Abstract

We report a 12.5 Gb/s physical random number generator (RNG) that uses high-speed threshold detection of the spectrally-sliced incoherent light produced by a fiber amplifier. The system generates a large-amplitude, easily measured, fluctuating signal with bandwidth that is constrained only by the optical filter and electrical detector used. The underlying physical process (spontaneous emission) is inherently quantum mechanical in origin, and therefore cannot be described deterministically. Unlike competing optical RNG approaches that require photon counting electronics, chaotic laser cavities, or state-of-the-art analog-to-digital converters, the system employs only commonly available telecommunications-grade fiber optic components and can be scaled to higher speeds or multiplexed into parallel channels. The quality of the resulting random bitstream is verified using industry-standard statistical tests.

© 2010 OSA

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2010 (5)

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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

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]

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]

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

S. Pironio, A. Acín, 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]

2009 (1)

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

2008 (2)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

2006 (1)

P. Xu, Y. Wong, T. Horiuchi, and P. Abshire, “Compact floating-gate true random number generator,” Electron. Lett. 42, 1346 –1347 (2006).
[Crossref]

2003 (1)

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

2001 (2)

T. Stojanovski and L. Kocarev, “Chaos-based random number generators – Part I: analysis,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 281–288 (2001).
[Crossref]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators – Part II: practical realization,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 382–385 (2001).
[Crossref]

2000 (3)

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]

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 615–621 (2000).
[Crossref]

M. S. Leeson, “Performance analysis of direct detection spectrally sliced receivers using Fabry-Perot filters,” J. Lightwave Technol. 18, 13–25 (2000).
[Crossref]

1999 (1)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun. 17, 539–550 (1999).
[Crossref]

1997 (2)

A. J. Keating and D. D. Sampson, “Reduction of excess intensity noise in spectrum-sliced incoherent light for WDM applications,” J. Lightwave Technol. 15, 53–61 (1997).
[Crossref]

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

1996 (1)

J.-S. Lee, “Signal-to-noise ratio of spectrum-sliced incoherent light sources including optical modulation effects,” J. Lightwave Technol. 14, 2197–2201 (1996).
[Crossref]

1992 (1)

A. M. Ferrenberg, D. P. Landau, and Y. J. Wong, “Monte Carlo simulations: hidden errors from ‘good’ random number generators,” Phys. Rev. Lett. 69, 3382–3384 (1992).
[Crossref] [PubMed]

1991 (2)

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[Crossref]

R. C. Steele, G. R. Walker, and N. G. Walker, “Sensitivity of optically preamplified receivers with optical filtering,” IEEE Photon. Technol. Lett. 3, 545–547 (1991).
[Crossref]

1990 (1)

G. Bernstein and M. Lieberman, “Secure random number generation using chaotic circuits,” IEEE Trans. Circuits Syst. 37, 1157–1164 (1990).
[Crossref]

1989 (1)

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[Crossref]

1956 (1)

M. Isida and H. Ikeda, “Random number generator,” Ann. Inst. Stat. Math. 8, 119–126 (1956).
[Crossref]

Abshire, P.

P. Xu, Y. Wong, T. Horiuchi, and P. Abshire, “Compact floating-gate true random number generator,” Electron. Lett. 42, 1346 –1347 (2006).
[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]

Acín, A.

S. Pironio, A. Acín, 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,” Nature Photon. 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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nature Photon. 4, 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, 024102 (2009).
[Crossref] [PubMed]

Azizog~lu, M.

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[Crossref]

Banks, D.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Barker, E.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Bernstein, G.

G. Bernstein and M. Lieberman, “Secure random number generation using chaotic circuits,” IEEE Trans. Circuits Syst. 37, 1157–1164 (1990).
[Crossref]

Bucci, M.

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

Chi, Y.-M.

Cohen, E.

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

Connelly, J.

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 615–621 (2000).
[Crossref]

Connelly, J. A.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 521–528 (1997).
[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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

de la Giroday, A. B.

S. Pironio, A. Acín, 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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Dowlatabadi, A. B.

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

Dray, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Dynes, J. F.

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

Ferrenberg, A. M.

A. M. Ferrenberg, D. P. Landau, and Y. J. Wong, “Monte Carlo simulations: hidden errors from ‘good’ random number generators,” Phys. Rev. Lett. 69, 3382–3384 (1992).
[Crossref] [PubMed]

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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Germani, L.

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

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985). p. 246.

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. Acín, 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]

Heckert, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

Holman, W. T.

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

Horiuchi, T.

P. Xu, Y. Wong, T. Horiuchi, and P. Abshire, “Compact floating-gate true random number generator,” Electron. Lett. 42, 1346 –1347 (2006).
[Crossref]

Humblet, P. A.

P. A. Humblet and M. Azizog̃lu, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. 9, 1576–1582 (1991).
[Crossref]

Ikeda, H.

M. Isida and H. Ikeda, “Random number generator,” Ann. Inst. Stat. Math. 8, 119–126 (1956).
[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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

Isida, M.

M. Isida and H. Ikeda, “Random number generator,” Ann. Inst. Stat. Math. 8, 119–126 (1956).
[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]

Jun, B.

B. Jun and P. Kocher, “The Intel Random Number Generator,” Cryptography Research Inc., white paper prepared for Inter Corp. (1999).

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nature Photon. 4, 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, 024102 (2009).
[Crossref] [PubMed]

Keating, A. J.

A. J. Keating and D. D. Sampson, “Reduction of excess intensity noise in spectrum-sliced incoherent light for WDM applications,” J. Lightwave Technol. 15, 53–61 (1997).
[Crossref]

Knuth, D.

D. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed.) (Addison-Wesley, 1996). pp. 64–65.

Kocarev, L.

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators – Part II: practical realization,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 382–385 (2001).
[Crossref]

T. Stojanovski and L. Kocarev, “Chaos-based random number generators – Part I: analysis,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 281–288 (2001).
[Crossref]

Kocher, P.

B. Jun and P. Kocher, “The Intel Random Number Generator,” Cryptography Research Inc., white paper prepared for Inter Corp. (1999).

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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

Landau, D. P.

A. M. Ferrenberg, D. P. Landau, and Y. J. Wong, “Monte Carlo simulations: hidden errors from ‘good’ random number generators,” Phys. Rev. Lett. 69, 3382–3384 (1992).
[Crossref] [PubMed]

Lee, J.-S.

J.-S. Lee, “Signal-to-noise ratio of spectrum-sliced incoherent light sources including optical modulation effects,” J. Lightwave Technol. 14, 2197–2201 (1996).
[Crossref]

Leeson, M. S.

Leigh, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Levenson, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Lieberman, M.

G. Bernstein and M. Lieberman, “Secure random number generation using chaotic circuits,” IEEE Trans. Circuits Syst. 37, 1157–1164 (1990).
[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. Acín, 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]

Luzzi, R.

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

Manning, T. A.

S. Pironio, A. Acín, 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]

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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Massar, S.

S. Pironio, A. Acín, 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. Acín, 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,” Nature Photon. 4, 711–715 (2010).
[Crossref]

Maunz, P.

S. Pironio, A. Acín, 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]

Monroe, C.

S. Pironio, A. Acín, 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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

Nechvatal, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Olmschenk, S.

S. Pironio, A. Acín, 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]

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N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[Crossref]

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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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

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C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 615–621 (2000).
[Crossref]

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T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators – Part II: practical realization,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 382–385 (2001).
[Crossref]

Pironio, S.

S. Pironio, A. Acín, 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.

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nature Photon. 4, 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, 024102 (2009).
[Crossref] [PubMed]

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I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nature Photon. 4, 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, 024102 (2009).
[Crossref] [PubMed]

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A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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A. J. Keating and D. D. Sampson, “Reduction of excess intensity noise in spectrum-sliced incoherent light for WDM applications,” J. Lightwave Technol. 15, 53–61 (1997).
[Crossref]

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

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

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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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

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A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

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A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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T. Stojanovski and L. Kocarev, “Chaos-based random number generators – Part I: analysis,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 281–288 (2001).
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T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators – Part II: practical realization,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 382–385 (2001).
[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,” Nature Photon. 4, 711–715 (2010).
[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]

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M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[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,” Nature Photon. 2, 728–732 (2008).
[Crossref]

Vangel, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

Varanonuovo, M.

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

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A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications (NIST Special Publication 800-22, Revision 1a), National Institute of Standards and Technology (2010).

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R. C. Steele, G. R. Walker, and N. G. Walker, “Sensitivity of optically preamplified receivers with optical filtering,” IEEE Photon. Technol. Lett. 3, 545–547 (1991).
[Crossref]

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]

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.

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,” Nature Photon. 4, 711–715 (2010).
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P. Xu, Y. Wong, T. Horiuchi, and P. Abshire, “Compact floating-gate true random number generator,” Electron. Lett. 42, 1346 –1347 (2006).
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A. M. Ferrenberg, D. P. Landau, and Y. J. Wong, “Monte Carlo simulations: hidden errors from ‘good’ random number generators,” Phys. Rev. Lett. 69, 3382–3384 (1992).
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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,” Nature Photon. 2, 728–732 (2008).
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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,” Nature Photon. 2, 728–732 (2008).
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J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
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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).
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M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
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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,” Nature Photon. 2, 728–732 (2008).
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Figures (8)

Fig. 1
Fig. 1

Simplified block diagram of a spectrally-filtered ASE noise source. The input optical signal u(t) is assumed to be white optical noise with spectral density S0, which passes through a bandpass filter (HBP), square-law photodetector with responsivity ℛ, and low-pass filter (HLP) to produce an output photocurrent i(t).

Fig. 2
Fig. 2

System used to generate random bits at 12.5 Gb/s. Amplified spontaneous emission (ASE) is generated in an Er/Yb-doped fiber that is continuously pumped by a 1 W, fiber-coupled 915 nm semiconductor laser diode. The resulting broadband ASE spectrum is bandpass-filtered using a 14.5 GHz (0.1 nm) fiber Bragg grating and optical circulator. The filtered noise is amplified in a conventional Er-doped fiber amplifier (EDFA). A fiber polarization splitter is used to produce two independent, identically distributed optical noise signals that are separately detected in a pair of matched 11 GHz photoreceivers, each comprised of a photodiode (PD) and transimpedance amplifier (TIA). A 12.5 Gb/s bit error rate tester (BERT) is used to perform a clocked comparison of the two received signals, producing a random string of bits. Two variable attenuators (ATT1, ATT2) are used to control the power of the noise signal, and compensate for loss mismatch between the two arms.

Fig. 3
Fig. 3

(a) Optical spectrum of the amplified spontaneous emission produced by the Er/Yb fiber amplifier, measured with a resolution bandwidth (RBW) of 0.1 nm. The shaded band indicates the approximate region where the subsequent optical bandpass filter is located. (b) Reflection spectrum of the fiber-Bragg grating filter, measured using a tunable laser, circulator and power meter. The full-width at half-max (FWHM) bandwidth of the filter was measured to be 14.5 GHz (approximately 0.1 nm.)

Fig. 4
Fig. 4

(a) Electrical spectrum of the ASE-ASE beat noise after square-law detection, estimated by performing a self-convolution of the optical bandpass filter spectrum shown in Fig. 3(b). The spectrum is normalized relative to its DC value. (b) Measured electrical speed of the photoreceiver and transimpedance amplifer, which form an equivalent lowpass filter. (c) Electrical spectrum obtained from one polarization channel, measured directly from one photoreceiver using a resolution bandwidth (RBW) of 3 MHz. The signal exhibits a broad, flat noise spectrum with a (single-sided) bandwidth of 7.5 GHz. The dashed red line shows the spectral shape obtained by multiplying and scaling the curves from (a) and (b). The dotted black line indicates the electrical noise obtained by extinguishing the optical signal. Over the frequency range of interest, the electrical noise remains negligible in comparison to the optical noise arising from ASE.

Fig. 5
Fig. 5

Representative time traces and statistical histograms measured on a 20 GHz, 50 GS/s digital oscilloscope. The symbols on the time traces inticate the times at which the waveform would be sampled to produce random bits. (a) Single-polarization channel (b) orthogonal polarization channel and (c) differential signal obtained by subtracting two. The theoretical noise distribution shown by the solid curves in (a) and (b) is a best-fit gamma distribution with shape parameter a = 1.44 and scale parameter b = 0.21 V. The theoretical distribution shown in (c) was calculated by assuming that the two subtracted signals are independent and have identical gamma distributions as obtained in (a) and (b).

Fig. 6
Fig. 6

Normalized binary correlation as a function of lag (a) for the raw bit sequence produced by the experiment and (b) after computing the XOR with a 20-bit delayed copy of the signal. Positive correlation values are indicated with a filled symbol while negative correlations are indicated with open symbols. The correlation was calculated using a 109 bit record. For a truly random unbiased 109 bit record, one expects to obtain an average normalized correlation of 0 and a standard deviation of the correlation of 3.16 ×10−5 [31].

Fig. 7
Fig. 7

Summary of test results obtained from the NIST statistical test suite (STS-2.1) [32] applied to a 109 bit record obtained from the XORed data set. The NIST test suite comprises 15 types of tests, some of which return multiple results. (a) The composite p-values for each of the statistical tests and (b) the number of “failures” out of 1000 trials. For a truly random bit sequence, the p-values should be uniformly distributed on the interval [0,1], and the number of failures should follow binomial distribution with N = 1000 and α = 0.01. For tests that return multiple results, all composite p-values are plotted in (a), and (b) shows a gray-scale histogram reflecting the number of failures out of 1000*. The passing criteria are that all of the computed p-values must exceed 0.0001 and each test must yield between 1 and 19 failures out of 1000 trials. *The random excursions variant test is applied to only 561 records, and may have no more than 13 failures.

Fig. 8
Fig. 8

Summary of test results obtained from the Diehard test suite applied to a 74 × 106 bit record obtained from the XORed data set. For tests that return multiple p-values, all are shown. For tests that compute a composite p-value by applying the Kolmogorov-Smirnov (K-S) test, the resulting p-value is indicated in red. In order to pass the tests, all p-values (or, where appropriate, the composite K-S p-value) must exceed 0.0001.

Equations (14)

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| H BP ( f ) | 2 = exp [ ( 4 ln 2 ) ( f f 0 ) 2 B BP 2 ] , | H LP ( f ) | 2 = exp [ ( ln 2 ) f 2 B LP 2 ] ,
i = S 0 H LP ( 0 ) | H BP ( f ) | 2 df
= S 0 B BP π 4 ln 2 ( Gaussian ) ,
S i ( f ) = 2 S 0 2 | H LP ( f ) | 2 | H BP ( f ) H BP ( f + f ) | 2 df
= 2 S 0 2 B BP π 8 ln 2 exp [ ( ln 2 ) ( 1 B LP 2 + 2 B BP 2 ) f 2 ] ( Gaussian ) ,
B noise = ( 1 B LP 2 + 2 B BP 2 ) 1 / 2 ( Gaussian ) .
σ i 2 = S i ( f ) df = 2 S 0 2 | H LP ( f ) H BP ( f ) H BP ( f + f ) | 2 df df
= 2 S 0 2 B BP 2 ( π 4 ln 2 ) ( 1 + B BP 2 2 B LP 2 ) 1 / 2 ( Gaussian ) ,
p i ( x ) = x a 1 exp ( x / b ) b a Γ ( a ) , x > 0 ,
a = i 2 σ i 2 = H LP 2 ( 0 ) ( | H BP ( f ) | 2 d f ) 2 | H LP ( f ) H BP ( f ) H BP ( f + f ) | df df
= ( 1 + B BP 2 2 B LP 2 ) 1 / 2 ( Gaussian ) .
ρ k = b [ n ] b [ n + k ] b [ n ] 2 b 2 [ n ] b [ n ] 2 ,
p = 2 p ( 1 p ) , ρ k = ρ k ( 1 ρ ) ( 1 2 ρ + ρ k p ) .
y [ n ] = ( x [ n ] 9 x [ n 1 ] + 36 x [ n 2 ] 84 x [ n 3 ] + 126 x [ n 4 ] 126 x [ n 5 ] + 84 x [ n 6 ] 36 x [ n 7 ] + 9 x [ n 8 ] x [ n 9 ] ) & 0 x 000000 FF .

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