Abstract

Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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  17. M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
    [CrossRef]
  18. 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, 711–715 (2010).
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    [CrossRef]
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  22. H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
    [CrossRef]
  23. P. R. Tapster and P. M. Gorman, “Apparatus and Method for Generating Random Numbers,” US patent 2009013019 (2009).
  24. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
    [CrossRef]
  25. M. D. Sturge, “Optical absorption of gallium arsenide between 0.6 and 2.75 ev,” Phys. Rev. 127, 768–773 (1962).
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  26. Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000).
    [CrossRef]
  27. P. Barreto and V. Rijmen, “The Whirlpool hashing fFunction,” pheattarchive.emporia.edu (2010).
  28. Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).
    [CrossRef]
  29. N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999).
    [CrossRef]
  30. P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

2011

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[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, 231103 (2011).
[CrossRef]

2010

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010).
[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, 711–715 (2010).
[CrossRef]

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010).
[CrossRef] [PubMed]

M. Wayne and P. Kwiat, “Low-bias high-speed quantum number generator via shaped optical pulses,” Opt. Express 18, 9351–9357 (2010).
[CrossRef] [PubMed]

M. Fürst, H. Weier, S. Nauerth, D. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express 18, 13029–13037 (2010).
[CrossRef] [PubMed]

2009

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” Appl. Opt. 48, 1774–1778 (2009).
[CrossRef] [PubMed]

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

2008

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, 728–732 (2008).
[CrossRef]

2007

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

P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2000

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000).
[CrossRef]

1999

N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999).
[CrossRef]

1992

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).
[CrossRef]

1984

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

1962

M. D. Sturge, “Optical absorption of gallium arsenide between 0.6 and 2.75 ev,” Phys. Rev. 127, 768–773 (1962).
[CrossRef]

1949

N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statist. Assoc. 44, 335–341 (1949).
[CrossRef]

1890

F. Galton, “Dice for statistical experiments,” Nature 42, 13–14 (1890).
[CrossRef]

Achleitner, U.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

Acin, A.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 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, 711–715 (2010).
[CrossRef]

Arai, S.

Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000).
[CrossRef]

Assad, S. M.

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, 231103 (2011).
[CrossRef]

Banks, S.

S. Banks, P. Beadling, and A. Ferencz, “FPGA Implementation of Pseudo Random Number Generators for Monte Carlo Methods in Quantitative Finance,” in Proceedings of the 2008 International Conference on Reconfigurable, Computing and FPGAs, RECONFIG’08, (IEEE, 2008), pp. 271–276.
[CrossRef]

Barreto, P.

P. Barreto and V. Rijmen, “The Whirlpool hashing fFunction,” pheattarchive.emporia.edu (2010).

Beadling, P.

S. Banks, P. Beadling, and A. Ferencz, “FPGA Implementation of Pseudo Random Number Generators for Monte Carlo Methods in Quantitative Finance,” in Proceedings of the 2008 International Conference on Reconfigurable, Computing and FPGAs, RECONFIG’08, (IEEE, 2008), pp. 271–276.
[CrossRef]

Benson, O.

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

Berlin, M.

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

Bronner, P.

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

Cerf, N.

N. Cerf and L.-P. Lamooureux, “Network distributed quantum random number generation,” International patent GB2473078 (2009).

Chi, Y.-M.

Cho, Y.-W.

Collett, M. J.

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Davis, P.

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, 728–732 (2008).
[CrossRef]

de la Giroday, A. B.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

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, 711–715 (2010).
[CrossRef]

Ferencz, A.

S. Banks, P. Beadling, and A. Ferencz, “FPGA Implementation of Pseudo Random Number Generators for Monte Carlo Methods in Quantitative Finance,” in Proceedings of the 2008 International Conference on Reconfigurable, Computing and FPGAs, RECONFIG’08, (IEEE, 2008), pp. 271–276.
[CrossRef]

Ferguson, N.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, Inc., 2010).

Fürst, M.

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, 711–715 (2010).
[CrossRef]

Galton, F.

F. Galton, “Dice for statistical experiments,” Nature 42, 13–14 (1890).
[CrossRef]

Gardiner, C. W.

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Gorman, P. M.

P. R. Tapster and P. M. Gorman, “Apparatus and Method for Generating Random Numbers,” US patent 2009013019 (2009).

Guinnard, O.

G. Ribordy and O. Guinnard, “Method and apparatus for generating true random numbers by way of a quantum optics process,” US patent 2007127718 (2007).

Guo, H.

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

Hayes, D.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Hirano, K.

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

Inoue, M.

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

Jennewein, T.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

Kanai, T.

T. Kanai, M. Tarui, and Y. Yamada, “Random number generator,” International patent WO2010090328 (2009).

Kim, Y.-H.

Kohno, T.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, Inc., 2010).

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, 728–732 (2008).
[CrossRef]

Kurtsiefer, C.

Kwiat, P.

Kwon, O.

L’Ecuyer, P.

P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

Lam, P. K.

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, 231103 (2011).
[CrossRef]

Lamooureux, L.-P.

N. Cerf and L.-P. Lamooureux, “Network distributed quantum random number generation,” International patent GB2473078 (2009).

Leifgen, M.

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

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, 711–715 (2010).
[CrossRef]

Liu, Y.

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

Lo, H.-K.

Luo, L.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Manning, T. A.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Marangon, D.

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, 711–715 (2010).
[CrossRef]

Massar, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Matsukevich, D. N.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

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, 711–715 (2010).
[CrossRef]

Maunz, P.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statist. Assoc. 44, 335–341 (1949).
[CrossRef]

Meyn, J. P.

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

Monroe, C.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

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, 728–732 (2008).
[CrossRef]

Nauerth, S.

Nisan, N.

N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999).
[CrossRef]

Olmschenk, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Oowada, I.

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

Peres, Y.

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).
[CrossRef]

Pironio, S.

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

Qi, B.

Qian, L.

Rahn, H.-J.

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

Rhlicke, T.

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

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

G. Ribordy and O. Guinnard, “Method and apparatus for generating true random numbers by way of a quantum optics process,” US patent 2007127718 (2007).

Rijmen, V.

P. Barreto and V. Rijmen, “The Whirlpool hashing fFunction,” pheattarchive.emporia.edu (2010).

Rogina, B. M.

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

Schneier, B.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, Inc., 2010).

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, 728–732 (2008).
[CrossRef]

Silberhorn, C.

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

Simard, R.

P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

Someya, H.

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

Stipcevic, M.

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

Strunz, A.

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

Sturge, M. D.

M. D. Sturge, “Optical absorption of gallium arsenide between 0.6 and 2.75 ev,” Phys. Rev. 127, 768–773 (1962).
[CrossRef]

Suematsu, Y.

Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000).
[CrossRef]

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, 711–715 (2010).
[CrossRef]

Symul, T.

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, 231103 (2011).
[CrossRef]

Tang, W.

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

Tapster, P. R.

P. R. Tapster and P. M. Gorman, “Apparatus and Method for Generating Random Numbers,” US patent 2009013019 (2009).

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T. Kanai, M. Tarui, and Y. Yamada, “Random number generator,” International patent WO2010090328 (2009).

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N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999).
[CrossRef]

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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Uchida, A.

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, 728–732 (2008).
[CrossRef]

Ulam, S.

N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statist. Assoc. 44, 335–341 (1949).
[CrossRef]

Wahl, M.

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

Wayne, M.

Wei, W.

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

Weier, H.

Weihs, G.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

Weinfurter, H.

M. Fürst, H. Weier, S. Nauerth, D. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express 18, 13029–13037 (2010).
[CrossRef] [PubMed]

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

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, 711–715 (2010).
[CrossRef]

Yamada, Y.

T. Kanai, M. Tarui, and Y. Yamada, “Random number generator,” International patent WO2010090328 (2009).

Yoshimori, 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, 728–732 (2008).
[CrossRef]

Yoshimura, K.

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

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Zeilinger, A.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

ACM Trans. Math. Softw.

P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

Ann. Stat.

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[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, 231103 (2011).
[CrossRef]

Eur. J. Phys.

P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000).
[CrossRef]

J. Am. Statist. Assoc.

N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statist. Assoc. 44, 335–341 (1949).
[CrossRef]

J. Comput. Syst. Sci.

N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999).
[CrossRef]

Nat. Photonics

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, 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, 711–715 (2010).
[CrossRef]

Nature

S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef] [PubMed]

F. Galton, “Dice for statistical experiments,” Nature 42, 13–14 (1890).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

M. D. Sturge, “Optical absorption of gallium arsenide between 0.6 and 2.75 ev,” Phys. Rev. 127, 768–773 (1962).
[CrossRef]

Phys. Rev. A

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Phys. Rev. E

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

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

Rev. Sci. Instrum.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000).
[CrossRef]

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

Other

P. R. Tapster and P. M. Gorman, “Apparatus and Method for Generating Random Numbers,” US patent 2009013019 (2009).

N. Cerf and L.-P. Lamooureux, “Network distributed quantum random number generation,” International patent GB2473078 (2009).

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, Inc., 2010).

S. Banks, P. Beadling, and A. Ferencz, “FPGA Implementation of Pseudo Random Number Generators for Monte Carlo Methods in Quantitative Finance,” in Proceedings of the 2008 International Conference on Reconfigurable, Computing and FPGAs, RECONFIG’08, (IEEE, 2008), pp. 271–276.
[CrossRef]

R. Corporation, ed., A Million Random Digits with 100,000 Normal Deviates (The Free Press, 1955).

T. Kanai, M. Tarui, and Y. Yamada, “Random number generator,” International patent WO2010090328 (2009).

G. Ribordy and O. Guinnard, “Method and apparatus for generating true random numbers by way of a quantum optics process,” US patent 2007127718 (2007).

P. Barreto and V. Rijmen, “The Whirlpool hashing fFunction,” pheattarchive.emporia.edu (2010).

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Figures (4)

Fig. 1
Fig. 1

Unbalanced Mach-Zehnder interferometer. Due to the random phase of the different input pulses, the output signals acquire random amplitudes. (a) Measured drive current (red, upper curve) and detected laser power (blue, lower curve), showing amplitude repeatability and clear pulse separation. (b) (LD Pulse Driver) denotes the electrical pulse generator to directly modulate the laser, (LD) laser diode, (OI) optical isolator, (PMF) polarization maintaining fiber, (ϕ0–3) optical phases of different consecutive pulses, (PMC) polarization maintaining coupler, (ϕloop) phase introduced by the delay line and (PIN) fast photodiode.

Fig. 2
Fig. 2

Generation of amplified vacuum within the laser cavity. (a) The LD is first taken below threshold, to attenuate the cavity field to a weak thermal state (in red), independent of its previous value (in blue). (b) The LD is then taken above threshold, so that phase-insensitive amplification brings the field amplitude |α| to a level fixed by saturation, while the phase retains the random thermal-state value.

Fig. 3
Fig. 3

Inter-pulse coherence measured by output energy distributions. (a) Distributions for: individual pulse energies ui,vi+1, interfering pulse energies u i ( out ) under different PRF and hence different trep. (b) Output pulse energy histogram for delay-loop temperatures of 25 °C (fixed), and 24 °C to 26 °C (scanned). Loop phase has no observable effect on the distribution, indicating statistical independence of the pulses’ phases.

Fig. 4
Fig. 4

Measured correlation and entropy of acquired pulses. (a) Normalized correlation of successive samples as a function of sample delay of the raw data. The correlation data samples follows a delta-function like behavior indicating a random sequence. (b) Total entropy, calculated from the measured distribution shown in Fig. 3. Distribution is divided into 2b bins, from which the Shannon entropy is calculated. Optical contribution, up to 11.1 bits per pulse, is found by subtracting entropy of the measured electronic noise.

Equations (2)

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d dt a = i ω a 1 2 γ a + Γ ,
u i ( out ) = u i + v i + 1 + 2 | g ( t loop ) | u i v i + 1 cos ( ϕ i ϕ i + 1 ϕ loop )

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