Abstract

Chaotic external-cavity semiconductor laser (ECL) is a promising entropy source for generation of high-speed physical random bits or digital keys. The rate and randomness is unfortunately limited by laser relaxation oscillation and external-cavity resonance, and is usually improved by complicated post processing. Here, we propose using a physical broadband white chaos generated by optical heterodyning of two ECLs as entropy source to construct high-speed random bit generation (RBG) with minimal post processing. The optical heterodyne chaos not only has a white spectrum without signature of relaxation oscillation and external-cavity resonance but also has a symmetric amplitude distribution. Thus, after quantization with a multi-bit analog-digital-convertor (ADC), random bits can be obtained by extracting several least significant bits (LSBs) without any other processing. In experiments, a white chaos with a 3-dB bandwidth of 16.7 GHz is generated. Its entropy rate is estimated as 16 Gbps by single-bit quantization which means a spectrum efficiency of 96%. With quantization using an 8-bit ADC, 320-Gbps physical RBG is achieved by directly extracting 4 LSBs at 80-GHz sampling rate.

© 2017 Optical Society of America

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References

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2015 (4)

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

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]

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (4)

N. Oliver, M. Soriano, D. 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]

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express 21(7), 8701–8710 (2013).
[Crossref] [PubMed]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

2012 (5)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Enhancement of chaotic signal bandwidth in vertical-cavity surface-emitting lasers with optical injection,” J. Opt. Soc. Am. B 29(3), 415–419 (2012).
[Crossref]

X. Z. Li and S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

2010 (5)

2009 (1)

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 (2)

T. E. Murphy and R. Roy, “Chaotic lasers: The world’s fastest dice,” Nat. Photonics 2(12), 714–715 (2008).
[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]

2007 (1)

1992 (1)

J. P. Eckmann and D. Ruelle, “Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems,” Physica D 56(2), 185–187 (1992).
[Crossref]

1949 (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28(4), 656–715 (1949).
[Crossref]

Aida, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

Akizawa, Y.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Alan Shore, K.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

L. Hong, Y. H. Hong, and K. Alan Shore, “Experimental study of time-delay signatures in vertical-cavity surface-emitting lasers subject to double-cavity polarization-rotated optical feedback,” J. Lightwave Technol. 32(9), 1829–1836 (2014).
[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]

Araiet, K.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Argyris, A.

Aviad, Y.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (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]

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]

Bahi, J. M.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Bloch, M.

Bogris, A.

Butkovski, M.

Chan, S. C.

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref] [PubMed]

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

X. Z. Li and S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling,” Opt. Lett. 37(11), 2163–2165 (2012).
[Crossref] [PubMed]

Chizhevsky, V. N.

Citrin, D. S.

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.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

Deligiannidis, S.

Dudley, J. M.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Eckmann, J. P.

J. P. Eckmann and D. Ruelle, “Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems,” Physica D 56(2), 185–187 (1992).
[Crossref]

Fang, X.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Fischer, I.

N. Oliver, M. Soriano, D. 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]

Guyeux, C.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Harayama, T.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

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]

Hong, L.

Hong, Y. H.

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]

Iwakawa, K.

Kanno, K.

Kanter, I.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (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]

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]

Kim, B.

Kinzel, W.

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]

Larger, L.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Li, L.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express 21(7), 8701–8710 (2013).
[Crossref] [PubMed]

Li, N.

Li, S. S.

X. Z. Li, S. S. Li, J. P. Zhuang, and S. C. Chan, “Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback,” Opt. Lett. 40(17), 3970–3973 (2015).
[Crossref] [PubMed]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Li, X.

Li, X. Z.

Liu, Q.

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Locquet, A.

Mercier, E.

Merolla, J. M.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Morikatsu, S.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

Muramatsu, J.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

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]

Okumura, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

Oliver, N.

N. Oliver, M. Soriano, D. 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]

Pan, W.

Panajotov, K.

Peleg, Y.

Pikasis, E.

Reidler, I.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (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]

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]

Rontani, D.

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. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

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.

Ruelle, D.

J. P. Eckmann and D. Ruelle, “Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems,” Physica D 56(2), 185–187 (1992).
[Crossref]

Sakuraba, R.

Salevan, J. C.

Sciamanna, M.

Shannon, C. E.

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28(4), 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]

Shore, K. A.

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]

Soriano, M.

N. Oliver, M. Soriano, D. 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]

Spencer, P. S.

Sukow, D.

N. Oliver, M. Soriano, D. 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.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

Syvridis, D.

Thienpont, H.

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]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[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]

Virte, M.

Wang, A.

Wang, A. B.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Wang, B.

Wang, B. J.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Wang, Y.

Wang, Y. C.

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Wetzel, B.

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

Williams, C. R.

Xu, H.

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Yamazaki, T.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. 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]

Yang, Y.

Yang, Y. B.

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[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]

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.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. 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]

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, B.

Zhang, M. J.

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Zhuang, J. P.

Zigzag, M.

Appl. Phys. Lett. (1)

A. B. Wang, Y. C. Wang, Y. B. Yang, M. J. Zhang, H. Xu, and B. J. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).
[Crossref]

Bell Syst. Tech. J. (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28(4), 656–715 (1949).
[Crossref]

IEEE J. Quantum Electron. (2)

X. Z. Li and S. C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[Crossref]

N. Oliver, M. Soriano, D. 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 J. Sel. Top. Quantum Electron. (1)

A. B. Wang, B. J. Wang, L. Li, Y. C. Wang, and K. Alan Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 531–540 (2015).
[Crossref]

IEEE Photon. J. (1)

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Araiet, K. Yoshimura, and P. Davis, “Fast Random Number Generation With Bandwidth-Enhanced Chaotic Semiconductor Lasers at 8×50 Gb/s,” IEEE Photonics Technol. Lett. 24(12), 1042–1044 (2012).
[Crossref]

IEEE Trans. Circuits Syst. I (1)

X. Fang, B. Wetzel, J. M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, and J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Circuits Syst. I 61(3), 888–901 (2014).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Nat. Photonics (4)

T. E. Murphy and R. Roy, “Chaotic lasers: The world’s fastest dice,” Nat. Photonics 2(12), 714–715 (2008).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[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]

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 (8)

A. Wang, Y. Yang, B. Wang, B. Zhang, L. Li, and Y. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express 21(7), 8701–8710 (2013).
[Crossref] [PubMed]

N. Li, B. Kim, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser,” Opt. Express 22(6), 6634–6646 (2014).
[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]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[Crossref] [PubMed]

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]

C. R. Williams, J. C. Salevan, X. 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]

M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).
[Crossref] [PubMed]

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]

Opt. Lett. (3)

Phys. Rev. Lett. (2)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

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]

Physica D (1)

J. P. Eckmann and D. Ruelle, “Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems,” Physica D 56(2), 185–187 (1992).
[Crossref]

Other (2)

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dary, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800–22, Revision 1a (2010).

D. R. Stinson, Cryptography: Theory and Practice (CRC Press, 1995).

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Figures (8)

Fig. 1
Fig. 1 Experimental setup. DFB1,2: distributed feedback semiconductor laser; PC1,2: polarization controller; FC1,2, FC: fiber coupler; VA1,2: variable attenuator; OI1,2: optical isolator; M1,2: fiber mirror; BPD: balanced photodetector; ADC: analog-to-digital converter; MSB: most significant bit; LSB: least significant bit.
Fig. 2
Fig. 2 Comparison of characteristics of experimental white chaos and intensity chaos of ECL1: (a1)-(a3) radio-frequency spectrum, autocorrelation trace, and temporal waveform and amplitude distribution of ECL1, and (b1)-(b3) those of the white chaos.
Fig. 3
Fig. 3 Number of passed NIST tests as a function of the sampling period for random bits generated from (a) heterodyne white chaos and (b) ECL1. The tests for each generation rate are examined five times, and the median of the numbers of passed terms is denoted as black dots, and the maximum and minimum numbers of passed terms are indicated with red bars. The random bit sequence is treated as passing the NIST tests when the median equals 15.
Fig. 4
Fig. 4 Radio-frequency spectra of (a1)-(a3) the quantized heterodyne white chaos and (b1)-(b3) the quantized ECL1 chaos recovered with 6 LSBs, 5 LSBs, and 4 LSBs, respectively.
Fig. 5
Fig. 5 Autocorrelation traces of the decimal sequences separately converted from the binary series of (a) 5 LSBs, (b) 4 LSBs and (c) 3 LSBs, respectively. Red (gray): heterodyne white chaos; blue (black): ECL1 chaos.
Fig. 6
Fig. 6 (a) Amplitude probability distribution of 5-LSB sequence extracted from the 8-bit quantized heterodyne white chaos (upper) and ECL1 intensity chaos (lower); (b) Cumulative probability deviation to uniform distribution Δ = i = 0 2 N 1 | P i 2 N | , where N is the number of LSBs retained, Pi is the probability of an N-bit binary number corresponding to a decimal integer i between 0 and 2 N −1. The amplitude distribution is calculated from 1 M data points.
Fig. 7
Fig. 7 Number of passed NIST tests as a function of the extracted LSBs for (a1), (a2) heterodyne white chaos and (b1), (b2) ECL1 under different sampling rates of 40 GS/s and 80 GS/s.
Fig. 8
Fig. 8 Autocorrelation traces of the decimal sequences recovered from the binary series of heterodyne white chaos with (a) 5 LSBs and (b) 4 LSBs at a sampling rate of 80 GS/s.

Tables (1)

Tables Icon

Table 1 Results of NIST test for 200-Gbps (5 LSBs × 40 GS/s) and 320-Gbps (4 LSBs × 80 GS/s) random bit sequences extracted from the heterodyne white chaos. Using 1000 samples of 1 Mbit data and significance level α = 0.01, for “Success”, the p-value should be larger than 0.0001 and the proportion should be in the range of 0.99 ± 0.0094392. For tests which produce multiple p-values and proportions, the worst case is shown.

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