Abstract

We experimentally realize a robust real-time random number generator by differentially comparing the signal from a chaotic semiconductor laser and its delayed signal through a 1-bit analog-to-digital converter. The probability density distribution of the output chaotic signal based on the differential comparison method possesses an extremely small coefficient of Pearson’s median skewness (1.5 × 10−6), which can yield a balanced random sequence much easily than the previously reported method that compares the signal from the chaotic laser with a certain threshold value. Moveover, we experimently demonstrate that our method can stably generate good random numbers at rates of 1.44 Gbit/s with excellent immunity from external perturbations while the previously reported method fails.

© 2012 OSA

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  1. Security requirements for cryptographic modules. FIPS 140–2 (2001). http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf
  2. R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
    [CrossRef]
  3. N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
    [CrossRef] [PubMed]
  4. M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
    [CrossRef]
  5. C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000).
    [CrossRef]
  6. M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
    [CrossRef]
  7. T. Stojanovski and L. Kocarev, “Chaos-based random number generators-Part I: analysis,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001).
    [CrossRef]
  8. T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
    [CrossRef] [PubMed]
  15. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
    [CrossRef] [PubMed]
  16. 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]
  17. A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
    [CrossRef]
  18. C. R. S. Williams, J. C. Salevan, X. W. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18(23), 23584–23597 (2010).
    [CrossRef] [PubMed]
  19. Pearson's skewness coefficients. http://en.wikipedia.org/wiki/Skewness#cite_note-4 .
  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 random and pseudorandom number generators for cryptographic applications,” http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html
  21. G. Marsaglia, “Diehard: A battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/

2011

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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

2009

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]

2008

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]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[CrossRef]

2003

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

2001

T. Stojanovski and L. Kocarev, “Chaos-based random number generators-Part I: analysis,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001).
[CrossRef]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
[CrossRef]

2000

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000).
[CrossRef]

1989

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

1982

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
[CrossRef]

1949

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[CrossRef] [PubMed]

Aida, H.

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]

Arai, K.

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]

Bogris, A.

Bucci, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

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]

Connelly, J.

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000).
[CrossRef]

Davis, P.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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]

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.

Foster, S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Germani, L.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

Giffard, R. P.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Harayama, T.

He, H. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[CrossRef]

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]

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]

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]

Kocarev, L.

T. Stojanovski and L. Kocarev, “Chaos-based random number generators-Part I: analysis,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001).
[CrossRef]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
[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, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Li, P.

Li, X. W.

Luzzi, R.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[CrossRef] [PubMed]

Milstein, L. B.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
[CrossRef]

Moberly, D. S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Morikatsu, S.

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

Nazarathy, M.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Newton, S. A.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Okumura, H.

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]

Petrie, C.

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000).
[CrossRef]

Pickholtz, R. L.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
[CrossRef]

Pihl, J.

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
[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]

Roy, R.

Salevan, J. C.

Schilling, D. L.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
[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]

Sischka, F.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[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]

Stojanovski, T.

T. Stojanovski and L. Kocarev, “Chaos-based random number generators-Part I: analysis,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001).
[CrossRef]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
[CrossRef]

Sunada, S.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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.

Trifiletti, A.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

Trutna, W. R.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Tsuzuki, K.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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]

Uchida, A.

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]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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]

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]

Ulam, S.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[CrossRef] [PubMed]

Varanonuovo, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

Wang, A. B.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[CrossRef]

Wang, Y. C.

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18(19), 20360–20369 (2010).
[CrossRef] [PubMed]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[CrossRef]

Williams, C. R. S.

Yamazaki, T.

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]

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.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

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]

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]

Zhang, J. Z.

IEEE Photon. Technol. Lett.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[CrossRef]

IEEE Trans. Circ. Syst. I Fundam. Theory Appl.

C. Petrie and J. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000).
[CrossRef]

T. Stojanovski and L. Kocarev, “Chaos-based random number generators-Part I: analysis,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 281–288 (2001).
[CrossRef]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-Part II: Practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 382–385 (2001).
[CrossRef]

IEEE Trans. Commun.

R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications-a tutorial,” IEEE Trans. Commun. 30(5), 855–884 (1982).
[CrossRef]

IEEE Trans. Comput.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Trans. Comput. 52(4), 403–409 (2003).
[CrossRef]

J. Am. Stat. Assoc.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[CrossRef] [PubMed]

J. Lightwave Technol.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[CrossRef]

Nat. Photonics

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]

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]

Opt. Express

Phys. Rev. A

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. Lett.

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]

Other

Pearson's skewness coefficients. http://en.wikipedia.org/wiki/Skewness#cite_note-4 .

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,” http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html

G. Marsaglia, “Diehard: A battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/

Security requirements for cryptographic modules. FIPS 140–2 (2001). http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf

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Figures (6)

Fig. 1
Fig. 1

Experimental setup of random number generation based on the differential comparison of the chaotic laser signals, DFB-LD: distributed feedback laser diode; PC, polarization controller; FM: fiber mirror; VOA, variable optical attenuator; OI: optical isolator; PD: photo-detector; T: T-type connector; 1-bit ADC: 1-bit analog-to-digital converter consisting of a comparator and a D flip-flop; OSC: oscilloscope.

Fig. 2
Fig. 2

(a) The RF spectrum of the chaotic signal. The red line and blue line denote the chaotic signal and the noise base, respectively. (b) The autocorrelation trace of the chaotic signal.

Fig. 3
Fig. 3

The correlation trace of the chaotic signal. The inset shows the overall correlation trace of the chaotic signal with the maximum delay time of 200 ns.

Fig. 4
Fig. 4

(a) and (b) show statistical histograms of the chaotic signals before and after the differential comparison (The corresponding Pearson’s median skewness coefficients are 0.384 and 1.5 × 10−6, respectively). (c) and (d) show time series of the chaotic signals before and after the differential comparison (The corresponding deviations of zeros and ones in the extracted random sequences are 16% and 0.0098%, respectively).

Fig. 5
Fig. 5

Typical output signals from RNG experimental system. (a) shows the temporal waveform of the random sequence at 1.44 Gbit/s after the XOR operation; (b) depicts an eye diagram of the random sequence; (c) illustrates a random dot diagram of the random sequence; Random bit patterns with 500 × 500 bits are shown in a two-dimensional plane. Bits “1” and “0” are converted to white and black dots, respectively, and placed from left to right (and from top to bottom).

Fig. 6
Fig. 6

(a) and (c) show the temporal waveforms of the chaotic signals before and after the differential comparison, respectively; (b) and (d) show the correspondingly extracted random code sequence, respectively. The jamming fluctuations are introduced by the ripple effect of laser current source on purpose. The modulation depth of the jamming signal relative to bias current is close to 1 and its average modulation frequency is about 5 MHz.

Tables (2)

Tables Icon

Table 1 Results of NIST Special Publication 800-22 statistical tests. For ‘success’ using 1000 samples of 1-Mbit data and significance level α = 0.01, the P-value (uniformity of P-values) should be larger than 0.0001 and the Proportion should be within the range of 0.99 ± 0.0094392. For the tests which produce multiple P-values and Proportions, the worst case is shown.

Tables Icon

Table 2 Typical results of Diehard statistical tests. Using 74-Mbit data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001. “KS” indicates that single P-value is obtained by the Kolmogorov-Smirnov (KS) test. For tests with multiple P-value, the worst case is selected.

Equations (7)

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ρ = 1 n i = 1 n b i b i + k ( 1 n i = 1 n b i ) 2 1 n i = 1 n b i 2 ( 1 n i = 1 n b i ) 2
F ( z ) = + [ z + y f ( x , y ) d x ] d y
f z ( z ) = + f ( z + y , y ) d y = + f ( z + y ) f ( y ) d y
f z ( z ) = + f ( z + y ) f ( y ) d y
f z ( z ) = + f ( v ) f ( v + z ) d v
f z ( z ) = f z ( z )
γ = 3 × ( x ¯ M ) 1 n i = 1 n ( x i x ¯ )

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