Abstract

We demonstrate a random bit streaming system that uses a chaotic laser as its physical entropy source. By performing real-time bit manipulation for bias reduction, we were able to provide the memory of a personal computer with a constant supply of ready-to-use physical random bits at a throughput of up to 4 Gbps. We pay special attention to the end-to-end entropy source model describing how the entropy from physical sources is converted into bit entropy. We confirmed the statistical quality of the generated random bits by revealing the pass rate of the NIST SP800-22 test suite to be 65 % to 75 %, which is commonly considered acceptable for a reliable random bit generator. We also confirmed the stable operation of our random bit steaming system with long-term bias monitoring.

© 2017 Optical Society of America

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References

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    [Crossref]
  4. S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
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    [Crossref]
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  13. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
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  14. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
    [Crossref] [PubMed]
  15. Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
    [Crossref]
  16. N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  20. J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
    [Crossref] [PubMed]
  21. A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
    [Crossref] [PubMed]
  22. 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,” NIST Special Publication 800-22, Revision 1a (2010).
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  24. A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
    [Crossref]
  25. D. Lihua, Z. Yong, J. Ligang, and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite,” Proc. 10th International Conference on Computational Intelligence and Security, 402–404 (2015).
  26. T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
    [Crossref]
  27. M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).
  28. M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
    [Crossref]
  29. K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).
  30. C. Beck and F. Schlögl, Thermodynamics of chaotic systems (Cambridge University, 1993).
    [Crossref]
  31. D.J. Driebe, Fully chaotic maps and broken time symmetry (Kluwer Academic Publishers, 1999).
    [Crossref]

2015 (2)

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
[Crossref]

2014 (1)

2013 (2)

A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, and Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

2012 (4)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, and M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

2011 (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

2010 (5)

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

H. Okutomi and K. Nakamura, “A study on rational judgment method of randomness property using NIST randomness test (NIST SP. 800-22)),” (in Japanese) IEICE Trans. A J93-A(1), 11–22 (2010).

A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
[Crossref]

2009 (3)

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (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(2), 024102 (2009).
[Crossref] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[Crossref]

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

1979 (1)

A. Shamir, “How to share a secret,” Commun. ACM 22612–613 (1979).
[Crossref]

1949 (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

Aida, H.

Akizawa, Y.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Amano, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[Crossref]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Arai, K.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Argyris, A.

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[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(2), 024102 (2009).
[Crossref] [PubMed]

Baish, M. L.

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

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,” NIST Special Publication 800-22, Revision 1a (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,” NIST Special Publication 800-22, Revision 1a (2010).

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

Beck, C.

C. Beck and F. Schlögl, Thermodynamics of chaotic systems (Cambridge University, 1993).
[Crossref]

Blakley, G. R.

G. R. Blakley, “Safeguarding cryptographic keys,” Proc. AFIPS Nat. Computer Conf., 313–317 (1979).

Bogris, A.

Boyle, M.

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

Davis, P.

M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
[Crossref]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Deligiannidis, S.

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,” NIST Special Publication 800-22, Revision 1a (2010).

Driebe, D.J.

D.J. Driebe, Fully chaotic maps and broken time symmetry (Kluwer Academic Publishers, 1999).
[Crossref]

Fischer, I.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

Goldreich, O.

O. Goldreich, S. Micali, and A. Wigderson, “How to play any mental game,” Proc. 19th Annual ACM Conference on Theory of Computing, 218–222 (1987).

Harayama, T.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

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,” NIST Special Publication 800-22, Revision 1a (2010).

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Honjo, T.

Inoue, M.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Inubushi, M.

M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
[Crossref]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

Iwakawa, K.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

Kanno, K.

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[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(2), 024102 (2009).
[Crossref] [PubMed]

Kelsey, J.

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

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]

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,” NIST Special Publication 800-22, Revision 1a (2010).

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,” NIST Special Publication 800-22, Revision 1a (2010).

Li, L.

Li, P.

Ligang, J.

D. Lihua, Z. Yong, J. Ligang, and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite,” Proc. 10th International Conference on Computational Intelligence and Security, 402–404 (2015).

Lihua, D.

D. Lihua, Z. Yong, J. Ligang, and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite,” Proc. 10th International Conference on Computational Intelligence and Security, 402–404 (2015).

Liu, M.

McKay, K. A.

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

Micali, S.

O. Goldreich, S. Micali, and A. Wigderson, “How to play any mental game,” Proc. 19th Annual ACM Conference on Theory of Computing, 218–222 (1987).

Morikatsu, S.

Muramatsu, J.

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

Naito, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Nakamura, K.

H. Okutomi and K. Nakamura, “A study on rational judgment method of randomness property using NIST randomness test (NIST SP. 800-22)),” (in Japanese) IEICE Trans. A J93-A(1), 11–22 (2010).

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,” NIST Special Publication 800-22, Revision 1a (2010).

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 3 Edition (Springer-Verlag, 2013).

Okumura, H.

Okutomi, H.

H. Okutomi and K. Nakamura, “A study on rational judgment method of randomness property using NIST randomness test (NIST SP. 800-22)),” (in Japanese) IEICE Trans. A J93-A(1), 11–22 (2010).

Oliver, N.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[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]

Pikasis, E.

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[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(2), 024102 (2009).
[Crossref] [PubMed]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[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(2), 024102 (2009).
[Crossref] [PubMed]

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,” NIST Special Publication 800-22, Revision 1a (2010).

Sakuraba, R.

Schlögl, F.

C. Beck and F. Schlögl, Thermodynamics of chaotic systems (Cambridge University, 1993).
[Crossref]

Seo, T.

A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
[Crossref]

Shamir, A.

A. Shamir, “How to share a secret,” Commun. ACM 22612–613 (1979).
[Crossref]

Shannon, C. E.

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (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,” NIST Special Publication 800-22, Revision 1a (2010).

Someya, H.

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Soriano, M. C.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[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,” NIST Special Publication 800-22, Revision 1a (2010).

Sukow, D. W.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

Sunada, S.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Syvridis, D.

Takahashi, R.

Terashima, Y.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

Tokura, Y.

Tsuzuki, K.

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Turan, M. S.

M. S. Turan, E. Barker, J. Kelsey, K. A. McKay, M. L. Baish, and M. Boyle, “Recommendation for the entropy sources used for random bit generation,” NIST Special Publication 800-90B, Second draft (2016).

Uchida, A.

R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth-enhanced chaos in three-cascaded semiconductor lasers,” Opt. Express 23(2), 1470–1490 (2015).
[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

Ugajin, K.

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

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,” NIST Special Publication 800-22, Revision 1a (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,” NIST Special Publication 800-22, Revision 1a (2010).

Wang, A.

Wang, Y.

Wigderson, A.

O. Goldreich, S. Micali, and A. Wigderson, “How to play any mental game,” Proc. 19th Annual ACM Conference on Theory of Computing, 218–222 (1987).

Xucang, H.

D. Lihua, Z. Yong, J. Ligang, and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite,” Proc. 10th International Conference on Computational Intelligence and Security, 402–404 (2015).

Xue, L.

Yamaguchi, A.

A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
[Crossref]

Yamazaki, T.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

Yao, A. C.

A. C. Yao, “Protocols for secure computations (extended abstract),” Proc. 23rd Annual Symposium on Foundations of Computer Science, 160–164 (1982).

Yong, Z.

D. Lihua, Z. Yong, J. Ligang, and H. Xucang, “Study on the pass rate of NIST SP800-22 statistical test suite,” Proc. 10th International Conference on Computational Intelligence and Security, 402–404 (2015).

Yoshikawa, K.

A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
[Crossref]

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, K.

M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
[Crossref]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
[Crossref] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[Crossref] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, and Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[Crossref]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit” (preprint).

Zhang, J.

Zhang, M.

Bell Syst. Tech. J. (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

Chaos (1)

S. Sunada, T. Harayama, P. Davis, K. Tsuzuki, K. Arai, K. Yoshimura, and A. Uchida, “Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation,” Chaos 22(4), 047513 (2012).
[Crossref]

Commun. ACM (1)

A. Shamir, “How to share a secret,” Commun. ACM 22612–613 (1979).
[Crossref]

IEEE J. Quantum Electron. (2)

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: Approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[Crossref]

IEEE Photon. Tech. Lett. (1)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Tech. Lett. 24(12), 1042–1044 (2012).
[Crossref]

IEICE Trans. A (1)

H. Okutomi and K. Nakamura, “A study on rational judgment method of randomness property using NIST randomness test (NIST SP. 800-22)),” (in Japanese) IEICE Trans. A J93-A(1), 11–22 (2010).

JSIAM Lett. (1)

A. Yamaguchi, T. Seo, and K. Yoshikawa, “On the pass rate of NIST statistical test suite for randomness,” JSIAM Lett. 2, 123–126 (2010).
[Crossref]

Nat. Photonics (2)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Opt. Express (7)

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[Crossref] [PubMed]

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[Crossref] [PubMed]

R. Takahashi, Y. Akizawa, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Arai, K. Yoshimura, and P. Davis, “Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation,” Opt. Express 22(10), 11727–11740 (2014).
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[Crossref]

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Phys. Rev. A (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[Crossref]

Phys. Rev. E (2)

M. Inubushi, K. Yoshimura, and P. Davis, “Noise robustness of unpredictability in a chaotic laser system: Toward reliable physical random bit generation,” Phys. Rev. E 91(2), 022918 (2015).
[Crossref]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, and P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E 85(4), 046215 (2012).
[Crossref]

Phys. Rev. Lett. (1)

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[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic diagram of random bit streaming system. (b) Structure of chaotic laser chip.
Fig. 2
Fig. 2 (a) Radio-frequency spectrum and (b) time series of the chaotic laser output measured using the ADC board. In (a), the noise level is given for comparison. In (b), the sampling rate is set at 1 GSps.
Fig. 3
Fig. 3 Diagram of data flow managed with random bit server software.
Fig. 4
Fig. 4 Typical finite-time probability distributions. (a) Normalized probability distribution for the intensity of the chaotic laser. (b) Normalized probability distribution for the intensity of the electronic noise. (c) Same as (b) but the vertical axis is in log scale to enhance tiny probabilities. When calculating these probability distributions, the intensity was sampled at 1 GSps as shown in Fig. 2(b), and 10243 samples were used.
Fig. 5
Fig. 5 The bias of each bit for the chaotic laser’s signal, where 1-Gbit samples were used for calculating the bias (see Eq. (1) for the definition of the j-th bit’s bias). The filled circles (•) are for the raw binary data { A j } j = 0 7, while the filled squares (▪) are for the binary data, { C 1 ( s ) } s = 0 7, whose biases are reduced by bit manipulation (see text for details).
Fig. 6
Fig. 6 Real-time monitoring of the average throughput and bias of the generated random bits, where the parameters for the bit manipulation were set at m = 4 (four-bit extraction) and s = 0, yielding a generation rate of 4 Gbps. In (a), the throughput was measured in terms of the number of random bits supplied to the PC’s user memory space per time. In (b), the bias was calculated for 8-Mbit samples. The two lines at ± 1.29 / 8 × 1024 2 ± 4.5 × 10 4 correspond to the significance level α = 0.01 for the null hypothesis that the generated bits are random.
Fig. 7
Fig. 7 (a) Time dependence of the bias SN for generated random bits. The bias SN is calculated from N (= 8 × 10242) consecutive bits. (b) Normalized probability distribution of the scaled bias N for the data in (a) (see text for definitions of SN and N), where the solid curve is the normalized Gaussian distribution (Eq. (3)) predicted by the central limit theorem.
Fig. 8
Fig. 8 (a) Evolution of ρ0(x) under the Bernoulli map, Eq. (4). As j increases, ρj (x) converges to a uniform distribution ρ(x) ≡ 1. (b) Bias dependence on bit number j, where j = 0 corresponds to the LSB.

Tables (2)

Tables Icon

Table 1 The results of a single trial of the NIST test suite [22] for a data set obtained when the bit manipulation parameters were set at m = 2 and s = 3. For 1000 binary sequences with length 106 and significance level α = 0.01, each test is passed if the P-value (uniformity of p-values) is larger than 0.0001, and the proportion is in the 0.99 ± 0.0094392 range. For the tests with multiple sub-tests, the worst P-values and proportions are shown.

Tables Icon

Table 2 The counts for passing each test in the NIST test suite for 100 sample data sets, each consisting of 1000 binary sequences with lengths of 106 bits. Each column corresponds to a different bit manipulation condition designated by m and s, which respectively represent the number of extracted bits and the offset bit. The bottom row shows the pass rates for the NIST test suite. A pass rate with * indicates that those bits suspected of being affected by electronic noise were not used in the RBG.

Equations (7)

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Bias j : = | Prob { A j = 0 } 1 2 | .
S N = 1 N k = 1 N z k 1 2 .
P ( S ˜ N ) = 1 2 π e S ˜ N 2 / 2 .
B ( x ) = 2 x mod 1 = { 2 x for x [ 0 , 1 2 ) 2 x 1 for x [ 1 2 , 1 ) ,
Prob { A j = 0 } = Prob { B j ( x 0 ) < 1 / 2 } = 0 1 / 2 d x ρ j ( x ) , ( j = 0 , 1 , )
ρ j 1 ( x ) : = 1 2 [ ρ j 1 ( x 2 ) + ρ j 1 ( x + 1 2 ) ] .
ρ j ( x ) = 1 2 j m = 0 2 j 1 ρ 0 ( x + m 2 j ) .

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