Abstract

Random number generators are essential for applications in information security and numerical simulations. Most optical-chaos-based random number generators produce random bit sequences by offline post-processing with large optical components. We demonstrate a real-time hardware implementation of a fast physical random number generator with a photonic integrated circuit and a field programmable gate array (FPGA) electronic board. We generate 1-Tbit random bit sequences and evaluate their statistical randomness using NIST Special Publication 800-22 and TestU01. All of the BigCrush tests in TestU01 are passed using 410-Gbit random bit sequences. A maximum real-time generation rate of 21.1 Gb/s is achieved for random bit sequences in binary format stored in a computer, which can be directly used for applications involving secret keys in cryptography and random seeds in large-scale numerical simulations.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers

Ryohsuke Sakuraba, Kento Iwakawa, Kazutaka Kanno, and Atsushi Uchida
Opt. Express 23(2) 1470-1490 (2015)

Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation

Rie Takahashi, Yasuhiro Akizawa, Atsushi Uchida, Takahisa Harayama, Ken Tsuzuki, Satoshi Sunada, Kenichi Arai, Kazuyuki Yoshimura, and Peter Davis
Opt. Express 22(10) 11727-11740 (2014)

A robust random number generator based on differential comparison of chaotic laser signals

Jianzhong Zhang, Yuncai Wang, Ming Liu, Lugang Xue, Pu Li, Anbang Wang, and Mingjiang Zhang
Opt. Express 20(7) 7496-7506 (2012)

References

  • View by:
  • |
  • |
  • |

  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]
  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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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).
  11. 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]
  12. 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]
  13. 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]
  14. X. Tang, Z.-M. Wu, J.-G. Wu, T. Deng, J.-J. Chen, L. Fan, Z.-Q. Zhong, and G.-Q. Xia, “Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source,” Opt. Express 23(26), 33130–33141 (2015).
    [Crossref] [PubMed]
  15. T. Butler, C. Durkan, D. Goulding, S. Slepneva, B. Kelleher, S. P. Hegarty, and G. Huyet, “Optical ultrafast random number generation at 1 Tb/s using a turbulent semiconductor ring cavity laser,” Opt. Lett. 41(2), 388–391 (2016).
    [Crossref] [PubMed]
  16. P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
    [Crossref] [PubMed]
  17. 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]
  18. T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
    [Crossref]
  19. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
    [Crossref] [PubMed]
  20. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
    [Crossref] [PubMed]
  21. 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]
  22. A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization (Wiley-VCH, 2012).
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. M. Huang, A. Wang, P. Li, H. Xu, and Y. Wang, “Real-time 3 Gbit/s true random bit generator based on a super-luminescent diode,” Opt. Commun. 325, 165–169 (2014).
    [Crossref]
  28. 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]
  29. 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]
  30. 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]
  31. T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98(23), 231103 (2011).
    [Crossref]
  32. Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
    [Crossref] [PubMed]
  33. X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
    [Crossref] [PubMed]
  34. 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]
  35. 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]
  36. 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]
  37. 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) 448–452 (2009).
  38. D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (2013).
    [Crossref] [PubMed]
  39. S. Shinohara, K. Arai, P. Davis, S. Sunada, and T. Harayama are preparing a manuscript to be called “Chaotic laser based physical random bit streaming system with a computer application interface.”
  40. 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).
  41. 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]
  42. A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
    [Crossref] [PubMed]
  43. A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.
  44. M. Dichtl, “Bad and good ways of post-processing biased physical random numbers,” Lect. Notes Comput. Sci. 4593, 137–152 (2007).
    [Crossref]
  45. J. D. Hart, Y. Terashima, A. Uchida, G. B. Baumgartner, T. E. Murphy, and R. Roy, “Commentary: Evaluating photonic random number generators,” arXiv:1612.04415v2 (2016).
  46. J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
    [Crossref]

2016 (4)

2015 (4)

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[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]

X. Tang, Z.-M. Wu, J.-G. Wu, T. Deng, J.-J. Chen, L. Fan, Z.-Q. Zhong, and G.-Q. Xia, “Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source,” Opt. Express 23(26), 33130–33141 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (6)

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]

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]

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (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]

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 (4)

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]

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]

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]

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]

2011 (5)

2010 (5)

2009 (2)

2008 (2)

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]

2007 (3)

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]

M. Dichtl, “Bad and good ways of post-processing biased physical random numbers,” Lect. Notes Comput. Sci. 4593, 137–152 (2007).
[Crossref]

Aida, H.

Akizawa, Y.

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[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]

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. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

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]

Arai, K.

Argyris, A.

Assad, S. M.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98(23), 231103 (2011).
[Crossref]

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.

Bogris, A.

Butler, T.

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]

Chen, J.-J.

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]

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. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[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]

Deligiannidis, S.

Deng, T.

Dichtl, M.

M. Dichtl, “Bad and good ways of post-processing biased physical random numbers,” Lect. Notes Comput. Sci. 4593, 137–152 (2007).
[Crossref]

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).

Durkan, C.

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]

Fan, L.

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]

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]

Gauthier, D. J.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (2013).
[Crossref] [PubMed]

Goulding, D.

Guo, X.

Guo, Y.

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.

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[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]

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, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[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]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Haw, J. Y.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

Hegarty, S. P.

Hirano, K.

Honjo, T.

Huang, L.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Huang, M.

M. Huang, A. Wang, P. Li, H. Xu, and Y. Wang, “Real-time 3 Gbit/s true random bit generator based on a super-luminescent diode,” Opt. Commun. 325, 165–169 (2014).
[Crossref]

Huyet, G.

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]

Inubushi, M.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Iwakawa, K.

Kakesu, I.

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]

Karsaklian Dal Bosco, A.

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[Crossref] [PubMed]

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Kelleher, B.

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]

Lam, P. K.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98(23), 231103 (2011).
[Crossref]

Lance, A. M.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[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.

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]

Liang, H.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

Liu, M.

Liu, X.

Liu, Y.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Locquet, A.

Ma, X.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

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).

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]

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]

Ng, N. H. Y.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

Nie, Y.-Q.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Nozawa, T.

Ohara, S.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

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, J.-W.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Pan, W.

Panajotov, K.

Payne, F.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

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]

Rontani, D.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (2013).
[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]

Rosin, D. P.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (2013).
[Crossref] [PubMed]

Roy, R.

Sakuraba, R.

Salevan, J. C.

Sato, N.

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Sciamanna, M.

Sharma, V.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

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]

Slepneva, S.

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]

Sun, Y.

Sunada, S.

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]

Symul, T.

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98(23), 231103 (2011).
[Crossref]

Syvridis, D.

Takahashi, R.

Tang, X.

Thienpont, H.

Tokura, Y.

Tsuzuki, K.

Uchida, A.

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[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]

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]

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, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[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. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Virte, M.

Wang, A.

Wang, Y.

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, J.-G.

Wu, Z.-M.

Xia, G.-Q.

Xu, H.

M. Huang, A. Wang, P. Li, H. Xu, and Y. Wang, “Real-time 3 Gbit/s true random bit generator based on a super-luminescent diode,” Opt. Commun. 325, 165–169 (2014).
[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]

Yi, X.

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.

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[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]

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. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[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]

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, J.

Zhang, M.

Zhang, X.-G.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

Zhong, Z.-Q.

Zhou, H.

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

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. Phys. Lett. (2)

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]

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98(23), 231103 (2011).
[Crossref]

IEEE J. Quantum Electron. (2)

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]

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

Lect. Notes Comput. Sci. (1)

M. Dichtl, “Bad and good ways of post-processing biased physical random numbers,” Lect. Notes Comput. Sci. 4593, 137–152 (2007).
[Crossref]

Nat. Photonics (3)

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]

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]

Opt. Commun. (1)

M. Huang, A. Wang, P. Li, H. Xu, and Y. Wang, “Real-time 3 Gbit/s true random bit generator based on a super-luminescent diode,” Opt. Commun. 325, 165–169 (2014).
[Crossref]

Opt. Express (15)

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]

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. 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]

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]

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]

X. Tang, Z.-M. Wu, J.-G. Wu, T. Deng, J.-J. Chen, L. Fan, Z.-Q. Zhong, and G.-Q. Xia, “Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source,” Opt. Express 23(26), 33130–33141 (2015).
[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]

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]

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]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[Crossref] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[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]

A. Karsaklian Dal Bosco, Y. Akizawa, K. Kanno, A. Uchida, T. Harayama, and K. Yoshimura, “Photonic integrated circuits unveil crisis-induced intermittency,” Opt. Express 24(19), 22198–22209 (2016).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Phys. Rev. Appl. (1)

J. Y. Haw, S. M. Assad, A. M. Lance, N. H. Y. Ng, V. Sharma, P. K. Lam, and T. Symul, “Maximization of extractable randomness in a quantum random-number generator,” Phys. Rev. Appl. 3(5), 054004 (2015).
[Crossref]

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

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultrafast physical generation of random numbers using hybrid Boolean networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 87(4), 040902 (2013).
[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).
[Crossref] [PubMed]

Rev. Sci. Instrum. (3)

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 Gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

X.-G. Zhang, Y.-Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J.-W. Pan, “Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref] [PubMed]

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 (6)

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) 448–452 (2009).

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

S. Shinohara, K. Arai, P. Davis, S. Sunada, and T. Harayama are preparing a manuscript to be called “Chaotic laser based physical random bit streaming system with a computer application interface.”

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. D. Hart, Y. Terashima, A. Uchida, G. B. Baumgartner, T. E. Murphy, and R. Roy, “Commentary: Evaluating photonic random number generators,” arXiv:1612.04415v2 (2016).

A. Karsaklian Dal Bosco, S. Ohara, N. Sato, Y. Akizawa, A. Uchida, T. Harayama, and M. Inubushi, “Dynamics versus feedback delay time in photonic integrated circuits: Mapping the short cavity regime,” IEEE Photonics J.in press.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 Schematic diagram of photonic integrated circuit (PIC). The PIC consists of a photodetector (PD), a distributed-feedback (DFB) semiconductor laser, two semiconductor optical amplifiers (SOA 1 and SOA 2), a passive waveguide, and an external mirror. The external cavity length is 10.3 mm.
Fig. 2
Fig. 2 Photograph of experimental setup for real-time random number generator with photonic integrated circuit and FPGA electronic board. The dimensions of the box are 310 mm × 270 mm × 140 mm.
Fig. 3
Fig. 3 Experimental data for chaotic laser output of photonic integrated circuit. (a) Temporal waveform, (b) RF spectrum, (c) histogram of temporal waveform, and (d) histogram of difference between chaotic signal and its time-delayed signal (1.94-ns delay).
Fig. 4
Fig. 4 (a) Experimental data for absolute value of autocorrelation function for chaotic laser output of photonic integrated circuit. (b) Enlarged view of (a).
Fig. 5
Fig. 5 Schematic diagram of random number generation using bit-order reversal method. AD: analog-to-digital, LSB: least significant bit, PIC: photonic integrated circuit.
Fig. 6
Fig. 6 Bias (blue curves) of generated random bit sequences as function of number of generated bits N (a) without and (b) with the post-processing in Fig. 5. The black dotted-dashed line indicates the 3σ criterion for the bias of random bits, where σ=1/ ( 2 N ) .
Fig. 7
Fig. 7 Number of passed NIST SP 800-22 tests as function of extracted LSBs in post-processing for random number generation. On the vertical axis, 15 indicates that all of the NIST tests were passed. Nine 1-Gbit sequences of random bits are used for each NIST test, and the median of the nine test results is plotted with error bars indicating the maximum and minimum values.
Fig. 8
Fig. 8 Number of passed TestU01 tests as function of extracted LSBs in post-processing for random number generation. (a) Rabbit (black solid line with circles), Alphabit (blue dashed line with squares), and SmallCrush (red dotted line with diamonds) tests. On the vertical axis, 38, 17, and 15 indicate that all of the Rabbit, Alphabit, and SmallCrush tests, respectively, were passed. Nine sequences of 1.05-Mbit, 33.6-Mbit, and 1.64-Gbit data were used for the Rabbit, Alphabit, and SmallCrush tests, respectively, and the median of the nine test results is plotted with error bars indicating the maximum and minimum values. (b) Crush (black solid line with circles) and BigCrush (blue dashed line with squares) tests. On the vertical axis, 144 and 160 indicate that all of the Crush and BigCrush tests, respectively, were passed. Five sequences of 41-Gbit and 410-Gbit data were used for the Crush and BigCrush tests, respectively, and the median of the five test results is plotted with error bars indicating the maximum and minimum values.
Fig. 9
Fig. 9 Real-time generation rate for RNG as function of number of extracted LSBs in post-processing using bit-order-reversal method.
Fig. 10
Fig. 10 Schematic diagram of random number generation using bit-shift and bit-rotation method. AD: analog-to-digital, LSB: least significant bit, PIC: photonic integrated circuit.
Fig. 11
Fig. 11 Bias (blue curves) for random bit sequences generated by bit-shift and bit-rotation method as function of number of generated bits N. (a) Left bit-shift and bit-rotation method. (b) Right bit-shift and bit-rotation method. The dotted-dashed line indicates the 3σ criterion for the bias of random bits, where σ=1/ ( 2 N ) .
Fig. 12
Fig. 12 Number of passed NIST SP 800-22 tests as function of extracted LSBs for (a) left bit-shift and bit-rotation method and (b) right bit-shift and bit-rotation method. On the vertical axis, 15 indicates that all of the NIST tests were passed. Nine 1-Gbit sequences of random bits were used for each NIST test, and the median of the nine test results is plotted with error bars indicating the maximum and minimum values.

Metrics