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]

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]

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]

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]
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[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]
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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. 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]

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]

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]

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]

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]

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]

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]

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]

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. 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]

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

[CrossRef]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. 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]

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]

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

[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]

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. 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]

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]

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, 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]

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]

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).

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, 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]

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, 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]

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]

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]

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]

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

[CrossRef]
[PubMed]

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]

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).

[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]

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

[CrossRef]
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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).

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[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]

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]

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]

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[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]
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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]
[PubMed]

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