Abstract

We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators.

© 2010 Optical Society of America

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  1. “Ais 20: Functionality classes and evaluation methodology for deterministic random number generators, v2.0, bsi,” https://www.bsi.bund.de/cae/servlet/contentblob/478150/publicationFile/30276/ais20pdf.pdf (1999).
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    [CrossRef]
  4. W. Killmann, and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect. Notes Comput. Sci. 5154, 146–163 (2008).
    [CrossRef]
  5. B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).
  6. 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]
  7. A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).
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    [CrossRef]
  9. 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]
  10. 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]
  11. M. Stipcevic, and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
    [CrossRef] [PubMed]
  12. S. Tisa, and F. Zappa, “One-chip quantum random number generator,” Proc. SPIE 7236, 72360J (2009).
    [CrossRef]
  13. 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]
  14. P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
    [CrossRef]
  15. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).
  16. “Ais 31: Functionality classes and evaluation methodology for physical random number generators. v1.0,” (2001).
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    [CrossRef]
  20. J. Soto, “Statistical testing of random number generators,” Proc. 22nd National Information Systems Security Conference (1999).
  21. R. G. Brown, “Dieharder test suite,” http://www.phy.duke.edu/ rgb/General/dieharder.php (2009).
  22. J. Kim, and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
    [CrossRef]
  23. P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
    [CrossRef]
  24. R. Loudon, The quantum theory of light (Oxford University Press, 2000), third edition ed.
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    [CrossRef]
  26. A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
    [CrossRef]
  27. K. Omote, “Dead time effects in photon-counting distributions,” Nucl. Instrum. Methods 293, 582–588 (1990).
    [CrossRef]
  28. J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl. Instrum. Methods 117, 401–404 (1974).
    [CrossRef]
  29. D. E. Knuth, The Art of Computer Programming II (Addison-Wesley, 1998).
  30. N. H. Kuiper, ““Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet,” A 63, 38–47 (1962).

2010 (1)

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

2009 (4)

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[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]

S. Tisa, and F. Zappa, “One-chip quantum random number generator,” Proc. SPIE 7236, 72360J (2009).
[CrossRef]

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]

2008 (2)

W. Killmann, and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect. Notes Comput. Sci. 5154, 146–163 (2008).
[CrossRef]

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]

2007 (1)

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

2006 (1)

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

2000 (3)

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

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

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]

1997 (1)

J. Kim, and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

1994 (1)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

1990 (1)

K. Omote, “Dead time effects in photon-counting distributions,” Nucl. Instrum. Methods 293, 582–588 (1990).
[CrossRef]

1987 (1)

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

1983 (1)

R. Short, and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett. 51, 384 (1983).
[CrossRef]

1974 (1)

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl. Instrum. Methods 117, 401–404 (1974).
[CrossRef]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

1962 (1)

N. H. Kuiper, ““Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet,” A 63, 38–47 (1962).

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]

Aviad, Y.

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]

Bennet, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

Cho, Y.-W.

Connelly, J.

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

Dixon, A. R.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

Dynes, J. F.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

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]

Gisin, N.

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

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Guinnard, L.

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

Guinnard, O.

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

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]

Kanter, I.

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]

Killmann, W.

W. Killmann, and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect. Notes Comput. Sci. 5154, 146–163 (2008).
[CrossRef]

Kim, J.

J. Kim, and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Kim, Y.-H.

Kuiper, N. H.

N. H. Kuiper, ““Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet,” A 63, 38–47 (1962).

Kwon, O.

Li, Y.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

Long, G.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

Mandel, L.

R. Short, and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett. 51, 384 (1983).
[CrossRef]

Mueller, J. W.

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl. Instrum. Methods 117, 401–404 (1974).
[CrossRef]

Omote, K.

K. Omote, “Dead time effects in photon-counting distributions,” Nucl. Instrum. Methods 293, 582–588 (1990).
[CrossRef]

Owens, P. C. M.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

Petrie, C.

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

Prionio, S.

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

Rarity, J. G.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Reidler, I.

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]

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]

Rosenbluh, M.

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]

Satchell, J. S.

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Schindler, W.

W. Killmann, and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect. Notes Comput. Sci. 5154, 146–163 (2008).
[CrossRef]

Sharpe, A. W.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

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]

Shields, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

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]

Short, R.

R. Short, and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett. 51, 384 (1983).
[CrossRef]

Stefanov, A.

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

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]

Tapster, P. R.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

Tisa, S.

S. Tisa, and F. Zappa, “One-chip quantum random number generator,” Proc. SPIE 7236, 72360J (2009).
[CrossRef]

Wang, P.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[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]

Yamamoto, Y.

J. Kim, and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Yuan, Z. L.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

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]

Zappa, F.

S. Tisa, and F. Zappa, “One-chip quantum random number generator,” Proc. SPIE 7236, 72360J (2009).
[CrossRef]

Zbinden, H.

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

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]

A (1)

N. H. Kuiper, ““Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet,” A 63, 38–47 (1962).

Appl. Opt. (1)

Appl. Phys. Lett. (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. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

Europhys. Lett. (1)

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” Europhys. Lett. 4, 293–299 (1987).
[CrossRef]

IEEE Trans. Circ. Syst. I Fundam. Theory Appl. (1)

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

J. Appl. Phys. (1)

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

J. Mod. Opt. (2)

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

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

Lect. Notes Comput. Sci. (1)

W. Killmann, and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect. Notes Comput. Sci. 5154, 146–163 (2008).
[CrossRef]

Nature (1)

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

Nucl. Instrum. Methods (2)

K. Omote, “Dead time effects in photon-counting distributions,” Nucl. Instrum. Methods 293, 582–588 (1990).
[CrossRef]

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl. Instrum. Methods 117, 401–404 (1974).
[CrossRef]

Phys. Rev. (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Phys. Rev. B (1)

J. Kim, and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

R. Short, and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett. 51, 384 (1983).
[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]

Proc. SPIE (1)

S. Tisa, and F. Zappa, “One-chip quantum random number generator,” Proc. SPIE 7236, 72360J (2009).
[CrossRef]

Rev. Sci. Instrum. (2)

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

Other (10)

A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).

B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).

“Ais 20: Functionality classes and evaluation methodology for deterministic random number generators, v2.0, bsi,” https://www.bsi.bund.de/cae/servlet/contentblob/478150/publicationFile/30276/ais20pdf.pdf (1999).

“Fips 140-2, security requirements for cryptographic modules, nist,” http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf (2001).

J. Soto, “Statistical testing of random number generators,” Proc. 22nd National Information Systems Security Conference (1999).

R. G. Brown, “Dieharder test suite,” http://www.phy.duke.edu/ rgb/General/dieharder.php (2009).

“Ais 31: Functionality classes and evaluation methodology for physical random number generators. v1.0,” (2001).

W. Killmann andW. Schindler, “A proposal for: Functionality classes and evaluation methodology for true (physical) random number generators (v3.1).” https://www.bsi.bund.de/cae/servlet/contentblob/ 478134/publication-File/30230/trngk31e pdf.pdf (2001).

D. E. Knuth, The Art of Computer Programming II (Addison-Wesley, 1998).

R. Loudon, The quantum theory of light (Oxford University Press, 2000), third edition ed.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the setup (left) and picture of the fully integrated quantum random number generator (right). The main components are a light emitting diode (LED) mounted on the entrance window of a photomultiplier tube (PMT). The electrical pulses from the PMT are amplified (AMP) and fed into a threshold discriminator (ST). The signals are counted and processed by the FPGA, the resulting random bits are transferred to a PC via a USB connection. The total dimension of the housing is 22x16x8 cm3.

Fig. 2.
Fig. 2.

Normalized distributions of detected photon numbers (calculated). The black line shows the distribution for a Poisson process with mean µ = 4.8, i.e. without considering dead time effects. The red graph shows the expected distribution for an (extendable) dead time of the PMT of τd = 2.7 ns and a sampling interval of τs = 20 ns. This results in a strongly modified distribution, now with a mean µr = 2.51 (see text). Lines are guide to the eyes. The inset exhibits the origin of the extendable dead time, where overlapping PMT pulses are not resolved anymore by the threshold electronics.

Fig. 3.
Fig. 3.

Comparison between the dependency of the modulus of the bias of a random bit string on the detected mean photon number for an ideal Poisson process and for a process with extendable dead time. For this plot the dead time was chosen to be τd = 2.7 ns and the sampling frequency to be τs = 20 ns. The inset is a linear plot of the region of interest.

Fig. 4.
Fig. 4.

Measurement of the bias depending on the mean number of detected photons (a). Each data point is obtained from an 8 Gbit bit string for three different sampling times. Serial correlation coefficient SCCl of a single 40 Gbit string, collected with a sampling time of τs = 20 ns and a mean photon number of µr = 1.41, as a function of the bit distance (b). The statistical error levels shown in the plots are the 3-σ variance of the bias b or the SCCl to be expected for an ideal random bit sequence with finite sample length.

Fig. 5.
Fig. 5.

Typical results of the standard statistical test suites STS (a) and Dieharder(b) for a typical sequence of 40 Gbit. Without processing, the p-values are routinely above the significance level confirming the quality and the reliability of the QRNG

Equations (3)

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P ( n , μ ) = μ n n ! e μ .
P ( n , μ r ) = μ r n n ! e μ r · Poisson Σ k = 0 K n ( μ r ) k k ! e μ r · ( ( 1 ( k + n 1 ) τ d τ s ) ) n + k extendable dead time modification ,
b = 1 2 p 1 = 1 2 Σ n = 1 , 3 , . . . P ( n , μ ) .

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