Abstract

We propose what we believe to be a new approach to nondeterministic random-number generation. The randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon statistics and that of photon number detections is used to generate random bit, and the von Neumann correction method is used to extract the final random bit. This method is proved to be bias free in randomness generation, provided that the single photon detections are mutually independent. Further, it has the advantage in fast random bit generation, since no postprocessing is needed. A true random-number generator based on this method is realized, and its randomness is tested and guaranteed using three statistical test batteries.

© 2009 Optical Society of America

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References

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  1. S. L. Lohr, Sampling: Design and Analysis (Duxbury, 1999).
  2. J. E. Gentle, Random Number Generation and Monte Carlo Methods (Statistics & Computing), 2nd ed. (Springer-Verlag, 2003).
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    [CrossRef]
  6. J. Walker, http://www.fourmilab.ch/hotbits/hardware3.html.
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    [CrossRef]
  8. M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
    [CrossRef]
  9. M. Stipčević and B. Medved Rogina, Rev. Sci. Instrum. 78, 045104 (2007).
    [CrossRef] [PubMed]
  10. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
    [CrossRef]
  11. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).
  12. U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).
  13. J. von Neumann, in Monte Carlo Method, National Bureau of Standards Applied Mathematics Series (1951), Vol. 12, pp. 36-38.
  14. Y. Peres, Ann. Stat. 20, 590 (1992).
    [CrossRef]
  15. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
    [CrossRef]
  16. J. Walker, http://www.fourmilab.ch/random/.
  17. G. Marsaglia, http://www.stat.fsu.edu/pub/diehard/.
  18. NIST, http://csrc.nist.gov/rng/.

2008

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

2007

M. Stipčević and B. Medved Rogina, Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

2005

M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Cambridge U. Press, 2005).

2003

J. E. Gentle, Random Number Generation and Monte Carlo Methods (Statistics & Computing), 2nd ed. (Springer-Verlag, 2003).

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

2002

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

1999

S. L. Lohr, Sampling: Design and Analysis (Duxbury, 1999).

1997

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl. 44, 521 (1997).
[CrossRef]

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).

1994

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

1992

Y. Peres, Ann. Stat. 20, 590 (1992).
[CrossRef]

1951

J. von Neumann, in Monte Carlo Method, National Bureau of Standards Applied Mathematics Series (1951), Vol. 12, pp. 36-38.

Bucci, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

Connelly, J. A.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl. 44, 521 (1997).
[CrossRef]

Dowlatabadi, A. B.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl. 44, 521 (1997).
[CrossRef]

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Gentle, J. E.

J. E. Gentle, Random Number Generation and Monte Carlo Methods (Statistics & Computing), 2nd ed. (Springer-Verlag, 2003).

Germani, L.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

Guinnard, O.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

Holman, W. T.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl. 44, 521 (1997).
[CrossRef]

Leonhardt, U.

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).

Lohr, S. L.

S. L. Lohr, Sampling: Design and Analysis (Duxbury, 1999).

Luzzi, R.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

Marsaglia, G.

G. Marsaglia, http://www.stat.fsu.edu/pub/diehard/.

Medved Rogina, B.

M. Stipčević and B. Medved Rogina, Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Menezes, A. J.

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

Mitzenmacher, M.

M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Cambridge U. Press, 2005).

Peres, Y.

Y. Peres, Ann. Stat. 20, 590 (1992).
[CrossRef]

Ribordy, G.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Stipcevic, M.

M. Stipčević and B. Medved Rogina, Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Stucki, D.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Trifiletti, A.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

Upfal, E.

M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Cambridge U. Press, 2005).

van Oorschot, P. C.

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).

Vanstone, S. A.

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).

Varanonuovo, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

von Neumann, J.

J. von Neumann, in Monte Carlo Method, National Bureau of Standards Applied Mathematics Series (1951), Vol. 12, pp. 36-38.

Walker, J.

J. Walker, http://www.fourmilab.ch/hotbits/hardware3.html.

J. Walker, http://www.fourmilab.ch/random/.

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Zbinden, H.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Ann. Stat.

Y. Peres, Ann. Stat. 20, 590 (1992).
[CrossRef]

Appl. Phys. Lett.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, IEEE Trans. Circuits and Syst., I: Fundam. Theory Appl. 44, 521 (1997).
[CrossRef]

IEEE Trans. Comput.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, IEEE Trans. Comput. 52, 403 (2003).
[CrossRef]

New J. Phys.

D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, New J. Phys. 4, 41 (2002).
[CrossRef]

Rev. Mod. Phys.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).
[CrossRef]

Rev. Sci. Instrum.

M. Stipčević and B. Medved Rogina, Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Other

J. Walker, http://www.fourmilab.ch/hotbits/hardware3.html.

S. L. Lohr, Sampling: Design and Analysis (Duxbury, 1999).

J. E. Gentle, Random Number Generation and Monte Carlo Methods (Statistics & Computing), 2nd ed. (Springer-Verlag, 2003).

M. Mitzenmacher and E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Cambridge U. Press, 2005).

A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).

J. Walker, http://www.fourmilab.ch/random/.

G. Marsaglia, http://www.stat.fsu.edu/pub/diehard/.

NIST, http://csrc.nist.gov/rng/.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).

J. von Neumann, in Monte Carlo Method, National Bureau of Standards Applied Mathematics Series (1951), Vol. 12, pp. 36-38.

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Figures (4)

Fig. 1
Fig. 1

Schematic experiment setup of our TRNG. FA, flexible attenuator. 1, bit 1. 0, bit 0. N, not used.

Fig. 2
Fig. 2

Random-bit efficiency η TRNG as a function of η λ . η, detection efficiency of SPD; λ, mean photon number of each laser pulse.

Fig. 3
Fig. 3

Results of DIEHARD. All tests are passed at lower (upper) significance level of 0.01 (0.99).

Fig. 4
Fig. 4

Results of STS. All tests are passed at the significance level of 0.01.

Equations (2)

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P ( 1 ) = P ( 0 ) = P η ( n > 0 ) P η ( n = 0 ) = e η λ ( 1 e η λ ) .
η TRNG = P ( 1 ) + P ( 0 ) 2 = e η λ ( 1 e η λ ) .

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