common for a            sess a negligible counting dead time.
physical RNG) in order to improve random number quality.

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                                                                                                          10.1117/2.1200906.1698 Page 2/3

Figure 2. Photon count rate as a function of incident light intensity
recorded for a self-differencing indium gallium arsenide single-photon
APD. A maximum photon count rate of 497MHz is measured, which
                                                                            Figure 3. Byte correlation pattern of 500m bits generated by our
is very close to the value expected from a theoretical calculation (black
                                                                            52Mb/s quantum RNG.
line) assuming zero detector dead time.

                                                                            limited by the photon recording electronics, which can manage
   Semiconductor avalanche photodiodes (APDs) are well suited
                                                                            photons at only 5 million per second.
to this task. Operated under a self-differencing mode4 that was
                                                                               In future work, we aim to design electronics to cope with a
originally devised by us for megabit-per-second (Mb/s) secure
                                                                            photon rate of 1 billion per second and with such technology
key-rate quantum key distribution,1, 2 an analog telecommuni-
                                                                            available, we expect to see the bit rate surpassing 100Mb/s. Us-
cation APD can be converted into a high-speed single-photon
                                                                            ing finer timing, a bit rate of multi-gigabits per second is in sight.
detector. Using this system, we achieved a record photon count
                                                                               Finally, as this RNG is based on semiconductor components,
rate of ∼ 500MHz and an ultra-short dead time of less than 2ns
                                                                            we envisage high-level integration to obtain a compact and ro-
(see Figure 2).5
                                                                            bust high-speed RNG with randomness of the highest quality.
   Incorporating a self-differencing APD, we have initially
realized a quantum RNG with a random bit stream of 4Mb/s.3
Importantly, the quantum randomness has survived in this                    Author Information
physical realization, and the random number outputs are in-
trinsically free of bias and do not require mathematical post-              Zhiliang Yuan, James Dynes, and Andrew Shields
processing to pass random number statistical tests.                         Cambridge Research Laboratory
   It is the first time that any quantum RNG—and perhaps any                 Toshiba Research Europe Ltd
physical RNG—has not required post-processing to pass strin-                Cambridge, United Kingdom
gent randomness tests. Furthermore, by using finer photon tim-     
ing, the random bit rate can be increased by over an order of
magnitude to 52Mb/s with no degradation in randomness.6
Figure 3 shows a visualization of the random output from our                Zhiliang Yuan leads the quantum key distribution project at
52Mb/s RNG.                                                                 Toshiba Research Europe Ltd.
   Despite the state-of-the-art performance, the bit rate must be
improved to serve demanding applications, such as high bit-rate
quantum key distribution.1, 2 Presently, the random bit rate is
                                                                                                                        Continued on next page
                                                                                           10.1117/2.1200906.1698 Page 3/3

James Dynes obtained his PhD in strong laser field interactions
in 2005. After a post-doc at the London Centre for Nanotech-
nology, he began his current position as a research scientist at
Toshiba Research Europe Ltd. His research interests are quan-
tum key distribution and single photon detection.

Andrew Shields leads the quantum information group at
Toshiba Research Europe Ltd. His interests include semiconduc-
tor and photonic approaches to quantum information processing
and quantum communications.

1. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, Gigahertz
quantum key distribution with InGaAs avalanche photodiodes, Appl. Phys. Lett. 92,
p. 201104, 2008. doi:10.1063/1.2931070
2. A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, Gigahertz
decoy quantum key distribution with 1 Mbit/s secure key rate, Opt. Express 16 (23),
p. 18790, 2008.
3. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, A high speed, post-
processing free quantum random number generator, Appl. Phys. Lett. 93, p. 031109,
2008. doi:10.1063/1.2961000
4. Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, High speed sin-
gle photon detection in the near infrared, Appl. Phys. Lett. 91, p. 041114, 2007.
5. A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennett, and A. J. Shields,
Ultrashort dead time of photon counting InGaAs avalanche photodiodes, Appl. Phys. Lett.
94, p. 23113, 2009.
6. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, A 52-megabits/s, post-
processing free, quantum random number generator, CLEO/IQEC 2009, p. ITuM6, 2009.

                                     c 2009 SPIE

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