Abstract

We experimentally demonstrate fast physical random bit generation from bandwidth-enhanced chaos by using three-cascaded semiconductor lasers. The bandwidth-enhanced chaos is obtained with the standard bandwidth of 35.2 GHz, the effective bandwidth of 26.0 GHz and the flatness of 5.6 dB, whose waveform is used for random bit generation. Two schemes of single-bit and multi-bit extraction methods for random bit generation are carried out to evaluate the entropy rate and the maximum random bit generation rate. For single-bit generation, the generation rate at 20 Gb/s is obtained for physical random bit sequences. For multi-bit generation, the maximum generation rate at 1.2 Tb/s ( = 100 GS/s × 6 bits × 2 data) is equivalently achieved for physical random bit sequences whose randomness is verified by using both NIST Special Publication 800-22 and TestU01.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2014 (4)

2013 (5)

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

T. Yamazaki and A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (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]

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]

2012 (9)

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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

F.-Y. Lin, Y.-K. Chao, and T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[Crossref] [PubMed]

J. Zhang, Y. Wang, L. Xue, J. Hou, B. Zhang, A. Wang, and M. Zhang, “Delay line length selection in generating fast random numbers with a chaotic laser,” Appl. Opt. 51(11), 1709–1714 (2012).
[Crossref] [PubMed]

A. Argyris, E. Pikasis, S. Deligiannidis, and D. Syvridis, “Sub-Tb/s physical random bit generators based on direct detection of amplified spontaneous emission signals,” J. Lightwave Technol. 30(9), 1329–1334 (2012).
[Crossref]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

2011 (2)

X. Li, A. B. Cohen, T. E. Murphy, and R. Roy, “Scalable parallel physical random number generator based on a superluminescent LED,” Opt. Lett. 36(6), 1020–1022 (2011).
[Crossref] [PubMed]

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry-Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. 23(24), 1872–1874 (2011).
[Crossref]

2010 (5)

V. N. Chizhevsky, “Symmetrization of single-sided or nonsymmetrical distributions: The way to enhance a generation rate of random bits from a physical source of randomness,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 050101 (2010).
[Crossref] [PubMed]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

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]

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]

C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18(23), 23584–23597 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (3)

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]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

2007 (2)

M. Stipčević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

P. L’Ecuyer and R. Simard, “TestU01: A C library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33(4), 22 (2007).
[Crossref]

2003 (3)

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[Crossref]

Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28(5), 319–321 (2003).
[Crossref] [PubMed]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Aida, H.

Aida, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Amano, K.

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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]

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Aoyama, K.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

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]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

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]

Bahi, J. M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Bloch, M.

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]

Chao, Y.-K.

F.-Y. Lin, Y.-K. Chao, and T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

Chizhevsky, V. N.

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]

V. N. Chizhevsky, “Symmetrization of single-sided or nonsymmetrical distributions: The way to enhance a generation rate of random bits from a physical source of randomness,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 050101 (2010).
[Crossref] [PubMed]

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]

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]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (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]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Deligiannidis, S.

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Dudley, J. M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

Fang, X.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

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]

Fushimi, M.

H. Miyazawa and M. Fushimi, “An implementation of a 5-term GFSR random number generator for parallel computations,” in Proceedings of the International Symposium on Operations Research and Its Applications (ISORA, 2009) pp. 448–452.

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Guyeux, C.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

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]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (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]

He, H.

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Heil, T.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Hirano, K.

Honjo, T.

Hou, J.

Ikeguchi, T.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

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]

Kakesu, I.

Kanno, K.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

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.

Koizumi, H.

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]

L’Ecuyer, P.

P. L’Ecuyer and R. Simard, “TestU01: A C library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33(4), 22 (2007).
[Crossref]

Larger, L.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Li, L.

Li, N.

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]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Li, P.

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]

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[Crossref]

Lin, F.-Y.

F.-Y. Lin, Y.-K. Chao, and T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

Liu, J. M.

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[Crossref]

Liu, M.

Liu, T.

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry-Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. 23(24), 1872–1874 (2011).
[Crossref]

Liu, Y.

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Locquet, A.

Luo, B.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Mercier, E.

Merolla, J.-M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Mikami, T.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

Miyazawa, H.

H. Miyazawa and M. Fushimi, “An implementation of a 5-term GFSR random number generator for parallel computations,” in Proceedings of the International Symposium on Operations Research and Its Applications (ISORA, 2009) pp. 448–452.

Morikatsu, S.

Muramatsu, J.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

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]

Nozawa, T.

Ohtsubo, J.

Ohyagi, K.

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]

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.

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]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Panajotov, K.

Pikasis, E.

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]

Rogina, B. M.

M. Stipčević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

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.

Salevan, J. C.

Sciamanna, M.

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

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]

Simard, R.

P. L’Ecuyer and R. Simard, “TestU01: A C library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33(4), 22 (2007).
[Crossref]

Someya, H.

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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]

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]

Stipcevic, M.

M. Stipčević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

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]

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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Syvridis, D.

Takahashi, R.

Takiguchi, Y.

Thienpont, H.

Tokura, Y.

Tsuzuki, K.

Uchida, A.

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]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

T. Yamazaki and A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[Crossref]

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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (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]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[Crossref]

Virte, M.

Wang, A.

A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

J. Zhang, Y. Wang, L. Xue, J. Hou, B. Zhang, A. Wang, and M. Zhang, “Delay line length selection in generating fast random numbers with a chaotic laser,” Appl. Opt. 51(11), 1709–1714 (2012).
[Crossref] [PubMed]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[Crossref] [PubMed]

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry-Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. 23(24), 1872–1874 (2011).
[Crossref]

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Wang, Y.

A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[Crossref] [PubMed]

J. Zhang, Y. Wang, L. Xue, J. Hou, B. Zhang, A. Wang, and M. Zhang, “Delay line length selection in generating fast random numbers with a chaotic laser,” Appl. Opt. 51(11), 1709–1714 (2012).
[Crossref] [PubMed]

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry-Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. 23(24), 1872–1874 (2011).
[Crossref]

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

Wetzel, B.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Williams, C. R. S.

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Wu, T.-C.

F.-Y. Lin, Y.-K. Chao, and T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

Xiang, S. Y.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Xue, L.

Yamazaki, T.

T. Yamazaki and A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[Crossref]

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 Photon. 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]

Yan, L. S.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[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]

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (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]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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).
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Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

Zhang, B.

Zhang, J.

Zhang, M.

Zhu, H. N.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

Zou, X. H.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

ACM Trans. Math. Softw. (1)

P. L’Ecuyer and R. Simard, “TestU01: A C library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33(4), 22 (2007).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[Crossref]

IEEE J. Quantum Electron. (5)

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

F.-Y. Lin, Y.-K. Chao, and T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[Crossref]

A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003).
[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).
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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).
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IEEE J. Sel. Top. Quantum Electron. (1)

T. Yamazaki and A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (3)

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 Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry-Pérot laser diode with optical feedback,” IEEE Photon. Technol. Lett. 23(24), 1872–1874 (2011).
[Crossref]

IEEE Trans. Cir. Syst. I (1)

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

J. Lightwave Technol. (1)

Nat. Photonics (3)

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (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]

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]

Opt. Commun. (1)

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[Crossref]

Opt. Express (9)

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, and P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[Crossref] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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).
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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]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[Crossref] [PubMed]

C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18(23), 23584–23597 (2010).
[Crossref] [PubMed]

A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[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]

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[Crossref] [PubMed]

V. N. Chizhevsky, “Symmetrization of single-sided or nonsymmetrical distributions: The way to enhance a generation rate of random bits from a physical source of randomness,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(5), 050101 (2010).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

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).
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Rev. Sci. Instrum. (1)

M. Stipčević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

Other (5)

H. Miyazawa and M. Fushimi, “An implementation of a 5-term GFSR random number generator for parallel computations,” in Proceedings of the International Symposium on Operations Research and Its Applications (ISORA, 2009) pp. 448–452.

K. Kanno, A. Uchida, and M. Bunsen are preparing a manuscript to be called “Complexity and bandwidth enhancement in unidirectionally-coupled semiconductor lasers with time-delayed optical feedback.”

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, S. Vo, and L. E. Bassham III, National Institute of Standards and Technology, Special Publication 800–22, Revision 1a (2010).

J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, Third Edition (Springer-Verlag, 2013).

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).

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Figures (12)

Fig. 1
Fig. 1 Experimental setup for bandwidth enhancement of chaos and physical random bit generation using three-cascaded semiconductor lasers. FC, fiber coupler; ISO, optical fiber isolator; PD, photodetector.
Fig. 2
Fig. 2 Examples of the measurement of (a) standard bandwidth, (b) effective bandwidth and flatness of RF broadband spectra.
Fig. 3
Fig. 3 (a), (c), (e) Chaotic temporal waveforms and (b), (d), (f) their corresponding RF spectra of the three unidirectionally-coupled laser outputs. (a), (b) Laser 1, (c) (d) Laser 2, and (e), (f) Laser 3. The relaxation oscillation frequency of Laser 1 is fr1 ~6.5 GHz, the optical frequency detuning between Laser 1 and 2 is Δf12 = 16.5 GHz, and the optical frequency detuning between Laser 2 and 3 is Δf23 = 31.5 GHz.
Fig. 4
Fig. 4 (a) Standard bandwidth, (b) effective bandwidth and flatness as a function of the optical frequency detuning between Laser 2 and 3 Δf23. The optical frequency detuning between Laser 1 and 2 is fixed at Δf12 = 16.5 GHz.
Fig. 5
Fig. 5 Schematics of single-bit extraction method for random bit generation [15].
Fig. 6
Fig. 6 Number of passed NIST tests for random bit sequences generated from chaotic temporal waveforms of (a) Laser 1, (b) Laser 2, and (c) Laser 3 as a function of the sampling time. The lower horizontal axis indicates the sampling time, and the upper horizontal axis indicates the sampling rate (the inverse of the sampling time), which corresponds to the random-bit generation rate. The vertical axis indicates the number of the NIST tests that pass the statistical tests of randomness, where “15” corresponds to the results that all the NIST tests are passed. Five 1-Gbit sequences of random bits are used for each NIST test and the median of the five test results is plotted with error bars of the maximum and minimum values. The red numbers on the upper horizontal axis indicate that the random bits generated at this sampling rate can pass all the NIST tests.
Fig. 7
Fig. 7 Autocorrelation function (absolute value) of the chaotic temporal waveform of Laser 3 as a function of the delay time and the result of NIST tests for generated random bit sequences. The results of NIST tests correspond to Fig. 6(c). Red circles: all the NIST tests are passed. Blue triangles: one or more NIST tests are failed. The dotted line indicates the autocorrelation value 7.7 × 10−2. The red numbers on the upper horizontal axis indicate that the random bits generated at this sampling rate can pass all the NIST tests.
Fig. 8
Fig. 8 Schematics of multi-bit extraction method for random bit generation.
Fig. 9
Fig. 9 Histograms (probability density functions) of the temporal waveforms when (a) the detection window size or (b) the off-set of the temporal waveforms is changed. (a) The off-set is fixed at 0. (b) The detection window size is fixed at ± 4.0σ, corresponding to ± 50 mV.
Fig. 10
Fig. 10 Bias b for each significant bit of the 8-bit chaotic waveform as a function of (a) the window step size and (b) the off-set for 1-Gbit chaotic data. (a) The off-set is fixed at 0. (b) The detection window size is fixed at ± 4.0σ, corresponding to ± 50 mV. The light yellow region indicates that the peak value is larger than 10−4 at the edge −127 in the histogram of Fig. 9.
Fig. 11
Fig. 11 Number of passed NIST tests as a function of the extracted LSBs for the multi-bit extraction method for random bit generation. “15” on the vertical axis indicates that all the NIST tests are passed. Five 1-Gbit sequences of random bits are used for each NIST test and the median of the five test results is plotted with error bars of the maximum and minimum values.
Fig. 12
Fig. 12 Number of passed TestU01 tests as a function of the extracted LSBs for the multi-bit extraction method for random bit generation. (a) Rabbit, Alphabit, SmallCrush, and (b) Crush. (a) “38,” “17,” and “15” on the vertical axis indicate that all the Rabbit, Alphabit, and SmallCrush tests are passed, respectively. Five sequences of random bits are used for each test and the median of the five test results is plotted with error bars of the maximum and minimum values. (b) “144” on the vertical axis indicate that all the Crush tests are passed. One sequence of 41-Gbit data is used for Crush tests.

Tables (4)

Tables Icon

Table 1 Standard bandwidth, effective bandwidth, and flatness of the RF spectra for the Laser 1, 2, and 3 outputs, shown in Fig. 3.

Tables Icon

Table 2 Result of NIST SP 800-22 for random bit sequences generated from the multi-bit extraction method with 7 LSBs. Significance level is set to α = 0.01. To pass the tests, the P-value of the uniformity of p-values should be larger than 0.0001, and the proportion of sequences satisfying p-value > α for 1000 samples of 1 Mbit data should be in the range of 0.99 ± 0.0094392 [39]. For tests which produce multiple P-values and proportions, the worst case is shown.

Tables Icon

Table 3 Results of (a) Rabbit, (b) Alphabit, and (c) SmallCrush in TestU01 for random bit sequences generated from the multi-bit extraction method with 8 LSBs. Rabbit, Alphabit, and SmallCrush consist of 38, 17, and 15 tests, respectively. The p-values for all the tests need to be greater than 0.001 or smaller than 0.999 to pass the statistical tests of randomness [40].

Tables Icon

Table 4 Results of Crush in TestU01 for 41-Gbit random bit sequences generated from the multi-bit extraction method with 6 LSBs. Crush consists of 144 tests. R indicates the result (S: Success, F: Fail) in Table 4. The p-values for all the tests need to be greater than 0.001 or smaller than 0.999 to pass the statistical tests of randomness [40].

Equations (2)

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L=SVD
b=| P0.5 |

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