Abstract

The use of the postprocessing method consisting of bitwise Exclusive-OR and least significant bits extraction to generate random bit sequences typically requires two distinct chaotic outputs. While the two signals are, in general, generated using two separated devices, e.g. two Fabry-Perot lasers, a single semiconductor ring laser can be used as an alternative due to its circular symmetry which facilitates lasing in two counterpropagating mode directions. We consider a chaotic semiconductor ring laser and investigate both numerically and experimentally its characteristics for fast random bit generation. In particular, we show that by sampling each directional mode’s output signal using a 8-bit analog-digital converter and through Exclusive-OR operation applied to the two resulting signals (after throwing away 4 most significant bits), we can achieve fast random bit-streams with a bit rate 4 × 10 = 40 Gbit/s, passing the statistical randomness tests. To optimize the system performance, we also study the dependence of randomness on the main system parameters and on noise.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010).
  2. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
    [CrossRef]
  3. T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.48, 281–288 (2001).
    [CrossRef]
  4. R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
    [CrossRef]
  5. R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express20, 25333–25344 (2012).
    [CrossRef] [PubMed]
  6. 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, 728–732 (2008).
    [CrossRef]
  7. T. E. Murphy and R. Roy, “The worlds fastest dice, Nat. Photonics2, 714–715 (2008).
    [CrossRef]
  8. K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
    [CrossRef]
  9. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
    [CrossRef] [PubMed]
  10. 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, 18763–18768 (2010).
    [CrossRef] [PubMed]
  11. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4, 58–61 (2010).
    [CrossRef]
  12. K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
    [CrossRef] [PubMed]
  13. 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, 4632 (2011).
    [CrossRef] [PubMed]
  14. C. R. S. Williams, J. C. Salevan, X.-W. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express18, 23584–23597 (2010).
    [CrossRef] [PubMed]
  15. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun.17, 539–550 (1999)
    [CrossRef]
  16. M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
    [CrossRef]
  17. J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect.45, 431–438 (2009).
    [CrossRef]
  18. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express19, 7439–7450 (2011)
    [CrossRef] [PubMed]
  19. I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
    [CrossRef]
  20. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
    [CrossRef] [PubMed]
  21. L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).
  22. N. Jiang, W. Pan, B. Luo, L. Yan, S. Xiang, L. Yang, D. Zheng, and N. Li, “Influence of injection current on the synchronization and communication performance of closed-loop chaotic semiconductor lasers,” Opt. Lett.36, 3197–3199 (2011).
    [CrossRef] [PubMed]
  23. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
    [CrossRef]
  24. R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
    [CrossRef] [PubMed]
  25. R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
    [CrossRef]
  26. M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
    [CrossRef]
  27. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).
  28. A. Argyris, E. Pikasis, S. Deligiannidis, and Dimitris Syvridis, “Sub-Tb/s physical random bit generators based on direct detection of amplified spontaneous emission signals,” J. Lightwave Technol.30, 1329–1334 (2010).
    [CrossRef]
  29. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, and M. Levenson, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Nat. Inst. Standards and Technology, Special Publication 800-22, 2001, Revision 1, 2008 [Online]. Available: http://csrc.nist.gov/publications/nist-pubs/800-22-rev1/SP800-22rev1.pdf .
  30. S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1.
  31. X. Leijtens, “JePPIX: the platform for InP-based photonics,” IET Optoelectronics5, 202–206 (2011).
    [CrossRef]
  32. I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
    [CrossRef]

2012

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express20, 25333–25344 (2012).
[CrossRef] [PubMed]

I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
[CrossRef] [PubMed]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

2011

2010

2009

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect.45, 431–438 (2009).
[CrossRef]

2008

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

T. E. Murphy and R. Roy, “The worlds fastest dice, Nat. Photonics2, 714–715 (2008).
[CrossRef]

2005

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

2003

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

2001

T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.48, 281–288 (2001).
[CrossRef]

2000

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
[CrossRef]

1999

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun.17, 539–550 (1999)
[CrossRef]

1997

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
[CrossRef]

1939

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Aida, H.

Amano, K.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Arai, K.

Argyris, A.

Ashour, M.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

Aviad, Y.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

Ballantyne, J. M.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
[CrossRef]

Balle, S.

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect.45, 431–438 (2009).
[CrossRef]

Beri, S.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Bogris, A.

Bolk, J.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

Booth, M. F.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
[CrossRef]

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Cohen, E.

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

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

Colet, P.

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express20, 25333–25344 (2012).
[CrossRef] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
[CrossRef] [PubMed]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

Connelly, J. A.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
[CrossRef]

Danckaert, J.

I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
[CrossRef] [PubMed]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Dauden, J.

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

Davis, P.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express19, 7439–7450 (2011)
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Deligiannidis, S.

Docter, B.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

Donati, S.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

Dowlatabadi, A. B.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
[CrossRef]

Ermakov, I. V.

I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
[CrossRef]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

Ferguson, N.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010).

Fischer, I.

Gelens, L.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Giuliani, G.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

Harayama, T.

Hasegawa, A.

S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1.

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Holman, W. T.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
[CrossRef]

Inoue, M.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Javaloyes, J.

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect.45, 431–438 (2009).
[CrossRef]

Jiang, N.

Kanter, I.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

Kim, S. J.

S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1.

Kocarev, L.

T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.48, 281–288 (2001).
[CrossRef]

Kohno, T.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010).

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, 728–732 (2008).
[CrossRef]

Larger, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

Laybourn, J. P. R.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

Leijtens, X.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

X. Leijtens, “JePPIX: the platform for InP-based photonics,” IET Optoelectronics5, 202–206 (2011).
[CrossRef]

Li, N.

Li, X.-W.

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Luo, B.

Mezosi, G.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Miglierina, R.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

Morikatsu, S.

Murphy, T. E.

Naito, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

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, 728–732 (2008).
[CrossRef]

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Pan, W.

Pesquera, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

Pikasis, E.

Reidler, I.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Rosenbluh, M.

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

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

Roy, R.

Salevan, J. C.

Schneier, B.

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010).

Schremer, A.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
[CrossRef]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Sciré, A.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[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, 728–732 (2008).
[CrossRef]

Someya, H.

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

Sorel, M.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Soriano, M. C.

Stojanovski, T.

T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.48, 281–288 (2001).
[CrossRef]

Sukow, D. W.

Sunada, S.

Syvridis, D.

Syvridis, Dimitris

Toral, R.

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

Tsuzuki, K.

Uchida, A.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express19, 7439–7450 (2011)
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Umeno, K.

S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1.

Van der Sande, G.

I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
[CrossRef] [PubMed]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Verschaffelt, G.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
[CrossRef] [PubMed]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

Vicente, R.

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

Walden, R. H.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun.17, 539–550 (1999)
[CrossRef]

Williams, C. R. S.

Xiang, S.

Yamazaki, T.

Yan, L.

Yang, L.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Yoshimura, K.

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express19, 7439–7450 (2011)
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18, 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[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, 728–732 (2008).
[CrossRef]

Zheng, D.

Appl. Phys. Lett.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett.76, 1095–1097 (2000).
[CrossRef]

Commun. Nonlinear Sci. Numer. Simul.

I. V. Ermakov, G. Van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul.17, 4767–4779 (2012).
[CrossRef]

IEEE J. Quantum Elect.

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect.45, 431–438 (2009).
[CrossRef]

IEEE J. Quantum Electron.

M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAl-GaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron.39, 1187–1195 (2003).
[CrossRef]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron.45, 1367–1379 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron.41, 541–548 (2005).
[CrossRef]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron.48, 129–136 (2012).
[CrossRef]

IEEE J. Sel. Areas Commun.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun.17, 539–550 (1999)
[CrossRef]

IEEE Trans. Circuits Syst. I

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521–528 (1997).
[CrossRef]

IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.

T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat.48, 281–288 (2001).
[CrossRef]

IET Optoelectronics

X. Leijtens, “JePPIX: the platform for InP-based photonics,” IET Optoelectronics5, 202–206 (2011).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

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

T. E. Murphy and R. Roy, “The worlds fastest dice, Nat. Photonics2, 714–715 (2008).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multi-stability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett.102, 193904 (2009).

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103, 024102 (2009).
[CrossRef] [PubMed]

Other

N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010).

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1–8 (2010), 5861 (2010).

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, and M. Levenson, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Nat. Inst. Standards and Technology, Special Publication 800-22, 2001, Revision 1, 2008 [Online]. Available: http://csrc.nist.gov/publications/nist-pubs/800-22-rev1/SP800-22rev1.pdf .

S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic of SRL with self-feedback. CW: clockwise mode, CCW: counterclockwise mode, PD: Photodetector, XOR: Exclusive-OR, ADC: analog-digital converter.

Fig. 2
Fig. 2

Left: (a) Part of intensity time series of |Eccw|2 (black) and |Ecw|2 (grey, red in color). (b) corresponding RF spectrum in dB. (c) Autocorrelation function computed from |Eccw|2, (d) cross-correlation function between |Ecw|2 and |Eccw|2.

Fig. 3
Fig. 3

Bifurcation diagram as a function of the delay time considering η = 2.5 ns−1

Fig. 4
Fig. 4

Operating principle for ADCs. The inset table shows how different ADCs translate the analogic signals A,B,C,D into binary.

Fig. 5
Fig. 5

Left: (a) Part of experimental intensity time series of |Eccw|2 (black) and |Ecw|2 (grey, red in color). (b) corresponding RF spectrum and noise floor. The vertical shift (at low frequencies) between the CW and CCW spectra is due to the different responsivity of the different detectors used to measure the two directional modes.

Tables (4)

Tables Icon

Table 1 Results of NIST SP 800-22 statistical tests considering Dm = 0. For ”success” using 1000 samples of 1 Mbit data and significance level a = 0.01, the P value (uniformity of p values) should be larger than 0.0001 and the proportion should be greater than 0.9805608 [8]. For the tests which produce multiple P-values and proportions, the worst case is shown.

Tables Icon

Table 2 Results of NIST Special Publication 800-22 statistical tests. Same parameters as in Table 1 considering Dm = 5 × 106ns−1

Tables Icon

Table 3 Range of the parameters found to pass all the NIST tests.

Tables Icon

Table 4 Results of NIST SP 800-22 statistical tests, generated from experimental data

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E ˙ c w = κ ( 1 + i α ) [ 𝒢 c w N 1 ] E c w ( k d + i k c ) E c c w + η E c w ( t T ) e i ω 0 T + D ξ c w ,
E ˙ c c w = κ ( 1 + i α ) [ 𝒢 c c w N 1 ] E c c w ( k d + i k c ) E c w + η E c c w ( t T ) e i ω 0 T + D ξ c c w ,
N ˙ = γ [ μ N 𝒢 c w N | E c w | 2 𝒢 c c w N | E c c w | 2 ] ,

Metrics