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]

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]

X. Li, A. B. Cohen, T. E. Murphy, and R. Roy, “Scalable parallel physical random number generator based on a superluminescent LED,” Opt. Lett.36(6), 1020–1022 (2011).

[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]

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87-Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett.9, 031404 (2011).

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]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett.36(23), 4632–4634 (2011).

[CrossRef]
[PubMed]

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]

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]

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]

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]

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

[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]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[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]

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]

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]

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

[CrossRef]
[PubMed]

X. Li, A. B. Cohen, T. E. Murphy, and R. Roy, “Scalable parallel physical random number generator based on a superluminescent LED,” Opt. Lett.36(6), 1020–1022 (2011).

[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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]
[PubMed]

X. Li, A. B. Cohen, T. E. Murphy, and R. Roy, “Scalable parallel physical random number generator based on a superluminescent LED,” Opt. Lett.36(6), 1020–1022 (2011).

[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]

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]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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]

X. Li, A. B. Cohen, T. E. Murphy, and R. Roy, “Scalable parallel physical random number generator based on a superluminescent LED,” Opt. Lett.36(6), 1020–1022 (2011).

[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]

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

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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]

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]

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]

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87-Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett.9, 031404 (2011).

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

[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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[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]

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87-Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett.9, 031404 (2011).

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

[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]

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]

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]

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87-Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett.9, 031404 (2011).

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]

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]

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]

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

[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]

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]

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[CrossRef]

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[CrossRef]

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]

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[CrossRef]
[PubMed]

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[CrossRef]

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]

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).

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[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]
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[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).

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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]

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]

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[CrossRef]
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