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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 6 — Mar. 15, 2010
  • pp: 5512–5524

Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers

Kunihito Hirano, Taiki Yamazaki, Shinichiro Morikatsu, Haruka Okumura, Hiroki Aida, Atsushi Uchida, Shigeru Yoshimori, Kazuyuki Yoshimura, Takahisa Harayama, and Peter Davis  »View Author Affiliations

Optics Express, Vol. 18, Issue 6, pp. 5512-5524 (2010)

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We experimentally demonstrate random bit generation using multi-bit samples of bandwidth-enhanced chaos in semiconductor lasers. Chaotic fluctuation of laser output is generated in a semiconductor laser with optical feedback and the chaotic output is injected into a second semiconductor laser to obtain a chaotic intensity signal with bandwidth enhanced up to 16 GHz. The chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 12.5 Giga samples per second (GS/s). Random bits are generated by bitwise exclusive-OR operation on corresponding bits in samples of the chaotic signal and its time-delayed signal. Statistical tests verify the randomness of bit sequences obtained using 1 to 6 bits per sample, corresponding to fast random bit generation rates from 12.5 to 75 Gigabit per second (Gb/s) ( = 6 bit × 12.5 GS/s).

© 2010 OSA

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(140.1540) Lasers and laser optics : Chaos
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.3100) Nonlinear optics : Instabilities and chaos

ToC Category:
Lasers and Laser Optics

Original Manuscript: December 7, 2009
Revised Manuscript: February 12, 2010
Manuscript Accepted: February 14, 2010
Published: March 3, 2010

Kunihito Hirano, Taiki Yamazaki, Shinichiro Morikatsu, Haruka Okumura, Hiroki Aida, Atsushi Uchida, Shigeru Yoshimori, Kazuyuki Yoshimura, Takahisa Harayama, and Peter Davis, "Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers," Opt. Express 18, 5512-5524 (2010)

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  1. D. Eastlake, J. Schiller, and S. Crocker, “Randomness requirements for security,” RFC4086 (2005) http://tools.ietf.org/html/rfc4086
  2. Security requirements for cryptographic modules. FIPS 140–2 (2001) http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf
  3. N. Gisin, G. Robordy, W. Tittel, and H. Zbinden, “Quantum Cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  4. N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949). [CrossRef] [PubMed]
  5. D. Knuth, “The Art of Computer Programming,” Volume 2: Seminumerical Algorithms (3rd Edition), Addison-Wesley Professional (1996).
  6. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44(6), 521–528 (1997). [CrossRef]
  7. J. T. Gleeson, “Truly random number generator based on turbulent electroconvection,” Appl. Phys. Lett. 81(11), 1949 (2002). [CrossRef]
  8. M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “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]
  9. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 1–3 (2008). [CrossRef]
  10. 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]
  11. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008). [CrossRef]
  12. T. E. Murphy and R. Roy, “The world’s fastest dice,” Nat. Photonics 2(12), 714–715 (2008). [CrossRef]
  13. 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(11), 1367–1379 (2009). [CrossRef]
  14. 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. Express 17(11), 9053–9061 (2009). [CrossRef] [PubMed]
  15. 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), 1–4 (2009). [CrossRef]
  16. Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28(5), 319–321 (2003). [CrossRef] [PubMed]
  17. A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection,” IEEE J. Quantum Electron. 39(11), 1462–1467 (2003). [CrossRef]
  18. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003). [CrossRef]
  19. A. Wang, Y. Wang, and H. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008). [CrossRef]
  20. H. Someya, I. Oowada, H. Okumura, T. Kida, and A. Uchida, “Synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback and injection,” Opt. Express 17(22), 19536–19543 (2009). [CrossRef] [PubMed]
  21. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998). [CrossRef] [PubMed]
  22. J.-P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252 (1998). [CrossRef]
  23. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005). [CrossRef]
  24. F.-Y. Lin and J.-M. Liu, “Chaotic lider,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004). [CrossRef]
  25. J. Ohtsubo, “Semiconductor Lasers, -Stability, Instability and Chaos-,” Second Ed., Springer-Verlag, Berlin Heidelberg (2005).
  26. 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,” National Institute of Standards and Technology, Special Publication 800–22, 2001; Revision 1, August 2008. http://csrc.nist.gov/publications/nistpubs/800-22-rev1/SP800-22rev1.pdf
  27. S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” arXiv:nlin.CD/0401040v1, 2004.
  28. G. Marsaglia, DIEHARD: A battery of tests of randomness. http://stat.fsu.edu/ geo, 1996.
  29. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010). [CrossRef]

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