High-quality random number sequences extracted from chaos post-processed by phased-array semiconductor laser

Wu Jia-Chen; Song Zheng; Xie Yi-Feng; Zhou Xin-Yu; Zhou Pei; Mu Peng-Hua; Li Nian-Qiang

doi:10.7498/aps.70.20202034

Abstract

With the rapid development of the computer technology and communication technology, as well as the popularization of the Internet, information security has received much attention of all fields. To ensure the information security, a large number of random numbers must be generated. It is well accepted that random numbers can be divided into physical random numbers and pseudo random numbers. The pseudo random numbers are mainly generated based on algorithms, which can be reproduced once the seed is decoded. The physical random numbers are extracted from physical entropies. While the bandwidth of the traditional physical entropy source is quite small, the bit rate of generated physical random numbers is limited. In the literature, a lot of methods have been proposed to produce high-quality and high-speed random number sequences with the chaotic entropy source, which exhibits wide bandwidth, large amplitude and random fluctuations. Usually, a semiconductor laser with optical feedback, i.e, an external-cavity semiconductor laser (ECSL), is chosen as a chaotic entropy source to generate a chaotic signal output. However, the chaotic signal output has a high time delay characteristic, which is not conducive to the production of high-quality random numbers. In this paper, to produce high-quality chaos with time-delay signature (TDS) being well suppressed, we propose to employ an integration-oriented phased-array semiconductor laser to post-process the original chaos generated by an ECSL. It is shown that the proposed laser array is effective in TDS suppression, which improves the quality of optical chaos. After certain necessary post-processing, high-speed and high-quality random number sequences can be achieved. In this paper, we employ the conventional post-processing techniques, which include an 8-bit analog-to-digital converter (ADC) for sampling and quantization, and m-bits least significant bit (m-LSB) and exclusive OR (XOR) for removing bias. The simulation results show that the random number sequences obtained from the chaotic entropy source comprised of an ECSL and phased-array semiconductor lasers have uniform distribution characteristic and their scatter diagram contains no obvious pattern. Meanwhile, the obtained random number sequences can pass all tests of the standard randomness benchmark, NIST SP 800-22. Additionally, based on the extensibility of phased-array semiconductor lasers, random number generators that can generate parallel random numbers are achievable.

Keywords:

Authors and contacts

1.
School of Optoelectronic Science and Engineering, Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
2.
Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province, Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
3.
Institute of Science and Technology for Opto-Electornic Information, Yantai University, Yantai 264005, China

Corresponding author: Zhou Pei, peizhou@suda.edu.cn ; Li Nian-Qiang, nli@suda.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62004135, 62001317), the Natural Science Research Project of Jiangsu Higher Education Institutions, China (Grant No. 20KJA416001), and the Startup Funding of Soochow University, China (Grant No. Q415900119).

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References

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Cited By

图 1 基于激光器阵列后处理的混沌熵源获取高品质随机数的示意图($ \lambda /4 $为$ 1/4 $波片, PD1、PD2为光电转换器, ADC为模数转换器, LSB为最低有效位, XOR为异或处理)

Figure 1. Schematic diagram of high quality random number generation based on the chaotic entropy source generated by ECSL and post-processed by phased-array semiconductor lasers (λ/4, 1/4 wave plate; PD1 and PD2, photo detector; ADC, analog-to-digital converter; LSB, least significant bit; XOR, exclusive OR).

DownLoad: Full-Size Img PowerPoint

图 2 激光器输出混沌信号的时间序列(左列), 自相关函数谱(中列), 功率谱(右列)　(a) 光反馈半导体激光器; (b) 注入激光器; (c) 注入激光器阵列

Figure 2. Time series (left column), autocorrelation function (middle column), and power spectra (right column) of the chaotic signal output by laser: (a) ECSL; (b) injection to a single laser A; (c) injection to phased-array lasers.

DownLoad: Full-Size Img PowerPoint

图 3 经过激光器阵列后处理混沌熵源的ACF时延处峰值随着注入参数和激光器分离比d/a的演化情况　(a) d/a = 0.2; (b) d/a = 0.4; (c) d/a = 0.6; (d) d/a = 1.0

Figure 3. The evaluation of the ACF peak value located around the feedback delay of the chaotic entropy source that is processed by the phased-array in the plane of injection parameters for several values of laser separation: (a) d/a = 0.2, (b) d/a = 0.4, (c) d/a = 0.6, (d) d/a = 1.0.

DownLoad: Full-Size Img PowerPoint

图 4 激光器B输出的混沌信号量化后的统计直方图　(a) 8位ADC输出; (b) 3-LSB输出; (c) XOR输出

Figure 4. Statistical histogram of the quantized chaotic signal of the laser B: (a) The output of 8 bit ADC; (b) the output of 3-LSB; (c) the output of XOR.

DownLoad: Full-Size Img PowerPoint

图 5 散点图

Figure 5. Scatter diagram.

DownLoad: Full-Size Img PowerPoint

图 6 激光器输出的时间序列与自相关函数　(a) A激光器输出的时间序列; (b) A激光器输出的自相关函数; (c) B激光器输出的时间序列; (d) B激光器输出的自相关函数

Figure 6. Time series and autocorrelation function of the lasers: (a) Time series of laser A; (b) autocorrelation function of laser A; (c) time series of laser B; (d) autocorrelation function of laser. B.

DownLoad: Full-Size Img PowerPoint

表 1 NIST统计测试结果

Table 1. Result of NIST statistical tests.

测试名称	P-value	概率	结果
频数	0.538182	0.992	通过
块内频数	0.239266	0.982	通过
累加	0.755819	0.994	通过
游程	0.140453	0.988	通过
块内最长游程	0.965860	0.988	通过
矩阵秩	0.281232	0.990	通过
离散傅里叶变换	0.206629	0.982	通过
非重叠模块匹配	0.020831	0.982	通过
重叠模块匹配	0.699313	0.984	通过
通用统计	0.510153	0.994	通过
近似熵	0.699313	0.994	通过
随机游动	0.443665	0.986	通过
随机游动变量	0.290158	0.983	通过
连续性	0.096578	0.984	通过
线性复杂度	0.340858	0.986	通过

DownLoad: CSV

[1]	Shannon C E 1949 Bell Syst. Tech. J. 28 656 Google Scholar
[2]	Durt T, Beimonte C, Lamoureux L P, Panajotov K, van den Berghe F, Thienpont H 2013 Phys. Rev. A. 87 022339 Google Scholar
[3]	Williams C R S, Salevan J C, Li X W, Roy R, Murphy T E 2010 Opt. Express 18 23584 Google Scholar
[4]	Guo H, Tang W Z, Liu Y, Wei W 2010 Phys. Rev. E. 81 051137 Google Scholar
[5]	Ma X F, Xu F H, Xu H, Tan X Q, Qi B, Lo H K 2013 Phys. Rev. A. 87 062327 Google Scholar
[6]	David P. Rosin, Damien Rontani, Daniel J. Gauthier 2013 Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87 040902 Google Scholar
[7]	Li N Q, Kim B, Chizhevsky V N, Locquet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634 Google Scholar
[8]	郭弘, 刘钰, 党安红, 韦韦 2009 科学通报 54 3651 Google Scholar Guo H, Liu Y, Dang A H, Wei W 2009 Chin. Sci. Bull. 54 3651 Google Scholar
[9]	Ren M, Wu E, Liang Y, Jian Y, Wu G, Zeng H 2011 Phys. Rev. A 83 023820 Google Scholar
[10]	周庆, 胡月, 廖晓峰 2008 物理学报 57 5413 Google Scholar Zhou Q, Hu Y, Liao X F 2008 Acta Phys. Sin. 57 5413 Google Scholar
[11]	李念强 2016 博士学位论文 (成都: 西南交通大学) Li N Q 2016 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese)
[12]	Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimori S, Yoshimura K, Davis P 2008 Nat. Photon. 2 728 Google Scholar
[13]	Reidier I, Aviad Y, Rosenblush M, Kanter I 2009 Phys. Rev. Lett. 103 024102 Google Scholar
[14]	Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58 Google Scholar
[15]	Harayama T, Sunada S, Yoshimura K, Davis P, Tsuzuki K, Uchida A 2011 Phys. Rev. A. 83 031803 Google Scholar
[16]	Argyris A, Deligiannidis S, Pikasis E, Bogris A, Syvridis D 2010 Opt. Express 18 18763 Google Scholar
[17]	Zhang J Z, Wang Y C, Liu M, Xue L G, Li P, Wang A B, Zhang M J 2012 Opt. Express 20 7496 Google Scholar
[18]	Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360 Google Scholar
[19]	Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476 Google Scholar
[20]	Li X Z, Chan S C 2013 IEEE J. Quantum Electron. 49 829 Google Scholar
[21]	Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452 Google Scholar
[22]	Li P, Zhang J G, Sang L X, Liu X L, Guo Y Q, Guo X M, Wang A B, Shore K A, Wang Y C 2017 Opt. Lett. 42 2699 Google Scholar
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[29]	Li N Q, Pan W, Xiang S Y, Zhao Q C, Zhang L Y 2014 IEEE Photon. Technol. Lett. 26 1886 Google Scholar
[30]	Mu P H, Pan W, Xiang S Y, Li N Q, Liu X K, Zou X H 2015 Mod. Phys. Lett. B 29 1550142
[31]	Wang Y, Xiang S Y, Wang B, Cao X Y, Wen A J, Hao Y 2019 Opt. Express 27 8446 Google Scholar
[32]	Xiang S Y, Wang B, Wang Y, Han Y N, Wen A J, Hao Y 2019 J. Light. Technol. 37 3987 Google Scholar
[33]	Xue C P, Jiang N, Qiu K, Lv Y X 2015 Opt. Express 23 14510 Google Scholar
[34]	Zhao A K, Jiang N, Wang Y J, Liu S Q, Li B C, Qiu K 2019 Opt. Lett. 44 5957 Google Scholar
[35]	Li N Q, Pan W, Locquet A, Citrin D S 2015 Opt. Lett. 40 4416 Google Scholar
[36]	Li S S, Li X Z, Chan S C 2018 Opt. Lett. 43 4751 Google Scholar
[37]	Xiang S Y, Wen A J, Pan W, Lin L, Zhang H X, Zhang H, Guo X X, Li J F 2016 J. Light. Technol. 34 4221 Google Scholar
[38]	Jiang N, Wang C, Xue C P, Li G L, Lin S Q, Qiu K 2017 Opt. Express 25 14359 Google Scholar
[39]	Jiang X X, Liu D M, Cheng M F, Deng L, Fu S N, Zhang M M, Tang M, Shum P 2016 Opt. Lett. 41 1157 Google Scholar
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[43]	Adams M J, Li N Q, Cemlyn B R, Susanto H, Henning I D 2017 Phys. Rev. A 95 053869 Google Scholar
[44]	Fang Q, Zhou P, Mu P H, Li N Q 2021 IEEE J. Quantum Electron. 57 1200109.

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