Abstract

We propose an approach to generate true random number sequences based on the discretized encoding of the time interval between photons. The method is simple and efficient, and can produce a highly random sequence several times longer than that of other methods based on threshold or parity selection, without the need for hashing. A proof-of-principle experiment has been performed, showing that the system could be easily integrated and applied to quantum cryptography and other fields.

© 2012 Optical Society of America

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References

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  1. A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography (CRC, 1997).
  2. P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
    [CrossRef]
  3. S. L. Lohr, Sampling: Design and Analysis (Duxbury, 1999).
  4. J. E. Gentle, Random Number Generation and Monte Carlo Methods (Statistics & Computing), 2nd ed. (Springer-Verlag, 2003).
  5. G. S. Fishman, Principles of Discrete Event Simulation (Wiley, 1978).
  6. R. Y. Rubenstein, Simulation and the Monte Carlo Method(Wiley, 1981).
  7. J. Walker, “HotBits Hardware,” http://www.fourmilab.ch/hotbits/hardware3.html .
  8. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
    [CrossRef]
  9. D. Davis, R. Ihaka, and P. R. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” in Proceedings of Advances in Cryptology—CRYPTO’94 Conference, Yvo G. Desmedt, ed. Lecture Notes in Computer Science 839(Springer-Verlag, 1994), pp. 114–120.
  10. C. H. Vincent, “The generation of truly random binary number,” J. Phys. E 3, 594–598 (1970).
    [CrossRef]
  11. G. Agnew, “Random source for cryptographic systems,” in Advances in Cryptology CRYPTO’85 (Springer, 1986), pp. 77–81.
  12. C. S. Wallace, “Physically random generator,” Comput. Syst. Sci. Eng. 5, 82–88 (1990).
  13. W. Dultz and E. Hildebrandt, “Optical Random-Check Generator based on the individual photon statistics at the optical beamsplitter,” PCT Patent No. WO 98/16008 (16April1998).
  14. J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
    [CrossRef]
  15. C. Gabriel, C. Wittmann, D. Sych, R. F. 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]
  16. A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).
    [CrossRef]
  17. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1679 (2000).
    [CrossRef]
  18. J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).
  19. M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).
  20. H. Q. Ma, Y. J. Xie, and L. A. Wu, “Random number generation based on the time of arrival of single photons,” Appl. Opt. 44, 7760–7763 (2005).
    [CrossRef]
  21. H. Guo, W. Z. 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]
  22. J. Walker, “ENT_A Pseudorandom Number Sequence Test Program,” http://www.fourmilab.ch/random .

2012

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

2010

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

H. Guo, W. Z. 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]

2005

2003

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

2001

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

2000

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (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, 1675–1679 (2000).
[CrossRef]

1997

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

1994

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[CrossRef]

1990

C. S. Wallace, “Physically random generator,” Comput. Syst. Sci. Eng. 5, 82–88 (1990).

1970

C. H. Vincent, “The generation of truly random binary number,” J. Phys. E 3, 594–598 (1970).
[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, 1675–1679 (2000).
[CrossRef]

Agnew, G.

G. Agnew, “Random source for cryptographic systems,” in Advances in Cryptology CRYPTO’85 (Springer, 1986), pp. 77–81.

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Andersson, E.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

Buller, G. S.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

Clarke, P. J.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

Collins, R. J.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[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 44, 521–528 (1997).
[CrossRef]

Davis, D.

D. Davis, R. Ihaka, and P. R. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” in Proceedings of Advances in Cryptology—CRYPTO’94 Conference, Yvo G. Desmedt, ed. Lecture Notes in Computer Science 839(Springer-Verlag, 1994), pp. 114–120.

Ding, L. E.

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

Dong, R. F.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

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 44, 521–528 (1997).
[CrossRef]

Dultz, W.

W. Dultz and E. Hildebrandt, “Optical Random-Check Generator based on the individual photon statistics at the optical beamsplitter,” PCT Patent No. WO 98/16008 (16April1998).

Dunjko, V.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

Feng, M. M.

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

Fenstermacher, P. R.

D. Davis, R. Ihaka, and P. R. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” in Proceedings of Advances in Cryptology—CRYPTO’94 Conference, Yvo G. Desmedt, ed. Lecture Notes in Computer Science 839(Springer-Verlag, 1994), pp. 114–120.

Fishman, G. S.

G. S. Fishman, Principles of Discrete Event Simulation (Wiley, 1978).

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Gentle, J. E.

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

Gisin, N.

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

Guinnard, L.

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

Guo, H.

H. Guo, W. Z. 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]

Hildebrandt, E.

W. Dultz and E. Hildebrandt, “Optical Random-Check Generator based on the individual photon statistics at the optical beamsplitter,” PCT Patent No. WO 98/16008 (16April1998).

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 44, 521–528 (1997).
[CrossRef]

Ihaka, R.

D. Davis, R. Ihaka, and P. R. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” in Proceedings of Advances in Cryptology—CRYPTO’94 Conference, Yvo G. Desmedt, ed. Lecture Notes in Computer Science 839(Springer-Verlag, 1994), pp. 114–120.

Jeffers, J.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[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, 1675–1679 (2000).
[CrossRef]

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Liang, C.

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

Liao, J.

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

Liu, Y.

H. Guo, W. Z. 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]

Lohr, S. L.

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

Ma, H. Q.

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Menezes, A. J.

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

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, 2435–2444 (1994).
[CrossRef]

Pan, S. H.

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

Qin, X. L.

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

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, 2435–2444 (1994).
[CrossRef]

Rubenstein, R. Y.

R. Y. Rubenstein, Simulation and the Monte Carlo Method(Wiley, 1981).

Stefanov, A.

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

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Tang, W. Z.

H. Guo, W. Z. 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.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[CrossRef]

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).

Vincent, C. H.

C. H. Vincent, “The generation of truly random binary number,” J. Phys. E 3, 594–598 (1970).
[CrossRef]

Wallace, C. S.

C. S. Wallace, “Physically random generator,” Comput. Syst. Sci. Eng. 5, 82–88 (1990).

Wei, W.

H. Guo, W. Z. 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]

Wei, Y. J.

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

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, 1675–1679 (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, 1675–1679 (2000).
[CrossRef]

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Wu, L. A.

H. Q. Ma, Y. J. Xie, and L. A. Wu, “Random number generation based on the time of arrival of single photons,” Appl. Opt. 44, 7760–7763 (2005).
[CrossRef]

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

Xie, Y. J.

Xiong, L.

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

Yao, D. C.

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

Zbinden, H.

A. Stefanov, N. Gisin, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).
[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, 1675–1679 (2000).
[CrossRef]

Zhou, C. Y.

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

Acta Phys. Sinica

J. Liao, C. Liang, Y. J. Wei, L. A. Wu, S. H. Pan, and D. C. Yao, “True random number generator based on a photon beamsplitter,” Acta Phys. Sinica 50, 467–472 (2001) (in Chinese).

M. M. Feng, X. L. Qin, C. Y. Zhou, L. Xiong, and L. E. Ding, “Quantum random number generator based on polarization,” Acta Phys. Sinica 52, 72–76 (2003) (in Chinese).

Appl. Opt.

Comput. Syst. Sci. Eng.

C. S. Wallace, “Physically random generator,” Comput. Syst. Sci. Eng. 5, 82–88 (1990).

IEEE Trans. Circuits Syst. I

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

J. Mod. Opt.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[CrossRef]

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

J. Phys. E

C. H. Vincent, “The generation of truly random binary number,” J. Phys. E 3, 594–598 (1970).
[CrossRef]

Nat. Commun.

P. J. Clarke, R. J. Collins, V. Dunjko, E. Andersson, J. Jeffers, and G. S. Buller, “Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light,” Nat. Commun. 3, 1174 (2012).
[CrossRef]

Nat. Photonics

C. Gabriel, C. Wittmann, D. Sych, R. F. 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]

Phys. Rev. E

H. Guo, W. Z. 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. 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, 1675–1679 (2000).
[CrossRef]

Other

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

J. Walker, “ENT_A Pseudorandom Number Sequence Test Program,” http://www.fourmilab.ch/random .

W. Dultz and E. Hildebrandt, “Optical Random-Check Generator based on the individual photon statistics at the optical beamsplitter,” PCT Patent No. WO 98/16008 (16April1998).

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).

G. S. Fishman, Principles of Discrete Event Simulation (Wiley, 1978).

R. Y. Rubenstein, Simulation and the Monte Carlo Method(Wiley, 1981).

J. Walker, “HotBits Hardware,” http://www.fourmilab.ch/hotbits/hardware3.html .

G. Agnew, “Random source for cryptographic systems,” in Advances in Cryptology CRYPTO’85 (Springer, 1986), pp. 77–81.

D. Davis, R. Ihaka, and P. R. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” in Proceedings of Advances in Cryptology—CRYPTO’94 Conference, Yvo G. Desmedt, ed. Lecture Notes in Computer Science 839(Springer-Verlag, 1994), pp. 114–120.

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Figures (6)

Fig. 1.
Fig. 1.

Block diagram of the scheme. TAC: time-to-amplitude converter.

Fig. 2.
Fig. 2.

Probability distribution of the time interval between two consecutive photons.

Fig. 3.
Fig. 3.

Probability distribution of the DC voltage corresponding to different time intervals.

Fig. 4.
Fig. 4.

Partitioning of the voltage values for n=2.

Fig. 5.
Fig. 5.

Experimental setup for the TRN generation. SFG, signal function generator; LD, 1310 nm semiconductor laser; ATT, attenuator; BS, 50/50 beamsplitter; SPD1 and SPD2, single-photon detectors; DG1 and DG2, delay generators; TAC: time-to-amplitude converter; DAQ: data acquisition.

Fig. 6.
Fig. 6.

Time sequence of the TRN generator.

Tables (2)

Tables Icon

Table 1. ENT Test Results for n=4

Tables Icon

Table 2. ENT Test Results for n=2, 5, and 6

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Pn=μneμ/n!,
P0=eμ1μ+μ22.
P1=μeμ,
Pn2=1P0P1=1eμ(1+μ).
P(T)=P1P0T1,
0V1P(V)dV=V1V2P(V)dV==V2n1+P(V)dV=12n,
2nTr/Tc,

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