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Journal articles on the topic 'Random number generator'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 March 2023

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1

Manli Xu, Manli Xu, Jingzheng Huang Jingzheng Huang, Wenye Liang Wenye Liang, Chunmei Zhang Chunmei Zhang, Shuang Wang Shuang Wang, Zhenqiang Yin Zhenqiang Yin, Wei Chen Wei Chen, and Zhengfu Han Zhengfu Han. "Adjustable unbalanced quantum random-number generator." Chinese Optics Letters 13, no. 2 (2015): 021405–21409. http://dx.doi.org/10.3788/col201513.021405.

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2

Iavich, Maksim, Tamari Kuchukhidze, Giorgi Iashvili, and Sergiy Gnatyuk. "Hybrid quantum random number generator for cryptographic algorithms." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 4 (November 29, 2021): 103–18. http://dx.doi.org/10.32620/reks.2021.4.09.

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The subject matter of the article is pseudo-random number generators. Random numbers play the important role in cryptography. Using not secure pseudo-random number generators is a very common weakness. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions but are not random, called pseudo-random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo-random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. The goal is to develop a mathematical model of the generator, which generates fast random numbers at a lower cost. At the same time, a high level of randomness is essential. Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. The goal of the research is also to develop the model of a hybrid semi self-testing certification method for quantum random number generators (QRNG). The tasks to be solved are to create the mathematical model of a random number generator, which generates the fast random numbers at a lower cost. To create the mathematical model of a hybrid semi self-testing certification method for quantum random number generators. To integrate a hybrid semi self-testing certification method to the hybrid random number generator. the methods used are mathematical optimization and simulation. The following results were obtained: we present the improved hybrid quantum random number generator, which is based on QRNG, which uses the time of arrival of photons. The model of a hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. Finally, the hybrid certification method is integrated into the model of the new quantum random number generator. Conclusions. The scientific novelty of the results obtained is as follows: 1. The hybrid quantum random number generator is offered, which is based on QRNG, which uses the time of the arrival of photons. It uses the simple version of the detectors with few requirements. The hybrid QRNG produces more than one random bit per the detection of each photon. It is rather efficient and has a high level of randomness. 2. The hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered. The Self-testing, as well as device-independent quantum random number generation methods, are analyzed. The advantages and disadvantages of both methods are identified. Based on the result the hybrid method is offered. 3. The hybrid semi self-testing certification method for quantum random number generators is integrated into the offered model of the quantum random number generator. The paper analyzes its security and efficiency. The paper offers to use the new random number generator in the crypto-schemes.

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3

Park, Sungju, Kyungmin Kim, Keunjin Kim, and Choonsung Nam. "Dynamical Pseudo-Random Number Generator Using Reinforcement Learning." Applied Sciences 12, no. 7 (March 26, 2022): 3377. http://dx.doi.org/10.3390/app12073377.

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Pseudo-random number generators (PRNGs) are based on the algorithm that generates a sequence of numbers arranged randomly. Recently, random numbers have been generated through a reinforcement learning mechanism. This method generates random numbers based on reinforcement learning characteristics that select the optimal behavior considering every possible status up to the point of episode closing to secure the randomness of such random numbers. The LSTM method is used for the long-term memory of previous patterns and selection of new patterns in consideration of such previous patterns. In addition, feature vectors extracted from the LSTM are accumulated, and their images are generated to overcome the limitation of LSTM long-term memory. From these generated images, features are extracted using CNN. This dynamical pseudo-random number generator secures the randomness of random numbers.

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4

Thomas, Antu Annam, and Varghese Paul. "Nested Random Number Generator." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 5 (May 30, 2017): 767–73. http://dx.doi.org/10.23956/ijarcsse/sv7i5/0327.

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5

Chen, I.-Te. "Random Numbers Generated from Audio and Video Sources." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/285373.

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Random numbers are very useful in simulation, chaos theory, game theory, information theory, pattern recognition, probability theory, quantum mechanics, statistics, and statistical mechanics. The random numbers are especially helpful in cryptography. In this work, the proposed random number generators come from white noise of audio and video (A/V) sources which are extracted from high-resolution IPCAM, WEBCAM, and MPEG-1 video files. The proposed generator applied on video sources from IPCAM and WEBCAM with microphone would be the true random number generator and the pseudorandom number generator when applied on video sources from MPEG-1 video file. In addition, when applying NIST SP 800-22 Rev.1a 15 statistics tests on the random numbers generated from the proposed generator, around 98% random numbers can pass 15 statistical tests. Furthermore, the audio and video sources can be found easily; hence, the proposed generator is a qualified, convenient, and efficient random number generator.

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6

LUI, OI-YAN, CHING-HUNG YUEN, and KWOK-WO WONG. "A PSEUDO-RANDOM NUMBER GENERATOR EMPLOYING MULTIPLE RÉNYI MAPS." International Journal of Modern Physics C 24, no. 11 (October 14, 2013): 1350079. http://dx.doi.org/10.1142/s0129183113500794.

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The increasing risk along with the drastic development of multimedia data transmission has raised a big concern on data security. A good pseudo-random number generator is an essential tool in cryptography. In this paper, we propose a novel pseudo-random number generator based on the controlled combination of the outputs of several digitized chaotic Rényi maps. The generated pseudo-random sequences have passed both the NIST 800-22 Revision 1a and the DIEHARD tests. Moreover, simulation results show that the proposed pseudo-random number generator requires less operation time than existing generators and is highly sensitive to the seed.

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7

Dodge, Yadolah. "A Natural Random Number Generator." International Statistical Review / Revue Internationale de Statistique 64, no. 3 (December 1996): 329. http://dx.doi.org/10.2307/1403789.

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8

Stefanov, André, Nicolas Gisin, Olivier Guinnard, Laurent Guinnard, and Hugo Zbinden. "Optical quantum random number generator." Journal of Modern Optics 47, no. 4 (March 2000): 595–98. http://dx.doi.org/10.1080/09500340008233380.

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9

Li, Pu, Jian-Zhong Zhang, and Yun-Cai Wang. "All-optical Random Number Generator." IEICE Proceeding Series 1 (March 17, 2014): 130–33. http://dx.doi.org/10.15248/proc.1.130.

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10

Komo, John J., and William J. Park. "Decimal pseudo-random number generator." SIMULATION 57, no. 4 (October 1991): 228–30. http://dx.doi.org/10.1177/003754979105700405.

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11

Bellido, M. J., A. J. Acosta, M. Valencia, A. Barriga, and J. L. Huertas. "Simple binary random number generator." Electronics Letters 28, no. 7 (1992): 617. http://dx.doi.org/10.1049/el:19920389.

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12

LIU, Yu, Hong GUO, 韦. 韦, and AnHong WEI Wei DANG. "Physical true random number generator." Chinese Science Bulletin 54, no. 23 (December 1, 2009): 3651–57. http://dx.doi.org/10.1360/972009-1549.

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13

Savvidy, Konstantin G. "The MIXMAX random number generator." Computer Physics Communications 196 (November 2015): 161–65. http://dx.doi.org/10.1016/j.cpc.2015.06.003.

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14

Andrecut, M. "Logistic Map as a Random Number Generator." International Journal of Modern Physics B 12, no. 09 (April 10, 1998): 921–30. http://dx.doi.org/10.1142/s021797929800051x.

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For the largest value of the control parameter, the logistic map is able to generate an infinite chaotic sequence of numbers. Here we describe a simple method for obtaining a random number generator based on this property of the logistic map. Comparing to usual congruential random generators, which are periodic, the logistic random number generator is infinite, aperiodic and not correlated. An aperiodic random number generator is a valuable tool for computer simulation methods.

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15

Francis, Kennon. "True random numbers using the random number generator of the microcomputer." Trends in Pharmacological Sciences 7 (January 1986): 124–25. http://dx.doi.org/10.1016/0165-6147(86)90283-x.

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16

Abhishek, Kunal, and E. George Dharma Prakash Raj. "On Random Number Generation for Kernel Applications." Fundamenta Informaticae 185, no. 4 (June 21, 2022): 285–311. http://dx.doi.org/10.3233/fi-222111.

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An operating system kernel uses cryptographically secure pseudorandom number generator (CSPRNG) for creating address space layout randomization (ASLR) offsets to protect memory addresses of processes from exploitation, storing users’ passwords securely and creating cryptographic keys. However, at present, popular kernel CSPRNGs such as Yarrow, Fortuna and /dev/(u)random which are used by MacOS/iOS/FreeBSD, Windows and Linux/Android kernels respectively lack the very crucial property of non-reproducibility of their generated bitstreams which is used to nullify the scope of predicting the bitstream. This paper proposes a CSPRNG called Cryptographically Secure Pseudorandom Number Generator for Kernel Applications (KCS-PRNG) which generates non-reproducible bitstreams. The proposed KCS-PRNG presents an efficient design uniquely configured with two new non-standard and verified elliptic curves and clock-controlled Linear Feedback Shift Registers (LFSRs) and a novel method to consistently generate non-reproducible random bitstreams of arbitrary lengths. The generated bitstreams are statistically indistinguishable from true random bitstreams and provably secure, resilient to important attacks, exhibits backward and forward secrecy, exhibits exponential linear complexity, large period and huge key space.

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17

Kao, Chiang. "A Random-Number Generator for Microcomputers." Journal of the Operational Research Society 40, no. 7 (July 1989): 687. http://dx.doi.org/10.2307/2582978.

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18

Akashi, Nozomi, Kohei Nakajima, Mitsuru Shibayama, and Yasuo Kuniyoshi. "A mechanical true random number generator." New Journal of Physics 24, no. 1 (January 1, 2022): 013019. http://dx.doi.org/10.1088/1367-2630/ac45ca.

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Abstract Random number generation has become an indispensable part of information processing: it is essential for many numerical algorithms, security applications, and in securing fairness in everyday life. Random number generators (RNGs) find application in many devices, ranging from dice and roulette wheels, via computer algorithms, lasers to quantum systems, which inevitably capitalize on their physical dynamics at respective spatio-temporal scales. Herein, to the best of our knowledge, we propose the first mathematically proven true RNG (TRNG) based on a mechanical system, particularly the triple linkage of Thurston and Weeks. By using certain parameters, its free motion has been proven to be an Anosov flow, from which we can show that it has an exponential mixing property and structural stability. We contend that this mechanical Anosov flow can be used as a TRNG, which requires that the random number should be unpredictable, irreproducible, robust against the inevitable noise seen in physical implementations, and the resulting distribution’s controllability (an important consideration in practice). We investigate the proposed system’s properties both theoretically and numerically based on the above four perspectives. Further, we confirm that the random bits numerically generated pass the standard statistical tests for random bits.

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19

Stipčević, M., and J. E. Bowers. "Spatio-temporal optical random number generator." Optics Express 23, no. 9 (April 24, 2015): 11619. http://dx.doi.org/10.1364/oe.23.011619.

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20

Stefanov, Andre, Nicolas Gisin, Olivier Guinnard, Laurent Guinnard, and Hugo Zbinden. "Letter Optical quantum random number generator." Journal of Modern Optics 47, no. 4 (March 20, 2000): 595–98. http://dx.doi.org/10.1080/095003400147908.

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21

Haas, Alexander. "The multiple prime random number generator." ACM Transactions on Mathematical Software 13, no. 4 (December 1987): 368–81. http://dx.doi.org/10.1145/35078.214349.

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22

Hong, Siang Lee, and Chang Liu. "Sensor-Based Random Number Generator Seeding." IEEE Access 3 (2015): 562–68. http://dx.doi.org/10.1109/access.2015.2432140.

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23

Kao, Chiang. "A Random-number Generator for Microcomputers." Journal of the Operational Research Society 40, no. 7 (July 1989): 687–91. http://dx.doi.org/10.1057/jors.1989.112.

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24

Li, Pu, Yun-Cai Wang, and Jian-Zhong Zhang. "All-optical fast random number generator." Optics Express 18, no. 19 (September 9, 2010): 20360. http://dx.doi.org/10.1364/oe.18.020360.

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25

Leva, Joseph L. "A fast normal random number generator." ACM Transactions on Mathematical Software 18, no. 4 (December 1992): 449–53. http://dx.doi.org/10.1145/138351.138364.

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26

Ahmed, Tanvir, and Mahbubur Rahman. "The Hybrid Pseudo Random Number Generator." International Journal of Hybrid Information Technology 9, no. 7 (July 31, 2016): 299–312. http://dx.doi.org/10.14257/ijhit.2016.9.7.27.

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27

Wei, Wei, and Hong Guo. "Bias-free true random-number generator." Optics Letters 34, no. 12 (June 11, 2009): 1876. http://dx.doi.org/10.1364/ol.34.001876.

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28

Tsoi, K. H., K. H. Leung, and P. H. W. Leong. "High performance physical random number generator." IET Computers & Digital Techniques 1, no. 4 (2007): 349. http://dx.doi.org/10.1049/iet-cdt:20050173.

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29

Murphy, J. P. "Field-programmable true random number generator." Electronics Letters 48, no. 10 (2012): 565. http://dx.doi.org/10.1049/el.2012.0432.

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30

Marsaglia, George, Arif Zaman, and Wai Wan Tsang. "Toward a universal random number generator." Statistics & Probability Letters 9, no. 1 (January 1990): 35–39. http://dx.doi.org/10.1016/0167-7152(90)90092-l.

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31

Marsaglia, George, B. Narasimhan, and Arif Zaman. "A random number generator for PC's." Computer Physics Communications 60, no. 3 (October 1990): 345–49. http://dx.doi.org/10.1016/0010-4655(90)90033-w.

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32

Hennecke, Michael. "RANEXP: experimental random number generator package." Computer Physics Communications 79, no. 2 (April 1994): 261–67. http://dx.doi.org/10.1016/0010-4655(94)90072-8.

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33

Seo, Hwa-Jeong, and Ho-Won Kim. "Two layered Secure Password Generation with Random Number Generator." Journal of the Korea Institute of Information and Communication Engineering 18, no. 4 (April 30, 2014): 867–75. http://dx.doi.org/10.6109/jkiice.2014.18.4.867.

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34

PEYTON JONES, SIMON. "27 Random Numbers." Journal of Functional Programming 13, no. 1 (January 2003): 235–40. http://dx.doi.org/10.1017/s0956796803002910.

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35

Pikuza, M. O. "Statistical Characteristics Improvement of a Hardware Random Number Generator by a Software Method." Doklady BGUIR 20, no. 7 (December 10, 2022): 43–47. http://dx.doi.org/10.35596/1729-7648-2022-20-7-43-47.

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As a source of random numbers, hardware random number generators are often used, the operation of which is based on randomly changing parameters of various physical processes. The statistical characteristics of such generators do not always allow their use in the field of information security. To improve the statistical characteristics, various software tools for processing the output data of the generator are used. The purpose of this work is to study the possibility to improve the statistical characteristics of a hardware random number generator by software. The investigated hardware random number generator is based on the ND103L noise diode and has a random digital sequence of binary numbers at the output. To improve the statistical characteristics, the output stream of random numbers was processed using a software method based on the calculation of high-order finite differences. This method would allow one to get a more symmetrical distribution of random numbers, as well as increase the speed of their generation. After processing, the data from the generator under study have better statistical characteristics, which is confirmed by the NIST and Diehard tests, and the generation rate has also increased by more than 5 times. The results of this work may be useful to developers of hardware random number generators who need to improve the performance of the generator.

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36

Yakut, Selman, Taner Tuncer, and Ahmet Bedri Ozer. "Secure and Efficient Hybrid Random Number Generator Based on Sponge Constructions for Cryptographic Applications." Elektronika ir Elektrotechnika 25, no. 4 (August 7, 2019): 40–46. http://dx.doi.org/10.5755/j01.eie.25.4.23969.

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Random numbers constitute the most important part of many applications and have a vital importance in the security of these applications, especially in cryptography. Therefore, there is a need for secure random numbers to provide their security. This study is concerned with the development of a secure and efficient random number generator that is primarily intended for cryptographic applications. The generator consists of two subsystems. The first is algorithmic structure, Keccak, which is the latest standard for hash functions. The structure provides to generate secure random numbers. The second is additional input that generates with ring oscillators that are implemented on the FPGA. The additional inputs prevent reproduction and prediction of the subsequent random numbers. It is shown that the proposed generator is satisfies security requirements for cryptographic applications. In addition, NIST 800-22 test suite and autocorrelation test are used to demonstrate that generated random numbers have no statistical weaknesses and relationship among itself, respectively. Successful results from these tests show that generated numbers have no statistical weaknesses. Moreover, important advantage of the proposed generator is that it is more efficient than existing RNGs in the literature.

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37

Ramesh, G. P., and A. Rajan. "SRAM Based Random Number Generator for Non-Repeating Pattern Generation." Applied Mechanics and Materials 573 (June 2014): 181–86. http://dx.doi.org/10.4028/www.scientific.net/amm.573.181.

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—Field-programmable gate array (FPGA) optimized random number generators (RNGs) are more resource-efficient than software-optimized RNGs because they can take advantage of bitwise operations and FPGA-specific features. A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Several computational methods for random number generation exist, but often fall short of the goal of true randomness though they may meet, with varying success, some of the statistical tests for randomness intended to measure how unpredictable their results are (that is, to what degree their patterns are discernible).LUT-SR Family of Uniform Random Number Generators are able to handle randomness only based on seeds that is loaded in the look up table. To make random generation efficient, we propose new approach based on SRAM storage device.Keywords: RNG, LFSR, SRAM

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38

Kwon, Osung, Young-Wook Cho, and Yoon-Ho Kim. "Quantum random number generator using photon-number path entanglement." Applied Optics 48, no. 9 (March 19, 2009): 1774. http://dx.doi.org/10.1364/ao.48.001774.

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39

Averin, A. S., N. D. Zyulyarkina, and E. M. Izhberdeeva. "RANDOM NUMBER GENERATOR BASED ON HUMAN-COMPUTER INTERACTION." Journal of the Ural Federal District. Information security, no. 2 (2020): 17–23. http://dx.doi.org/10.14529/secur200203.

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The paper is devoted to the development and analysis of a software random number gen-erator based on human-computer interaction for software and cryptographic applications. De-scribed is a method of generating random numbers based on human-computer interaction, using time and position of a cursor on a computer or smartphone display. Based on this meth-od, a random number generator has been developed and programmatically implemented. A preliminary analysis of the algorithm was performed, during which 11,000 numbers were gen-erated. The test software for this method has been created, preliminary indicators of generated random numbers have been considered. The random number distribution function is shown to be uniform. The advantage of this generator is its ease of manufacture and operation

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40

YAO, WEIGUANG, PEI YU, and CHRISTOPHER ESSEX. "COMMUNICATION BETWEEN SYNCHRONIZED RANDOM NUMBER GENERATORS." International Journal of Bifurcation and Chaos 14, no. 11 (November 2004): 3995–4008. http://dx.doi.org/10.1142/s0218127404011685.

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In most published chaos-based communication schemes, the system's parameters used as a key could be intelligently estimated by a cracker based on the fact that information about the key is contained in the chaotic carrier. In this paper, we will show that the least significant digits (LSDs) of a signal from a chaotic system can be so highly random that the system can be used as a random number generator. Secure communication could be built between the synchronized generators nonetheless. The Lorenz system is used as an illustration.

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41

Roussille, Hugo, Lionel Djadaojee, and Frédéric Chevy. "A simple quantum generator of random numbers." Emergent Scientist 1 (2017): 7. http://dx.doi.org/10.1051/emsci/2017009.

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Cryptography techniques rely on chains of random numbers used to generate safe encryption keys. Since random number generator algorithms are in fact pseudo-random their behavior can be predicted if the generation method is known and as such they cannot be used for perfectly safe communications. In this article, we present a perfectly random generator based on quantum measurement processes. The main advantage of such a generator is that using quantum mechanics, its behavior cannot be predicted in any way. We verify the randomness of our generator and compare it to commonly used pseudo-random generators.

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42

PARESCHI, FABIO, GIANLUCA SETTI, and RICCARDO ROVATTI. "STATISTICAL TESTING OF A CHAOS BASED CMOS TRUE-RANDOM NUMBER GENERATOR." Journal of Circuits, Systems and Computers 19, no. 04 (June 2010): 897–910. http://dx.doi.org/10.1142/s0218126610006517.

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As faster Random Number Generators become available, the possibility to improve the accuracy of randomness tests through the analysis of a larger number of generated bits increases. In this paper we first introduce a high-performance true-random number generator designed by authors, which use a set of discrete-time piecewise-linear chaotic maps as its entropy source. Then, we present by means of suitably improved randomness tests, the validation of this generator and the comparison with other high-end solutions. We consider the NIST test suite SP 800-22 and we show that, as suggested by NIST itself, to increase the so-called power of the test, a more in-depth analysis should be performed using the outcomes of the suite over many generated sequences. With this approach we build a framework for RNG high quality testing, with which we are able to show that the designed prototype has a comparable quality with respect to the other high-quality commercial solutions, with a working speed that is one order of magnitude faster.

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43

Lee, Kyungroul, and Manhee Lee. "True Random Number Generator (TRNG) Utilizing FM Radio Signals for Mobile and Embedded Devices in Multi-Access Edge Computing." Sensors 19, no. 19 (September 24, 2019): 4130. http://dx.doi.org/10.3390/s19194130.

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As transmissions of data between mobile and embedded devices in multi-access edge computing (MEC) increase, data must be protected, ensuring confidentiality and integrity. These issues are usually solved with cryptographic algorithms systems, which utilize a random number generator to create seeds and keys randomly. Their role in cryptography is so important that they need to be generated securely. In this paper, a true random number generator (TRNG) utilizing FM radio signals as a source is proposed. The proposed method can generate random numbers with high entropy, increased by at least 118% and up to 431% compared to existing generators.

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44

NavyaDeepthi, V., A. Ruhan Bevi, and V. Sai Keerthi. "High Quality FPGA Optimized Random Number Generator." International Journal of Computer Applications 67, no. 17 (April 18, 2013): 1–4. http://dx.doi.org/10.5120/11484-7186.

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45

Seo, Hwa-Jeong, and Ho-Won Kim. "Always Metastable State True Random Number Generator." Journal of information and communication convergence engineering 10, no. 3 (September 30, 2012): 253–57. http://dx.doi.org/10.6109/jicce.2012.10.3.253.

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46

Barbosa, Geraldo A. "Harnessing Nature’s Randomness: Physical Random Number Generator." Journal of Information Security and Cryptography (Enigma) 1, no. 1 (December 7, 2015): 47. http://dx.doi.org/10.17648/enig.v1i1.18.

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47

Sezgin, Fatin. "On a Random-Number Generator for Microcomputers." Journal of the Operational Research Society 41, no. 12 (December 1990): 1191. http://dx.doi.org/10.2307/2583126.

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48

YU Heng-wei, 余恒炜, 孙晓娟 SUN Xiao-juan, 王星辰 WANG Xing-chen, 蒋. 科. JIANG Ke, 吴. 忧. WU-You, 程东碧 CHENG Dong-bi, 石芝铭 SHI Zhi-ming, 贾玉萍 JIA Yu-ping, and 黎大兵 LI Da-bing. "Quantum random number Gaussian noise signal generator." Optics and Precision Engineering 27, no. 7 (2019): 1492–99. http://dx.doi.org/10.3788/ope.20192707.1492.

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49

Pervushin, B. E., M. A. Fadeev, A. V. Zinovev, R. K. Goncharov, A. A. Santev, A. E. Ivanova, and E. O. Samsonov. "Quantum random number generator using vacuum fluctuations." Nanosystems: Physics, Chemistry, Mathematics 12, no. 2 (April 29, 2021): 156–60. http://dx.doi.org/10.17586/2220-8054-2021-12-2-156-160.

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Feng MingMing, Qin XiaoLin, Zhou ChunYuan, Xiong Li, and Ding LiangEn. "Quantum random number generator based on polarization." Acta Physica Sinica 52, no. 1 (2003): 72. http://dx.doi.org/10.7498/aps.52.72.

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