True random number generator based on discretized
encoding of the time interval between photons
Shen Li,
1
Long Wang,
3
Ling-An Wu,
2,
* Hai-Qiang Ma,
2,3
and Guang-Jie Zhai
1
1
Laboratory of Space Science Experiment Technology, Center for Space Science and Applied Research, Chinese
Academy of Sciences, Beijing 100190, China
2
Laboratory of Optical Physics, Institute of Physics and Beijing National Laboratory for Condensed Matter Physics,
Chinese Academy of Sciences, Beijing 100190, China
3
College of Physics, Beijing University of Posts and Telecommunications, Beijing 100876, China
*Corresponding author: wula@aphy.iphy.ac.cn
Received October 8, 2012; revised December 5, 2012; accepted December 10, 2012;
posted December 11, 2012 (Doc. ID 177068); published December 20, 2012
We propose an approach to generate true random number sequences based on the discretized encoding of the time
interval between photons. The method is simple and efficient, and can produce a highly random sequence several
times longer than that of other methods based on threshold or parity selection, without the need for hashing. A
proof-of-principle experiment has been performed, showing that the system could be easily integrated and applied
to quantum cryptography and other fields. © 2013 Optical Society of America
OCIS codes: 270.5290, 030.5260, 230.0250.
1. INTRODUCTION
Random number generators are widely used in many fields,
such as quantum cryptography [
1], digital signature [2], statis-
tical sampling [
3], computer simulation [4], and so forth. In
quantum cryptography, trains of photons with randomly
modulated phase or polarization are used as bit carriers for
quantum key distribution, the security of which is guaranteed
by the laws of quantum mechanics. In digital signature,
whether classical or quantum, a sequence of true random bits
is also required to generate the encryption key. The random-
ness of the bits relates to the security of the communication,
so how to obtain true randomness with high efficiency is an
important research subject in information security and cryp-
tography. Ideally, a uniformly distributed, unpredictable, and
independent sequence of random bits should be produced.
The random numbers currently used are usually pseudoran-
dom sequences generated from a short random seed by em-
ploying deterministic algorithms. Although they can pass
many randomness tests provided the length of the sequence
is less than a certain limit [
5,6], once the algorithm and seed
are given, the generated numbers are deterministic and repea-
table, which poses a serious security threat for encryption sys-
tems based on these pseudorandom sequences. Fortunately,
there are many physically random phenomena which can pro-
vide us with true random number (TRN) generation, such as
the decay of radioactive nuclei [
7], thermal noise in resistors
[
8], air turbulence [9], and so on. Obviously, for secure infor-
mation communication, these TRN sequences based on unpre-
dictable physical processes are much more preferable than
pseudorandom numbers produced with a certain algorithm.
In recent years, many practical schemes have been demon-
strated [
10–15]. Some TRN generators based on the division
of a beam of photons on a beamsplitter (BS) have been rea-
lized, but the optical components can never be ideal. The light
sources currently used are not perfect single-photon sources
[
16–19], while the transmission/reflection ratio of the BS can
never be exactly 50∕50%. To correct the effect of this imbal-
ance, hashing of the raw bits is necessary, which inevitably
shortens the sequence length.
2. THEORY
In this paper, we propose a new approach to generate TRNs
based on the discretized encoding of the time interval be-
tween photons. Only a very simple setup is required, but it
can produce a bit sequence of high randomness with great ef-
ficiency, and no hashing is required. As in [
20], we consider
the time interval between photons emitted by a pulsed laser as
a noise source, with the beam attenuated to the extent that, on
average, the number of photons in each pulse is about 0.1.
We know that the photon number distribution in laser emis-
sion is Poissonian, so the probability for a pulse to contain n
photons is
P
n
μ
n
e
−μ
∕n!; (1)
where μ is the mean number of photons in one pulse. When
μ ≪ 1, the probability of a pulse containing no photons is
P
0
e
−μ
≈ 1 − μ
μ
2
2
: (2)
The probability of a pulse containing one photon is
P
1
μe
−μ
; (3)
and that for a pulse to contain two or more photons is
P
n≥2
1 − P
0
− P
1
1 − e
−μ
1 μ : (4)
124 J. Opt. Soc. Am. A / Vol. 30, No. 1 / January 2013 Li et al.
1084-7529/13/010124-04$15.00/0 © 2013 Optical Society of America