High-quality random number sequences extracted from chaos post-processed by phased-array semiconductor laser
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摘要: 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.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.
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Key words:
- semiconductor lasers /
- phased-array semiconductor lasers /
- laser chaos /
- random number
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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 $ 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).
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.
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.
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.
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.
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 
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