Silicon photomultiplier (SiPM) arrays normally contain tens of photon detection channels, with each channel consisting of several thousand microcells and each microcell being a normal single-photon avalanche diode with a quenching resistor. The dark counts of SiPM arrays have independent spatial and temporal randomness, which will be used for true random number generation in this paper. Since the arrival times of the high dark count rate in each channel are measured with a fast, high precision time-to-digital converter, along with the number of channels, the entropy can be extracted with very high efficiency. The bias in the raw data due to the exponential distribution of the arrival time differences between successive dark counts is removed using the transformation of the cumulative distribution function. Except for the preamplifiers for a signal readout from a 4-channel SiPM, all electronics components in our prototype are implemented inside of one chip of a field programmable gate array. The prototype has a 63.54 Mbps generation throughput, and the statistical quality of the generated random numbers is evaluated. Since the property of the dark count is compatible with single-photons from laser beams, one can easily increase the generation bitrate by either adding more SiPM channels or irradiating the SiPM with extra laser beams.

1.
T.
Jennewein
,
U.
Achleitner
,
G.
Weihs
,
H.
Weinfurter
, and
A.
Zeilinger
, “
A fast and compact quantum random number generator
,”
Rev. Sci. Instrum.
71
,
1675
1680
(
2000
).
2.
A.
Stefanov
,
N.
Gisin
,
O.
Guinnard
,
L.
Guinnard
, and
H.
Zbinden
, “
Optical quantum random number generator
,”
J. Mod. Opt.
47
,
595
598
(
2000
).
3.
H.
Fürst
,
H.
Weier
,
S.
Nauerth
,
D. G.
Marangon
,
C.
Kurtsiefer
, and
H.
Weinfurter
, “
High speed optical quantum random number generation
,”
Opt. Express
18
,
13029
13037
(
2010
).
4.
M.
Ren
,
E.
Wu
,
Y.
Liang
,
Y.
Jian
,
G.
Wu
, and
H.
Zeng
, “
Quantum random-number generator based on a photon-number-resolving detector
,”
Phys. Rev. A
83
,
023820
(
2011
).
5.
B.
Qi
,
Y.-M.
Chi
,
H.-K.
Lo
, and
L.
Qian
, “
High-speed quantum random number generation by measuring phase noise of a single-mode laser
,”
Opt. Lett.
35
,
312
314
(
2010
).
6.
Y.-Q.
Nie
,
L.
Huang
,
Y.
Liu
,
F.
Payne
,
J.
Zhang
, and
J.-W.
Pan
, “
The generation of 68 Gbps quantum random number by measuring laser phase fluctuations
,”
Rev. Sci. Instrum.
86
,
063105
(
2015
).
7.
M. A.
Wayne
,
E. R.
Jeffrey
,
G. M.
Akselrod
, and
P. G.
Kwiat
, “
Photon arrival time quantum random number generation
,”
J. Mod. Opt.
56
,
516
522
(
2009
).
8.
M.
Wahl
,
M.
Leifgen
,
M.
Berlin
,
T.
Röhlicke
,
H.-J.
Rahn
, and
O.
Benson
, “
An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements
,”
Appl. Phys. Lett.
98
,
171105
(
2011
).
9.
S. K.
Tawfeeq
, “
A random number generator based on single-photon avalanche photodiode dark counts
,”
J. Lightwave Technol.
27
,
5665
5667
(
2009
).
10.
F.-X.
Wang
,
C.
Wang
,
W.
Chen
,
S.
Wang
,
F.-S.
Lv
,
D.-Y.
He
,
Z.-Q.
Yin
,
H.-W.
Li
,
G.-C.
Guo
, and
Z.-F.
Han
, “
Robust quantum random number generator based on avalanche photodiodes
,”
J. Lightwave Technol.
33
,
3319
3326
(
2015
).
11.
ON Semiconductor
, ArrayC Series Silicon Photomultiplier (SiPM) 4-Side Scaleable Arrays,
2019
.
12.
A.
Ghassemi
,
K.
Sato
, and
K.
Kobayashi
, MPPC,
2017
.
13.
M.
Stipčević
and
J.
Bowers
, “
Spatio-temporal optical random number generator
,”
Opt. Express
23
,
11619
11631
(
2015
).
14.
H.
Xu
,
N.
Massari
,
L.
Gasparini
,
A.
Meneghetti
, and
A.
Tomasi
, “
A SPAD-based random number generator pixel based on the arrival time of photons
,”
Integration
64
,
22
28
(
2019
).
15.
M. A.
Wayne
and
P. G.
Kwiat
, “
Low-bias high-speed quantum random number generator via shaped optical pulses
,”
Opt. Express
18
,
9351
9357
(
2010
).
16.
S.
Li
,
L.
Wang
,
L.-A.
Wu
,
H.-Q.
Ma
, and
G.-J.
Zhai
, “
True random number generator based on discretized encoding of the time interval between photons
,”
J. Opt. Soc. Am. A
30
,
124
127
(
2013
).
17.
J.-m.
Wang
,
T.-y.
Xie
,
H.-f.
Zhang
,
D.-x.
Yang
,
C.
Xie
, and
J.
Wang
, “
A bias-free quantum random number generation using photon arrival time selectively
,”
IEEE Photonics J.
7
,
1
8
(
2015
).
18.
H.-Q.
Ma
,
Y.
Xie
, and
L.-A.
Wu
, “
Random number generation based on the time of arrival of single photons
,”
Appl. Opt.
44
,
7760
7763
(
2005
).
19.
C. E.
Shannon
, “
A mathematical theory of communication
,”
Bell Syst. Tech. J.
27
,
379
423
(
1948
).
20.
S. A.
Durai
and
E. A.
Saro
, “
Image compression with back-propagation neural network using cumulative distribution function
,”
World Acad. Sci. Eng. Technol.
17
,
60
64
(
2006
).
21.
J. D.
Golic
, “
New methods for digital generation and postprocessing of random data
,”
IEEE Trans. Comput.
55
,
1217
1229
(
2006
).
22.
Y.
Wang
,
J.
Kuang
,
C.
Liu
, and
Q.
Cao
, “
A 3.9-ps RMS precision time-to-digital converter using ones-counter encoding scheme in a kintex-7 FPGA
,”
IEEE Trans. Nucl. Sci.
64
,
2713
2718
(
2017
).
23.
Y.
Wang
,
C.
Hui
,
C.
Liu
, and
C.
Xu
, “
Theory and implementation of a very high throughput true random number generator in field programmable gate array
,”
Rev. Sci. Instrum.
87
,
044704
(
2016
).
24.
NIST
, Documentation-and-Software available at www.csrc.nist.gov,
2010
.
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