Abstract

We describe an optoelectronic system for simultaneously generating parallel, independent streams of random bits using spectrally separated noise signals obtained from a single optical source. Using a pair of nonoverlapping spectral filters and a fiber-coupled superluminescent LED (SLED), we produced two independent 10Gb/s random bit streams, for a cumulative generation rate of 20Gb/s. The system relies principally on chip-based optoelectronic components that could be integrated in a compact, economical package.

© 2011 Optical Society of America

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References

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  1. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
    [CrossRef]
  2. 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, Nat. Photon. 2, 728 (2008).
    [CrossRef]
  3. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, Opt. Lett. 35, 312 (2010).
    [CrossRef] [PubMed]
  4. H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
    [CrossRef]
  5. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, Opt. Express 18, 18763 (2010).
    [CrossRef] [PubMed]
  6. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
    [CrossRef]
  7. C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
    [CrossRef]
  8. Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
    [CrossRef]
  9. C. R. S. Williams, J. C. Salevan, X.-W. Li, R. Roy, and T. E. Murphy, Opt. Express 18, 23584 (2010).
    [CrossRef] [PubMed]
  10. M. Mascagni and A. Srinivasan, ACM Trans. Math. Softw. 26, 436 (2000).
    [CrossRef]
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    [CrossRef]
  12. P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
    [CrossRef]
  13. J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  15. F. Devos, P. Garda, and P. Chavel, Opt. Lett. 12, 152 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).
  18. A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
    [CrossRef]

2010 (7)

B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, Opt. Lett. 35, 312 (2010).
[CrossRef] [PubMed]

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, Opt. Express 18, 18763 (2010).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
[CrossRef]

C. R. S. Williams, J. C. Salevan, X.-W. Li, R. Roy, and T. E. Murphy, Opt. Express 18, 23584 (2010).
[CrossRef] [PubMed]

2008 (1)

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

2003 (1)

A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
[CrossRef]

2001 (1)

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

2000 (2)

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

M. Mascagni and A. Srinivasan, ACM Trans. Math. Softw. 26, 436 (2000).
[CrossRef]

1989 (1)

P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
[CrossRef]

1987 (1)

1986 (2)

Achleitner, U.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Ackermann, J.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Argyris, A.

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Bödekker, B.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

Bogris, A.

Breyer, J.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

Card, H.

P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
[CrossRef]

Ceperley, D.

A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
[CrossRef]

Chavel, P.

Chi, Y.-M.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-Interscience, 1991).
[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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Deligiannidis, S.

Devos, F.

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Garda, P.

Guo, H.

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Hortensius, P.

P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
[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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Jennewein, T.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Li, X.-W.

Liu, Y.

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Lo, H.-K.

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Marron, J.

Martino, A. J.

Mascagni, M.

A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
[CrossRef]

M. Mascagni and A. Srinivasan, ACM Trans. Math. Softw. 26, 436 (2000).
[CrossRef]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

McCaskill, J. S.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

McLeod, R.

P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
[CrossRef]

Morris, G. M.

Murphy, T. E.

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, Nat. Photon. 2, 728 (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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Pikasis, E.

Qi, B.

Qian, L.

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

Roy, R.

Rukhin, 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Salevan, J. C.

Shen, Y.

Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
[CrossRef]

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Smid, 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Soto, 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Srinivasan, A.

A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
[CrossRef]

M. Mascagni and A. Srinivasan, ACM Trans. Math. Softw. 26, 436 (2000).
[CrossRef]

Stoll, E.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Syvridis, D.

Tang, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Tangen, U.

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-Interscience, 1991).
[CrossRef]

Tian, L.

Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
[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, Nat. Photon. 2, 728 (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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Vo, 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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

Wei, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Weihs, G.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Weinfurter, H.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Williams, C. R. S.

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[CrossRef]

Wolfram, S.

S. Wolfram, Adv. Appl. Math. 7, 123 (1986).
[CrossRef]

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, Nat. Photon. 2, 728 (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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Zeilinger, A.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Zou, H.

Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
[CrossRef]

ACM Trans. Math. Softw. (1)

M. Mascagni and A. Srinivasan, ACM Trans. Math. Softw. 26, 436 (2000).
[CrossRef]

Adv. Appl. Math. (1)

S. Wolfram, Adv. Appl. Math. 7, 123 (1986).
[CrossRef]

Appl. Opt. (1)

Comput. Phys. Commun. (1)

J. Ackermann, U. Tangen, B. Bödekker, J. Breyer, E. Stoll, and J. S. McCaskill, Comput. Phys. Commun. 140, 293 (2001).
[CrossRef]

IEEE Trans. Comput. (1)

P. Hortensius, R. McLeod, and H. Card, IEEE Trans. Comput. 38, 1466 (1989).
[CrossRef]

Nat. Photon. (3)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, Nat. Photon. 4, 58 (2010).
[CrossRef]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, Nat. Photon. 4, 711 (2010).
[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, Nat. Photon. 2, 728 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Parallel Comput. (1)

A. Srinivasan, M. Mascagni, and D. Ceperley, Parallel Comput. 29, 69 (2003).
[CrossRef]

Phys. Rev. A (1)

Y. Shen, L. Tian, and H. Zou, Phys. Rev. A 81, 063814 (2010).
[CrossRef]

Phys. Rev. E (1)

H. Guo, W. Tang, Y. Liu, and W. Wei, Phys. Rev. E 81, 051137 (2010).
[CrossRef]

Rev. Sci. Instrum. (1)

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Other (2)

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-Interscience, 1991).
[CrossRef]

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,” National Institute of Standards and Technology (NIST) Special Publication 800-22, Revision 1a (NIST, 2010).

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Figures (4)

Fig. 1
Fig. 1

Optoelectronic system used to generate parallel random bit sequences. A SLED is spectrally sliced into multiple channels, each of which is detected with a 11 GHz photodiode and transimpedance amplifier. A variable delay ( τ ) and attenuator are used to equalize the time delay and power between the channels. The resulting signals are threshold detected using clocked comparators to simultaneously produce parallel independent binary sequences x [ n ] and y [ n ] . PD, photodiode; TIA, transimpedance amplifier; ATT, attenuator.

Fig. 2
Fig. 2

(a) Optical spectra of the SLED and the two spectrally sliced channels measured with a resolution bandwidth of 0.1 nm . (b) Electrical spectrum of the optical noise measured directly from one photoreceiver and the electrical background noise obtained by extinguishing the optical input signal. Both spectra were measured with a resolution bandwidth of 3 MHz .

Fig. 3
Fig. 3

(a) Representative bitmap images constructed from the two data channels x [ n ] and y [ n ] . The third panel shows the XOR between the two channels, x [ n ] y [ n ] , which exhibits no apparent bias, pattern, or correlation with the original sequences. (b) Statistically computed absolute correlation | ρ x y | and mutual information I x y [ k ] between the two 10 9 bit sequences x [ n ] and y [ n + k ] as a function of the relative delay k. The solid line shows the theoretical median level one would expect for two independent, unbiased 10 9 bit sequences.

Fig. 4
Fig. 4

Summary of the NIST test results. (a) Composite p value obtained for each of the 188 statistical tests. (b) Gray-scale histogram reflecting the number of failures out of 1000 trials.

Equations (2)

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ρ x y [ k ] = x y x y ( x 2 x 2 ) ( y 2 y 2 ) ,
I x y [ k ] = x ¯ y ¯ log 2 ( x ¯ y ¯ x ¯ y ¯ ) + x ¯ y log 2 ( x ¯ y x ¯ y ) + x y ¯ log 2 ( x y ¯ x y ¯ ) + x y log 2 ( x y x y ) ,

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