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Real-time high-speed physical random numbers are crucial for a broad spectrum of applications in cryptography, communications as well as numerical computations and simulations.Chaotic laser is promising to construct high-speed physical random numbers in real time benefitting from its complex nonlinear dynamics.However,the real-time generation rate of physical random numbers by using single-bit extraction is confronted with a bottleneck because of the bandwidth limitation caused by laser relaxation,which dominates the laser chaos and then limits the effective bandwidth only to a few GHz.Although some bandwidth-enhanced methods have been proposed to increase the single-bit generation rate, the potential is very limited,and meanwhile the defects of system complexity will be introduced.An alternative method is to construct high-speed physical random numbers by using the multi-bit extraction.In this method,each sampling point is converted to N digital bits by using multi-bit analog-to-digital converter (ADC) and their M(M 6 N) least significant bits are retained as an output of random bits,where N and M are the numbers of ADC bits and retained bits,respectively.The generation rate of random numbers is thus equal to M times sampling rate and can be greatly increased.Whereas,in the multi-bit extraction demonstrations,the intensity output of chaotic laser is usually digitized by the commercial oscilloscope and then processed with least-significant-bit retention followed by other postprocessing methods such as derivative,exclusive-OR,and bit-order reversal.These followed post-processing operations have to be implemented off-line and thus cannot support the real-time generation of random numbers.Resultantly,it is still an ongoing challenge to develop high-speed generation schemes of physical random numbers with the capability of real-time output.In this paper,a real-time high-speed generation method of physical random numbers by using multi-bit quantization of chaotic laser is proposed and demonstrated experimentally.In the proposed generation scheme,an external-cavity feedback semiconductor laser is utilized as a source of chaotic laser.Through quantizing the chaotic laser with 6-bit ADC, which is triggered by a clock at a sampling rate of 7 GHz,a binary sequence with six significant bits can be achieved. After the selection of the two least-significant bits and self-delayed exclusive-OR operation in the field-programmable gate array (FPGA),a real-time 14-Gb/s binary stream is finally achieved.This binary stream has good uniformity and independence,and has passed the industry-standard statistical test suite provided by the National Institute of Standards and Technology (NIST),showing a good statistical randomness.It is believed that this work provides an alternative method of generating the real-time high-speed random numbers and promotes its applications in the field of information security.
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Keywords:
- semiconductor laser /
- laser chaos /
- multi-bit quantization /
- physical random number
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[1] Metropolis N, Ulam S 1949 J. Amer. Stat. Assoc. 44 335
[2] Zhao Q C, Yin H X 2013 Optik 124 2161
[3] Petrie C S, Connelly J A 2000 IEEE Trans. Circ. Syst. I:Fundam. Theory Appl. 47 615
[4] Bucci M, Germani L, Luzzi R, Trifiletti A, Varanonuovo M 2003 IEEE Trans. Comput. 52 403
[5] 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
[6] Harayama T, Sunada S, Yoshimura K, Davis P, Tsuzuki K, Uchida A 2011 Phys. Rev. A 83 031803
[7] Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452
[8] Zhao D L, Li P, Liu X L, Guo X M, Guo Y Q, Zhang J G, Wang Y C 2017 Acta Phys. Sin. 66 050501 (in Chinese)[赵东亮, 李璞, 刘香莲, 郭晓敏, 郭龑强, 张建国, 王云才 2017 66 050501]
[9] Wang A B, Wang Y C, He H C 2008 IEEE Photon. Technol. Lett. 20 1633
[10] Wang A B, Wang Y C, Wang J F 2009 Opt. Lett. 34 1144
[11] Uchida A, Heil T, Liu Y, Davis P, Aida T 2003 IEEE J. Quantum Electron. 39 1462
[12] Zhang M J, Liu T G, Li P, Wang A B, Zhang J Z, Wang Y C 2011 IEEE Photon. Technol. Lett. 23 1872
[13] Hong Y H, Spencer P S, Shore K A 2012 J. Opt. Soc. Amer. B 29 415
[14] Wang A B, Wang Y C, Yang Y B, Zhang M J, Xu H, Wang B J 2013 Appl. Phys. Lett. 102 031112
[15] Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102
[16] Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509 (in Chinese)[唐曦, 吴加贵, 夏光琼, 吴正茂 2011 60 110509]
[17] Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58
[18] Li N Q, Kim B, Chizhevsky V N, Locquet A, Bloch M, Citrin D S, Pan W 2014 Opt. Express 22 6634
[19] Yang H B, Wu Z M, Tang X, Wu J G, Xia G Q 2015 Acta Phys. Sin. 64 084204 (in Chinese)[杨海波, 吴正茂, 唐曦, 吴加贵, 夏光琼 2015 64 084204]
[20] Akizawa Y, Yamazaki T, Uchida A, Harayama T, Sunada S, Araiet K, Yoshimura K, Davis P 2012 IEEE Photon. Technol. Lett. 24 1042
[21] Oliver N, Soriano M, Sukow D, Fischer I 2013 IEEE J. Quantum Electron. 49 910
[22] Li X Z, Li S S, Zhuang J P, Chan S C 2015 Opt. Lett. 40 3970
[23] Tang X, Wu Z M, Wu J G, Deng T, Chen J J, Fan L, Zhong Z Q, Xia G Q 2015 Opt. Express 23 33130
[24] Sun Y Y, Li P, Guo Y Q, Guo X M, Liu X L, Zhang J G, Sang L X, Wang Y C 2017 Acta Phys. Sin. 66 030503 (in Chinese)[孙媛媛, 李璞, 郭龑强, 郭晓敏, 刘香莲, 张建国, 桑鲁骁, 王云才 2017 66 030503]
[25] Wang A B, Wang L S, Li P, Wang Y C 2017 Opt. Express 25 3153
[26] Wu D Y, Zhou L, Huang Y K, Wang P, Wu J, Jin Z, Liu X Y 2016 Bipolar/BiCMOS Circuits and Technology Meeting New Jersey, America, September 25-27 2016 p90
[27] Lin F Y, Liu J M 2003 Opt. Commun. 221 173
[28] Rontani D, Locquet A, Sciamanna M, Citrin D S, Ortin S 2009 IEEE J. Quantum Electron. 45 879
[29] Sciamanna M, Shore K A 2015 Nat. Photon. 9 151
[30] Wang L S, Zhao T, Wang D M, Wu D Y, Zhou L, Wu J, Liu X Y, Wang Y C, Wang A B 2017 IEEE Photon. J. 9 7201412
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