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基于激光器阵列后处理的混沌熵源获取高品质随机数

吴佳辰 宋峥 谢溢锋 周心雨 周沛 穆鹏华 李念强

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基于激光器阵列后处理的混沌熵源获取高品质随机数

吴佳辰, 宋峥, 谢溢锋, 周心雨, 周沛, 穆鹏华, 李念强

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
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  • 本文提出采用可集成的激光器阵列后处理光反馈半导体激光器的输出, 进而获得无时延特征的优质混沌熵源, 进一步获取高速高品质随机数序列. 方案中采用常规的8位模数转换采样量化和多位最低有效位异或提取处理, 采用国际公认的随机数行业测试标准(NIST SP 800-22)来检验产生的序列. 结果表明, 通过激光器阵列后处理的混沌熵源所获取的随机数序列具有均匀的分布特性, 散点图无明显图案, 可以成功通过NIST SP 800-22的全部测试. 另外, 基于激光器阵列的可扩展性, 本方案可以拓展为可实现同时产生多路并行的高速高品质随机数发生器.
    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.
      通信作者: 周沛, peizhou@suda.edu.cn ; 李念强, nli@suda.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 62004135, 62001317)、江苏省高等学校自然科学研究重大项目(批准号: 20KJA416001)和苏州大学科研启动经费(批准号: Q415900119)资助的课题
      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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  • 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 $$ 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)

    Fig. 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).

    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

    Fig. 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.

    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

    Fig. 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.

    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

    Fig. 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.

    图 5  散点图

    Fig. 5.  Scatter diagram.

    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

    Fig. 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.

    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0.5381820.992通过
    块内频数0.2392660.982通过
    累加0.7558190.994通过
    游程0.1404530.988通过
    块内最长游程0.9658600.988通过
    矩阵秩0.2812320.990通过
    离散傅里叶变换0.2066290.982通过
    非重叠模块匹配0.0208310.982通过
    重叠模块匹配0.6993130.984通过
    通用统计0.5101530.994通过
    近似熵0.6993130.994通过
    随机游动0.4436650.986通过
    随机游动变量0.2901580.983通过
    连续性0.0965780.984通过
    线性复杂度0.3408580.986通过
    下载: 导出CSV
  • [1]

    Shannon C E 1949 Bell Syst. Tech. J. 28 656Google Scholar

    [2]

    Durt T, Beimonte C, Lamoureux L P, Panajotov K, van den Berghe F, Thienpont H 2013 Phys. Rev. A. 87 022339Google Scholar

    [3]

    Williams C R S, Salevan J C, Li X W, Roy R, Murphy T E 2010 Opt. Express 18 23584Google Scholar

    [4]

    Guo H, Tang W Z, Liu Y, Wei W 2010 Phys. Rev. E. 81 051137Google Scholar

    [5]

    Ma X F, Xu F H, Xu H, Tan X Q, Qi B, Lo H K 2013 Phys. Rev. A. 87 062327Google Scholar

    [6]

    David P. Rosin, Damien Rontani, Daniel J. Gauthier 2013 Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87 040902Google Scholar

    [7]

    Li N Q, Kim B, Chizhevsky V N, Locquet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634Google Scholar

    [8]

    郭弘, 刘钰, 党安红, 韦韦 2009 科学通报 54 3651Google Scholar

    Guo H, Liu Y, Dang A H, Wei W 2009 Chin. Sci. Bull. 54 3651Google Scholar

    [9]

    Ren M, Wu E, Liang Y, Jian Y, Wu G, Zeng H 2011 Phys. Rev. A 83 023820Google Scholar

    [10]

    周庆, 胡月, 廖晓峰 2008 物理学报 57 5413Google Scholar

    Zhou Q, Hu Y, Liao X F 2008 Acta Phys. Sin. 57 5413Google 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 728Google Scholar

    [13]

    Reidier I, Aviad Y, Rosenblush M, Kanter I 2009 Phys. Rev. Lett. 103 024102Google Scholar

    [14]

    Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58Google Scholar

    [15]

    Harayama T, Sunada S, Yoshimura K, Davis P, Tsuzuki K, Uchida A 2011 Phys. Rev. A. 83 031803Google Scholar

    [16]

    Argyris A, Deligiannidis S, Pikasis E, Bogris A, Syvridis D 2010 Opt. Express 18 18763Google 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 7496Google Scholar

    [18]

    Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360Google Scholar

    [19]

    Wu J G, Tang X, Wu Z M, Xia G Q, Feng G Y 2012 Laser Phys. 22 1476Google Scholar

    [20]

    Li X Z, Chan S C 2013 IEEE J. Quantum Electron. 49 829Google Scholar

    [21]

    Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452Google Scholar

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    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 2699Google Scholar

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    Li P, Sun Y Y, Liu X L, Yi X G, Zhang J G, Guo X M, Guo Y Q, Wang Y C 2016 Opt. Lett. 41 3347Google Scholar

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    韩韬, 刘香莲, 李璞, 郭晓敏, 郭龑强, 王云才 2017 物理学报 66 124203Google Scholar

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    赵东亮, 李璞, 刘香莲, 郭晓敏, 郭龑强, 张建国, 王云才 2017 物理学报 66 050501Google Scholar

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    Tang X, Wu Z M, Wu J G, Deng T, Zhong Z Q, Chen J J, Xia G Q 2014 Laser Phys. Lett. 12 015003Google Scholar

    [27]

    Ran C, Tang X, Wu Z M, Xia G Q 2018 Laser Phys. 28 126202Google Scholar

    [28]

    姚晓洁, 唐曦, 吴正茂, 夏光琼 2018 物理学报 67 024204Google Scholar

    Yao X J, Tang X, Wu Z M, Xia G Q 2018 Acta Phys. Sin. 67 024204Google Scholar

    [29]

    Li N Q, Pan W, Xiang S Y, Zhao Q C, Zhang L Y 2014 IEEE Photon. Technol. Lett. 26 1886Google 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

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    Wang Y, Xiang S Y, Wang B, Cao X Y, Wen A J, Hao Y 2019 Opt. Express 27 8446Google Scholar

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    Xiang S Y, Wang B, Wang Y, Han Y N, Wen A J, Hao Y 2019 J. Light. Technol. 37 3987Google Scholar

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    Xue C P, Jiang N, Qiu K, Lv Y X 2015 Opt. Express 23 14510Google Scholar

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    Zhao A K, Jiang N, Wang Y J, Liu S Q, Li B C, Qiu K 2019 Opt. Lett. 44 5957Google Scholar

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    Li N Q, Pan W, Locquet A, Citrin D S 2015 Opt. Lett. 40 4416Google Scholar

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    Li S S, Li X Z, Chan S C 2018 Opt. Lett. 43 4751Google Scholar

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    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 4221Google Scholar

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    Jiang N, Wang C, Xue C P, Li G L, Lin S Q, Qiu K 2017 Opt. Express 25 14359Google Scholar

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    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 1157Google Scholar

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    Ma Y T, Xiang S Y, Guo X X, Song Z W, Wen A J, Hao Y 2020 Opt. Express 28 1665Google Scholar

    [41]

    Zhou P, Fang Q, Li N Q 2020 Opt. Lett. 45 399Google Scholar

    [42]

    Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M, Vangel M, Banks D, Heckert A, Dary J, Vo S 2001 http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html [2020-11-21]

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    Adams M J, Li N Q, Cemlyn B R, Susanto H, Henning I D 2017 Phys. Rev. A 95 053869Google Scholar

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    Fang Q, Zhou P, Mu P H, Li N Q 2021 IEEE J. Quantum Electron. 57 1200109.

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出版历程
  • 收稿日期:  2020-12-02
  • 修回日期:  2020-12-19
  • 上网日期:  2021-05-13
  • 刊出日期:  2021-05-20

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