Abstract

We present a first random number generator (RNG) which simultaneously uses independent spatial and temporal quantum randomness contained in an optical system. Availability of the two independent sources of entropy makes the RNG resilient to hardware failure and signal injection attacks. We show that the deviation from randomness of the generated numbers can be estimated quickly from simple measurements thus eliminating the need for usual time-consuming statistical testing of the output data. As a confirmation it is demonstrated that generated numbers pass NIST Statistical test suite.

© 2015 Optical Society of America

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References

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  1. P. Hellekalek, “Good random number generators are (not so) easy to find,” Math. Comput. Simul. 46(5-6), 485–505 (1998).
    [Crossref]
  2. I. Goldberg, and D. Wagner, “Randomness in the Netscape Browser,” Dr. Dobb's, January (1996).
  3. T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
    [Crossref] [PubMed]
  4. A. Proykova, “How to improve a random number generator,” Comput. Phys. Commun. 124(2-3), 125–131 (2000).
    [Crossref]
  5. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).
  6. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A Fast and Compact Quantum Random Number Generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
    [Crossref]
  7. A. Figotin, A. Y. Gordon, S. A. Molchanov, V. P. Popovich, J. E. Quinn, G. N. Stetsenko, N. M. Stravrakas, and I. M. Vitebskiy, “A random number generator based on spontaneous alpha-decay,” PCT application WO0038037A1 (2000).
  8. M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
    [Crossref]
  9. M. Stipcević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
    [Crossref] [PubMed]
  10. J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
    [Crossref]
  11. R. Davies, “Exclusive OR (XOR) and hardware random number generators,” February 28, 2002, URL: http://www.robertnz.net/pdf/xor2.pdf
  12. J. von Neumann, Various techniques for use in connection with random digits,” von Neumann Collected Works, Vol. 5, Pergamon, 768–770 (1963).
  13. M. Stipčević and D. J. Gauthier, “Precise Monte Carlo Simulation of Single-Photon Detectors,” Proc. SPIE Defense, Security and Sensing, 29 April - 3 May 2013, Baltimore, Maryland, USA, also appear as http://arXiv:1411.3663v1 [quant-ph].
  14. D. E. Knuth, The art of computer programming, Vol. 2, Third edition, (Addison-Wesley, Reading, 1997).
  15. R. Shaltiel, “Recent developments in explicit constructions of extractors,” Bull. EATCS 77, 67–95 (2002).
  16. R. Shaltiel, “How to get more mileage from randomness extractors,” Random Structures Algorithms 33(2), 157–186 (2008).
    [Crossref]
  17. B. Chor, O. Goldreich, J. Hasted, J. Freidmann, S. Rudich, and R. Smolensky, “The bit extraction problem or t-resilient functions,” 26th Annual Symposium on Foundations of Computer Science (FOCS), 396–407, IEEE (1985).
    [Crossref]
  18. P. Lacharme, “Analysis and Construction of Correctors,” IEEE Trans. Inf. Theory 55(10), 4742–4748 (2009).
    [Crossref]
  19. R. Davies, Statistics Research Associates Limited, 8 Bristol Street, Island Bay, Wellington, 6023, New Zealand (private communication 2013/2014).
  20. 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 the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications,” NIST Special Publication 800–22rev1a (dated April 2010). URL: http://csrc.nist.gov/groups/ST/toolkit/rng/documents/sts-2.1.1.zip
  21. A. Theodore Markettos and W. Simon, Moore. 2009. “The Frequency Injection Attack on Ring-Oscillator-Based True Random Number Generators,” Proc. 11th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '09), Christophe Clavier and Kris Gaj (Eds.). Springer-Verlag, Berlin, Heidelberg, 317–331 (2009).
  22. P. Bayon, L. Bossuet, A. Aubert, V. Fischer, F. Poucheret, B. Robisson, and P. Maurine, “Contactless electromagnetic active attack on ring oscillator based true random number generator,” Proc. Third international conference on Constructive Side-Channel Analysis and Secure Design (COSADE'12), Werner Schindler and Sorin A. Huss (Eds.). Springer-Verlag, Berlin, Heidelberg (2012).
    [Crossref]
  23. M. Dichtl and J. D. Golic, “High-speed true random number generation with logic gates only,” in 1248 Cryptographic Hardware and Embedded Systems (CHES), ed. by P. Paillier, I. Verbauwhede 1249 (Springer, Berlin, 2007), 45–62.
  24. 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,” Nat. Photonics 2(12), 728–732 (2008).
    [Crossref]
  25. D. Frauchiger, R. Renner, and M. Troyer, “True randomness from realistic quantum devices,” http://arXiv:1311.4547 [quant-ph].

2011 (1)

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
[Crossref] [PubMed]

2009 (2)

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

P. Lacharme, “Analysis and Construction of Correctors,” IEEE Trans. Inf. Theory 55(10), 4742–4748 (2009).
[Crossref]

2008 (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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

R. Shaltiel, “How to get more mileage from randomness extractors,” Random Structures Algorithms 33(2), 157–186 (2008).
[Crossref]

2007 (1)

M. Stipcević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

2002 (1)

R. Shaltiel, “Recent developments in explicit constructions of extractors,” Bull. EATCS 77, 67–95 (2002).

2000 (3)

A. Proykova, “How to improve a random number generator,” Comput. Phys. Commun. 124(2-3), 125–131 (2000).
[Crossref]

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

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A Fast and Compact Quantum Random Number Generator,” Rev. Sci. Instrum. 71(4), 1675–1680 (2000).
[Crossref]

1998 (1)

P. Hellekalek, “Good random number generators are (not so) easy to find,” Math. Comput. Simul. 46(5-6), 485–505 (1998).
[Crossref]

1994 (1)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[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(4), 1675–1680 (2000).
[Crossref]

Akselrod, G. M.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Click, T. H.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
[Crossref] [PubMed]

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,” Nat. Photonics 2(12), 728–732 (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).

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).

Hellekalek, P.

P. Hellekalek, “Good random number generators are (not so) easy to find,” Math. Comput. Simul. 46(5-6), 485–505 (1998).
[Crossref]

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,” Nat. Photonics 2(12), 728–732 (2008).
[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,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Jeffrey, E. R.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[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(4), 1675–1680 (2000).
[Crossref]

Kaminski, G. A.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
[Crossref] [PubMed]

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,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Kwiat, P. G.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Lacharme, P.

P. Lacharme, “Analysis and Construction of Correctors,” IEEE Trans. Inf. Theory 55(10), 4742–4748 (2009).
[Crossref]

Liu, A.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
[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,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Owens, P. C. M.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Proykova, A.

A. Proykova, “How to improve a random number generator,” Comput. Phys. Commun. 124(2-3), 125–131 (2000).
[Crossref]

Rarity, J. G.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Rogina, B. M.

M. Stipcević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

Shaltiel, R.

R. Shaltiel, “How to get more mileage from randomness extractors,” Random Structures Algorithms 33(2), 157–186 (2008).
[Crossref]

R. Shaltiel, “Recent developments in explicit constructions of extractors,” Bull. EATCS 77, 67–95 (2002).

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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[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. Stipcević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[Crossref] [PubMed]

Tapster, P. R.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[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,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Wayne, M. A.

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[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(4), 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(4), 1675–1680 (2000).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[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(4), 1675–1680 (2000).
[Crossref]

Bull. EATCS (1)

R. Shaltiel, “Recent developments in explicit constructions of extractors,” Bull. EATCS 77, 67–95 (2002).

Comput. Phys. Commun. (1)

A. Proykova, “How to improve a random number generator,” Comput. Phys. Commun. 124(2-3), 125–131 (2000).
[Crossref]

IEEE Trans. Inf. Theory (1)

P. Lacharme, “Analysis and Construction of Correctors,” IEEE Trans. Inf. Theory 55(10), 4742–4748 (2009).
[Crossref]

J. Comput. Chem. (1)

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of Random Number Generators Significantly Affects Results of Monte Carlo Simulations for Organic and Biological Systems,” J. Comput. Chem. 32(3), 513–524 (2011).
[Crossref] [PubMed]

J. Mod. Opt. (3)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generator and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

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

M. A. Wayne, E. R. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Math. Comput. Simul. (1)

P. Hellekalek, “Good random number generators are (not so) easy to find,” Math. Comput. Simul. 46(5-6), 485–505 (1998).
[Crossref]

Nat. Photonics (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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Random Structures Algorithms (1)

R. Shaltiel, “How to get more mileage from randomness extractors,” Random Structures Algorithms 33(2), 157–186 (2008).
[Crossref]

Rev. Sci. Instrum. (2)

M. Stipcević and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 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(4), 1675–1680 (2000).
[Crossref]

Other (13)

A. Figotin, A. Y. Gordon, S. A. Molchanov, V. P. Popovich, J. E. Quinn, G. N. Stetsenko, N. M. Stravrakas, and I. M. Vitebskiy, “A random number generator based on spontaneous alpha-decay,” PCT application WO0038037A1 (2000).

I. Goldberg, and D. Wagner, “Randomness in the Netscape Browser,” Dr. Dobb's, January (1996).

R. Davies, “Exclusive OR (XOR) and hardware random number generators,” February 28, 2002, URL: http://www.robertnz.net/pdf/xor2.pdf

J. von Neumann, Various techniques for use in connection with random digits,” von Neumann Collected Works, Vol. 5, Pergamon, 768–770 (1963).

M. Stipčević and D. J. Gauthier, “Precise Monte Carlo Simulation of Single-Photon Detectors,” Proc. SPIE Defense, Security and Sensing, 29 April - 3 May 2013, Baltimore, Maryland, USA, also appear as http://arXiv:1411.3663v1 [quant-ph].

D. E. Knuth, The art of computer programming, Vol. 2, Third edition, (Addison-Wesley, Reading, 1997).

R. Davies, Statistics Research Associates Limited, 8 Bristol Street, Island Bay, Wellington, 6023, New Zealand (private communication 2013/2014).

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 the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications,” NIST Special Publication 800–22rev1a (dated April 2010). URL: http://csrc.nist.gov/groups/ST/toolkit/rng/documents/sts-2.1.1.zip

A. Theodore Markettos and W. Simon, Moore. 2009. “The Frequency Injection Attack on Ring-Oscillator-Based True Random Number Generators,” Proc. 11th International Workshop on Cryptographic Hardware and Embedded Systems (CHES '09), Christophe Clavier and Kris Gaj (Eds.). Springer-Verlag, Berlin, Heidelberg, 317–331 (2009).

P. Bayon, L. Bossuet, A. Aubert, V. Fischer, F. Poucheret, B. Robisson, and P. Maurine, “Contactless electromagnetic active attack on ring oscillator based true random number generator,” Proc. Third international conference on Constructive Side-Channel Analysis and Secure Design (COSADE'12), Werner Schindler and Sorin A. Huss (Eds.). Springer-Verlag, Berlin, Heidelberg (2012).
[Crossref]

M. Dichtl and J. D. Golic, “High-speed true random number generation with logic gates only,” in 1248 Cryptographic Hardware and Embedded Systems (CHES), ed. by P. Paillier, I. Verbauwhede 1249 (Springer, Berlin, 2007), 45–62.

B. Chor, O. Goldreich, J. Hasted, J. Freidmann, S. Rudich, and R. Smolensky, “The bit extraction problem or t-resilient functions,” 26th Annual Symposium on Foundations of Computer Science (FOCS), 396–407, IEEE (1985).
[Crossref]

D. Frauchiger, R. Renner, and M. Troyer, “True randomness from realistic quantum devices,” http://arXiv:1311.4547 [quant-ph].

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Figures (8)

Fig. 1
Fig. 1

Optical part of the beam splitter quantum random number generator consists of the beam splitter BS, detectors D0 and D1, fixed neutral density filter NDF and variable neutral density filter VNDF. The two filters allow for fine equalizing the probabilities of generating ones and zeros.

Fig. 2
Fig. 2

Autocorrelation coefficient for the BSR method a as a function of the detection frequency f of detectors D0 and D1, for the blanking time Δt=17.6 ns. One sigma statistical error bars are smaller than the dots sizes.

Fig. 3
Fig. 3

Illustration of the T1T2 method. Three subsequent random events (detected photons) define two intervals: T 1 and T 2 . If T 1 > T 2 then 0 is generated, if T 2 > T 1 then 1 is generated whereas if T 1 = T 2 then events are skipped and no random bit is generated.

Fig. 4
Fig. 4

Functional schematic of the circuit for realizing the COMBO random number generating method illustrating how intermediate strings T, S, Y and final string C are generated.

Fig. 5
Fig. 5

Cross-correlation coefficients of spatial and temporal bit strings in the COMBO quantum random number generator.

Fig. 6
Fig. 6

Randomness merits (bias and autocorrelation) of the three sequences generated by the COMBO RNG in case when one detector is failing. Detection rate of one detector (D0) was kept at its nominal rate of 10 Mcps, while rate of the other detector (D1) was varied from 10 Mcps down to zero simulating its failure. Shown are ± 1 Gaussian sigma statistical error bars.

Fig. 7
Fig. 7

Randomness merits (bias and autocorrelation) of the three sequences Y, T and C generated by the COMBO RNG under attack by injection of a periodic signal which causes simultaneous fake photon detections in detector with a frequency f Inject . Shown are ± 1 Gaussian sigma statistical error bars.

Fig. 8
Fig. 8

Bit generation rate f G (quadratic dots) and blanked events rate f B (round dots) as functions of detection rates in three failure and attack scenarios (see the text). Both rates are sensitive to irregular operation of the RNG this allowing for robust monitoring and failure/attack detection.

Tables (1)

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Table 1 Typical results of the NIST Statistical Test Suite

Equations (10)

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b= p( 1 )p(0) 2 =p( 1 ) 1 2 .
b ^ = i=1 N x i N 1 2 .
a k = i=1 Nk ( x i x ¯ )( x i+k x ¯ ) i=1 Nk ( x i x ¯ ) 2
a= p d = e τ d τ 1  τ d τ
a= p a τ d τ . 
b Y =2 b S 2 2 a S ( 1 4 b S 2 )2 b S 2 a S 2
a Y =2 a S ( 1 a S ) b S 2 12( 1 a S )( 1 4 b S 2 ) 4 a S b S 2
b C =2 b T b Y
a C = a T a Y +4( a T b Y 2 + a Y b T 2 )
a TY ( k )= i=1 Nk ( t i t ¯ )( y i+k y ¯ )   ( i=1 Nk ( t i t ¯ ) 2 )( i=1 Nk ( y i y ¯ ) 2 )

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