Abstract

We report a prototype of high-speed real-time physical random bit generator based on a chaotic laser. The chaotic laser consists of a semiconductor laser with optical feedback in fiber external cavity configuration. The chaotic laser intensity signal is quantized into binary stream by differential comparison which makes the amplitude distribution symmetric with respect to zero mean value. An exclusive-OR gate operation between two raw binary streams from the chaotic signal and its delayed signal is used to overcome the influences of the weak periodicity induced by the external cavity resonance inherent in the chaotic laser. After exclusive-OR operation, the prototype can generate a single fast random bit stream in real time without any off-line processing procedures. Its bit rate can be handily and continuously tuned up to 4.5 Gbps by a trigger clock. Experiment results demonstrate that our generator possesses high-quality randomness with verified by the three-standard-deviation criterion and industry-benchmark statistical tests.

© 2013 OSA

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2013 (1)

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

2012 (8)

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron.48(11), 1371–1379 (2012).
[CrossRef]

P. Li, Y. C. Wang, A. B. Wang, L. Z. Yang, M. J. Zhang, and J. Z. Zhang, “Direct generation of all-optical random numbers from optical pulse amplitude chaos,” Opt. Express20(4), 4297–4308 (2012).
[CrossRef] [PubMed]

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. Express20(7), 7496–7506 (2012).
[CrossRef] [PubMed]

J. Zhang, Y. Wang, L. Xue, J. Hou, B. Zhang, A. Wang, and M. Zhang, “Delay line length selection in generating fast random numbers with a chaotic laser,” Appl. Opt.51(11), 1709–1714 (2012).
[CrossRef] [PubMed]

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]

A. Argyris, E. Pikasis, S. Deligiannidis, and D. Syvridis, “Sub-Tb/s physical random bit generators based on direct detection of amplified spontaneous emission signals,” J. Lightwave Technol.30(9), 1329–1334 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express20(27), 28603–28613 (2012).
[CrossRef] [PubMed]

2011 (7)

2010 (10)

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A81(6), 063814 (2010).
[CrossRef]

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett.35(3), 312–314 (2010).
[CrossRef] [PubMed]

M. A. Wayne and P. G. Kwiat, “Low-bias high-speed quantum random number generator via shaped optical pulses,” Opt. Express18(9), 9351–9357 (2010).
[CrossRef] [PubMed]

M. Fürst, H. Weier, S. Nauerth, D. G. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express18(12), 13029–13037 (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. Express18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express18(19), 20360–20369 (2010).
[CrossRef] [PubMed]

C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express18(23), 23584–23597 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (2)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008).
[CrossRef] [PubMed]

2003 (1)

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 (1)

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 (1)

C. S. Petrie and J. A. 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]

1994 (1)

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

1972 (1)

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

1949 (2)

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

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

Amano, K.

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. Express17(11), 9053–9061 (2009).
[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. Photonics2(12), 728–732 (2008).
[CrossRef]

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Anzolin, G.

Arai, K.

Arecchi, F. T.

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

Argyris, A.

Assad, S. M.

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett.98(23), 231103 (2011).
[CrossRef]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(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]

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Berlin, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Bogris, A.

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. Express18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008).
[CrossRef] [PubMed]

Bolk, J.

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]

Chan, S. C.

Chi, Y.-M.

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008).
[CrossRef] [PubMed]

Cohen, A. B.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Connelly, J. A.

C. S. Petrie and J. A. 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]

Curty, M.

Danckaert, J.

Dang, A.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

Davis, P.

Deligiannidis, S.

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Fischer, I.

Fürst, M.

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[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]

Giacomelli, G.

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

Guo, H.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett.34(12), 1876–1878 (2009).
[CrossRef] [PubMed]

Hamacher, M.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008).
[CrossRef] [PubMed]

Harayama, T.

Hirano, K.

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. Express17(11), 9053–9061 (2009).
[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. Photonics2(12), 728–732 (2008).
[CrossRef]

Honjo, T.

Hou, J.

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. Photonics2(12), 728–732 (2008).
[CrossRef]

Jofre, M.

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(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, 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. Photonics2(12), 728–732 (2008).
[CrossRef]

Kurtsiefer, C.

Kwiat, P. G.

Lam, P. K.

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett.98(23), 231103 (2011).
[CrossRef]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Leijtens, X.

Lepri, S.

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Li, P.

Li, X.

Li, X. Z.

Liu, M.

Liu, Y.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

Lo, H.-K.

Luo, B.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

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]

Maddocks, R. S.

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

Marangon, D. G.

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Matthews, S.

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Metropolis, N.

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

Mitchell, M. W.

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. Photonics2(12), 728–732 (2008).
[CrossRef]

Nauerth, S.

Nguimdo, R. M.

Okumura, H.

Oliver, N.

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. Photonics2(12), 728–732 (2008).
[CrossRef]

Petrie, C. S.

C. S. Petrie and J. A. 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]

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.

Politi, A.

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

Pruneri, V.

Qi, B.

Qian, L.

Rahn, H.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(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]

Röhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(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.

Shannon, C. E.

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

Shen, Y.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A81(6), 063814 (2010).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

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. Express17(11), 9053–9061 (2009).
[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. Photonics2(12), 728–732 (2008).
[CrossRef]

Soriano, M. C.

Steinlechner, F.

Stojanovski, T.

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]

Sukow, D. W.

Sunada, S.

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Symul, T.

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett.98(23), 231103 (2011).
[CrossRef]

Syvridis, D.

Tang, W.

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

Tian, L.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A81(6), 063814 (2010).
[CrossRef]

Tokura, Y.

Torres, J. P.

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]

Tsuzuki, K.

Uchida, A.

Ulam, S.

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

Van der Sande, G.

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]

Verschaffelt, G.

Vincent, C. H.

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

Walker, E. W.

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

Wang, A.

Wang, A. B.

P. Li, Y. C. Wang, A. B. Wang, L. Z. Yang, M. J. Zhang, and J. Z. Zhang, “Direct generation of all-optical random numbers from optical pulse amplitude chaos,” Opt. Express20(4), 4297–4308 (2012).
[CrossRef] [PubMed]

Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron.48(11), 1371–1379 (2012).
[CrossRef]

Wang, Y.

Wang, Y. C.

Wayne, M. A.

Wei, W.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett.34(12), 1876–1878 (2009).
[CrossRef] [PubMed]

Weier, H.

Weinfurter, H.

Williams, C. R. S.

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (2010).
[CrossRef]

Wu, Y.

Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron.48(11), 1371–1379 (2012).
[CrossRef]

Xie, G.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

Xue, L.

Yang, L. Z.

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Yoshimura, K.

Zhang, B.

Zhang, J.

Zhang, J. W.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

Zhang, J. Z.

Zhang, M.

Zhang, M. J.

Zhang, Y. Y.

Zhu, M. Y.

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

Zou, H.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A81(6), 063814 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett.98(17), 171105 (2011).
[CrossRef]

T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett.98(23), 231103 (2011).
[CrossRef]

Bell Syst. Tech. J. (1)

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

Chin. Opt. Lett. (1)

IEEE EEE Photon. Technol. Lett. (1)

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE EEE Photon. Technol. Lett.24(6), 437–439 (2012).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Wu, Y. C. Wang, P. Li, A. B. Wang, and M. J. Zhang, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron.48(11), 1371–1379 (2012).
[CrossRef]

IEEE Trans. Circ. Syst. I Fundam. Theory Appl. (2)

C. S. Petrie and J. A. 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, 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. Comput. (1)

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. (1)

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

J. Lightwave Technol. (1)

J. Phys. E (1)

R. S. Maddocks, S. Matthews, E. W. Walker, and C. H. Vincent, “A compact and accurate generator for truly random binary digits,” J. Phys. E5(6), 542–544 (1972).
[CrossRef]

Laser Phys. Lett. (1)

Y. Liu, M. Y. Zhu, B. Luo, J. W. Zhang, and H. Guo, “Implementation of 1.6 Tb s−1 truly random number generation based on a super-luminescent emitting diode,” Laser Phys. Lett.10(4), 045001 (2013).
[CrossRef]

Nat. Photonics (3)

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics4(10), 711–715 (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. Photonics2(12), 728–732 (2008).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Opt. Express (11)

M. A. Wayne and P. G. Kwiat, “Low-bias high-speed quantum random number generator via shaped optical pulses,” Opt. Express18(9), 9351–9357 (2010).
[CrossRef] [PubMed]

M. Fürst, H. Weier, S. Nauerth, D. G. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express18(12), 13029–13037 (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. Express18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express18(19), 20360–20369 (2010).
[CrossRef] [PubMed]

C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express18(23), 23584–23597 (2010).
[CrossRef] [PubMed]

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express19(21), 20665–20672 (2011).
[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. Express17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

P. Li, Y. C. Wang, A. B. Wang, L. Z. Yang, M. J. Zhang, and J. Z. Zhang, “Direct generation of all-optical random numbers from optical pulse amplitude chaos,” Opt. Express20(4), 4297–4308 (2012).
[CrossRef] [PubMed]

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. Express20(7), 7496–7506 (2012).
[CrossRef] [PubMed]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express20(27), 28603–28613 (2012).
[CrossRef] [PubMed]

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. Express19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (1)

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A81(6), 063814 (2010).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.81(5), 051137 (2010).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett.100(19), 194101 (2008).
[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)

S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, “High-dimensional chaos in delayed dynamical systems,” Physica D70(3), 235–249 (1994).
[CrossRef]

Other (4)

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 the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications”, http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html

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

R. G. Gallager, Principles of Digital Communication (Cambridge University Press, 2008).

S. Asmussen and P. W. Glynn, Stochastic Simulation: Algorithms and Analysis (Springer-Verlag, 2007).

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Figures (9)

Fig. 1
Fig. 1

Device structure. (a) Schematic block diagram of the prototype of physical random bit generator based on optical chaos. LD, a distributed feedback laser diode; OC, an optical circulator; VA, a variable optical attenuator; FC, a fiber coupler; PD, a photo-detector; Tee, Tee connector; COM, a 1-bit comparator; DFF, a D-type flip-flop; CLK, a trigger clock; XOR, an exclusive-OR gate. (b) External photograph and (c) internal photograph of the prototype with a overall size of 30 cm × 26 cm × 12 cm.

Fig. 2
Fig. 2

Characteristics of chaotic laser. (a) Measured power spectral density (PSD) and (b) temporal waveform of the chaotic laser; (c) probability density function (histogram) and (d) autocorrelation function of the temporal waveforms of the chaotic laser.

Fig. 3
Fig. 3

Characteristics of the calculated temporal waveform V(t)-V(t-τ) through doing subtraction between the measured chaotic signal V(t) and its delayed signal V(t-τ). (a) Time series and (b) its associated statistical histogram. The Pearson’s median skewness coefficient of the histogram is −0.001.

Fig. 4
Fig. 4

Photographs of the generated random bit stream after a XOR operation recorded by a real time oscilloscope (LeCroy SDA806Zi-A) when the CLK frequency is set to 4.5 GHz. (a) Temporal waveforms, where these units in vertical and horizontal axes are 200 mV/div and 5 ns/ div, respectively; (b) Eye diagram, where these units in vertical and horizontal axes are 200 mV/div and 37 ps/ div, respectively.

Fig. 5
Fig. 5

Bitmap image constructed from 500 × 500 bits of the generated random bit stream with a 4.5 Gbps bit rate. Here, blue and white dots denote logical bits ‘1’ and ‘0’, respectively.

Fig. 6
Fig. 6

(a) Bias |e[N]| versus the sample size of the generated 4.5 Gbps random bit sequence; The red line in (a) is its three-standard-deviation line, 3σe = (3N-1/2)/2 where N = 1, 2, 3, …, 16 Mbits. (b) Autocorrelation coefficient C[K] as a function of the delay bit K for a 16 × 106 bit stream with a 4.5 Gbps bit rate versus 4.5 Gbps random bit sequence after the XOR operation, respectively; The red lines in (b) is corresponding three-standard-deviation line, 3σc = 3N-1/2 where N = 16 Mbits.

Fig. 7
Fig. 7

Typical results of NIST statistical tests. Using 1000 samples of 1 Mb data and significance level β = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001 and the proportion should be greater than 0.9805608.

Fig. 8
Fig. 8

Measured frequency of ‘0’ bits for the 4.5 Gbps physical random bit generator. Note that the dash lines show the range 50.00 ± 0.13%.

Fig. 9
Fig. 9

Photographs of the temporal waveforms (left column, -I) and associated eye diagrams (right column, -II) of the generated random bit streams at different rates of 1 Gbps, 2 Gbps, 3 Gbps and 4 Gbps, which are also measured and recorded with the 6 GHz bandwidth real time oscilloscope(LeCroy SDA806Zi-A). (a) 1 Gbps, (b) 2Gbps, (c) 3 Gbps and (d) 4 Gbps.

Equations (2)

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| e[N] |=| a[n] 1 2 |,
C[k]= a[n]a[n+k] a[n] 2 ( a 2 [n] - a[n] 2 ) ,

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