Abstract

Using two mutually coupled semiconductor lasers (MC-SLs) outputs as chaotic entropy sources, a scheme for generating Tbits/s ultra-fast physical random bit (PRB) is demonstrated and analyzed experimentally. Firstly, two entropy sources originating from two chaotic outputs of MC-SLs are obtained in parallel. Secondly, by adopting multiple optimized post-processing methods, two PRB streams with the generation rate of 0.56 Tbits/s are extracted from the two entropy sources and their randomness are verified by using NIST Special Publication 800-22 statistical tests. Through merging the two sets of 0.56 Tbits/s PRB streams by an interleaving operation, a third set of 1.12 Tbits/s PRB stream, which meets all the quality criteria of NIST statistical tests, can be further acquired. Finally, after additionally taking into account the restriction of the min-entropy, the generation rate of two sets of PRB stream from the two entropy sources can still attain 0.48 Tbits/s, and then a third set of merging PRB stream is 0.96 Tbits/s. Moreover, for the sequence length of the order of 10 Gbits, the statistical bias and serial correlation coefficient of three sets of PRB streams are also analyzed.

© 2015 Optical Society of America

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2015 (2)

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (3)

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

2012 (3)

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

X. Z. Li and S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (6)

2009 (2)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

K. Svozil, “Three criteria for quantum random-number generators based on beam splitters,” Phys. Rev. A 79(5), 054306 (2009).
[Crossref]

2008 (1)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

2005 (1)

2003 (1)

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

2000 (1)

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

1997 (1)

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997).
[Crossref]

Aida, H.

Akizawa, Y.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Arai, K.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Argyris, A.

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Berlin, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Bloch, M.

Bogris, A.

Bucci, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

Chan, S. C.

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

X. Z. Li and S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

Chen, J. J.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Chi, Y. M.

Chizhevsky, V. N.

Citrin, D. S.

Cohen, A. B.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Connelly, J. A.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997).
[Crossref]

Davis, P.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Deligiannidis, S.

Deng, T.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Dowlatabadi, A. B.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997).
[Crossref]

Fan, L.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Fischer, I.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

Germani, L.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

Gisin, N.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guinnard, L.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guinnard, O.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guo, H.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(5), 051137 (2010).
[Crossref] [PubMed]

Harayama, T.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Holman, W. T.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997).
[Crossref]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Iwakawa, K.

Kanno, K.

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

Kim, B.

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Li, N.

Li, P.

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

Li, X.

Li, X. Z.

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

X. Z. Li and S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

Liang, J.

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

Liu, Y.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(5), 051137 (2010).
[Crossref] [PubMed]

Lo, H. K.

Locquet, A.

Luo, B.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

Luzzi, R.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

Ma, H. Q.

Mercier, E.

Morikatsu, S.

Murphy, T. E.

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Okumura, H.

Oliver, N.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Pan, W.

Panajotov, K.

Pikasis, E.

Qi, B.

Qian, L.

Rahn, H.-J.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

Röhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

Roy, R.

Sakuraba, R.

Sciamanna, M.

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Soriano, M. C.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

Stefanov, A.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Sukow, D. W.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

Sunada, S.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Svozil, K.

K. Svozil, “Three criteria for quantum random-number generators based on beam splitters,” Phys. Rev. A 79(5), 054306 (2009).
[Crossref]

Syvridis, D.

Takahashi, R.

Tang, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(5), 051137 (2010).
[Crossref] [PubMed]

Tang, X.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Thienpont, H.

Trifiletti, A.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

Tsuzuki, K.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Uchida, A.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Varanonuovo, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

Virte, M.

Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Wang, J.

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

Wang, Y.

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

Wang, Y. C.

Wei, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(5), 051137 (2010).
[Crossref] [PubMed]

Wu, J. G.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Wu, L. A.

Wu, Z. M.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Xia, G. Q.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Xie, Y.

Yamazaki, T.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

Yang, L.

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, K.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Zbinden, H.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Zhang, J. W.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

Zhang, J. Z.

Zhong, Z. Q.

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Zhu, M. Y.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98(17), 171105 (2011).
[Crossref]

Chaos (1)

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (2)

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

IEEE Trans. Circuits Syst. I (1)

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997).
[Crossref]

IEEE Trans. Comput. (1)

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[Crossref]

J. Mod. Opt. (1)

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Laser Phys. Lett. (2)

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s-1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett. 10(4), 045001 (2013).
[Crossref]

X. Tang, Z. M. Wu, J. G. Wu, T. Deng, L. Fan, Z. Q. Zhong, J. J. Chen, and G. Q. Xia, “Generation of multi-channel high-speed physical random numbers originated from two chaotic signals of mutually coupled semiconductor lasers,” Laser Phys. Lett. 12(1), 015003 (2015).
[Crossref]

Nat. Photonics (2)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Opt. Commun. (1)

J. Wang, J. Liang, P. Li, L. Yang, and Y. Wang, “All-optical random number generation using highly nonlinear fibers by numerical simulation,” Opt. Commun. 321, 1–5 (2014).
[Crossref]

Opt. Express (7)

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[Crossref] [PubMed]

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[Crossref] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

K. Svozil, “Three criteria for quantum random-number generators based on beam splitters,” Phys. Rev. A 79(5), 054306 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(5), 051137 (2010).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

Other (1)

D. Eastlake, J. Schiller, and S. Crocker, “Randomness requirements for security,” RFC4086, [Online]. Available: http://tools.ietf.org/html/rfc4086 (2005).

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Figures (10)

Fig. 1
Fig. 1 Experimental setup for generating multi-channel high-speed PRNs. SL: semiconductor laser, CC: current controller; TC: temperature controller; TA: tunable attenuator; PC: polarization controller; OC: optical coupler; OI: optical isolator; PD: photo-detector; FDL: fiber delay line; OSA: optical spectrum analyzer; ESA: electrical spectrum analyzer; PM: power meter; ADC: analog-to-digital converter; XOR: logical exclusive-OR; CH: channel; m-LSBs: the m least significant bits.
Fig. 2
Fig. 2 Mappings of optical spectra (first row), RF spectra (second row), and chaotic bandwidth (third row) evolution with coupling strength η varied from −28 dB to −10 dB. Left column corresponds to SL 1, and right column is corresponds to SL 2. Different colors represent different amplitude values of optical spectra (a1, a2) and RF spectra (b1, b2).
Fig. 3
Fig. 3 The Maps (a1, b1) of self-correlation curves evolution and the variation curve (a2, b2) of amplitude ρ with coupling strength η varied from −28 dB to −10 dB. Different colors represent different SF function values. The amplitude ρ is the maximum of the SF peak in the time shift window 58 ns < Δt < 60 ns. Left column is for SL 1, and right column is for SL 2.
Fig. 4
Fig. 4 Evolution mappings of the amplitude probability density distributions (APPDs) of sampled temporal waveforms for η varied from −28 dB to −10 dB, where (a) and (b) are for SL 1 and SL 2, respectively. Different colors represent different probability values.
Fig. 5
Fig. 5 Post-processing for PRB generation. The dotted box is for the post-processing in CH 1 which is taken as an example, and the post-processing in CH 2 is the same as that in CH 1.
Fig. 6
Fig. 6 Mappings of number of failed NIST tests for CH 1, CH 2 and CH 3 under η varied within (−28 dB, −10 dB). (a) 8 LSBs, (b) 7 LSBs, and (c) 6 LSBs.
Fig. 7
Fig. 7 Curves of mini-entropy for SL 1 and SL 2 outputs, where η varied from −28 dB to −10 dB.
Fig. 8
Fig. 8 (a) Variation of statistical bias b with sequence length N, and (b) first 200 serial autocorrelation coefficients for the binary sequence of 10 Gbits under η = 20 dB. Left column is for CH 1, and right column is for CH 2.
Fig. 9
Fig. 9 Further optimization process for obtaining final random bit stream. {bi } is the 6 LSBs random sequence, {Bi } is extracted from raw LSBs sequence by using the von Neumann unbiasing method.
Fig. 10
Fig. 10 After adopting short-timescale correlations eliminated scheme, under the case for η = 20 dB, (a) the bias b as a function of the number of generated bits N; (b) the first 200 serial autocorrelation coefficients for the binary sequence of 10 Gbits length.

Tables (1)

Tables Icon

Table 1 Results of NIST tests for final random bit streams of CH 3 under the case for η = 20 dB. 1000 samples of 1 Mbit data are used for evaluation and the significance level a = 0.01. The P value (uniformity of p values) should be larger than 0.0001 and the proportion should be in the range of 0.99 ± 0.0094392. For tests which produce multiple P values and proportions, the worst case is shown.

Equations (3)

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η = 10 lg P c P o u t
C ( Δ t ) = ( P ( t Δ t ) P ( t ) ) ( P ( t ) P ( t ) ) ( P ( t ) P ( t ) 2 P ( t + Δ t ) P ( t ) 2 ) 1 / 2
C k = ( a i a i ) ( a i + k a i ) ( a i a i ) 2

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