Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Fast physical random bit generation with chaotic semiconductor lasers

Nature Photonics volume 2, pages 728–732 (2008)Cite this article

Abstract

Random number generators in digital information systems make use of physical entropy sources such as electronic and photonic noise to add unpredictability to deterministically generated pseudo-random sequences1,2. However, there is a large gap between the generation rates achieved with existing physical sources and the high data rates of many computation and communication systems; this is a fundamental weakness of these systems. Here we show that good quality random bit sequences can be generated at very fast bit rates using physical chaos in semiconductor lasers. Streams of bits that pass standard statistical tests for randomness have been generated at rates of up to 1.7 Gbps by sampling the fluctuating optical output of two chaotic lasers. This rate is an order of magnitude faster than that of previously reported devices for physical random bit generators with verified randomness. This means that the performance of random number generators can be greatly improved by using chaotic laser devices as physical entropy sources.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Structure of random bit sequence generator using two chaotic lasers.
Figure 2: Typical output signals from an experimental system.
Figure 3: Autocorrelation and spectral characteristics.

Similar content being viewed by others

References

  1. Eastlake, D., Schiller, J., & Crocker, S. Randomness requirements for security. Available at http://tools.ietf.org/html/rfc4086 RFC4086 2005.

  2. Security requirements for cryptographic modules. Available at http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf FIPS 140-2 (2001).

  3. Metropolis, N., & Ulam, S. The Monte Carlo method. J. Am. Statist. Assoc. 44, 335–341 (1949).

    Article  Google Scholar 

  4. Gisin, N., Robordy, G., Tittel, W., & Zbinden, H. Quantum cryptography. Rev. Modern Phys. 74, 145–195 (2002).

    Article  ADS  Google Scholar 

  5. Marsaglia, G. DIEHARD: A battery of tests of randomness. Available at http://stat.fsu.edu/∼geo (1996).

  6. Rukhin, A. et al. A statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards and Technology, Special Publication 800-22 (2001).

  7. Kim, S. J., Umeno, K. & Hasegawa, A. Corrections of the NIST statistical test suite for randomness. arXiv:nlin.CD/0401040v1 (2004).

  8. Galton, F. Dice for statistical experiments. Nature 42, 13–14 (1890).

    Article  ADS  Google Scholar 

  9. Knuth, D. The Art of Computer Programming: Volume 2: Seminumerical Algorithms 3rd edn (Addison-Wesley Professional, 1996).

  10. Kelsey, J. Entropy and Entropy Sources in X9.82 (NIST, 2004).

  11. Schindler, W. & Killmann, W. Evaluation criteria for true (physical) random number generators used in cryptographic applications. CHES 2002, Lecture Notes in Computer Science 2523, 431–449 (2002).

    MATH  Google Scholar 

  12. Jun, B. & Kocher, P. The Intel random number generator. White paper prepared for Intel Corporation, Cryptography Research Inc. Available at http://www.cryptography.com/resources/whitepapers/IntelRNG.pdf. (1999).

  13. Holman, W. T., Connelly, J. A. & Dowlatabadi, A. B. An integrated analog/digital random noise source. IEEE Trans. Circuits and Systems I 44, 521–528 (1997).

    Article  Google Scholar 

  14. Dynes, J. F., Yuan, Z. L., Sharpe, A. W. & Shields, A. J. A high speed, post-processing free, quantum random number generator, arxiv/0807.4111v1 (July 2008).

  15. Cortigiani, F., Petri, C., Rocchi, S. & Vignoli, V. Very high-speed true random noise generator. The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

  16. Bucci, M., Germani, L., Luzzi, R., Trifiletti, A. & Varanouvo, M. A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC. IEEE Trans. Comput. 52, 403–409 (2003).

    Article  Google Scholar 

  17. Tokunaga, C., Blaauw, D. & Mudge, T. True random number generator with a metastability-based quality control. IEEE J. Solid-State Circuits 43, 78–85 (2008).

    Article  ADS  Google Scholar 

  18. Ornstein, D. S. Ergodic theory, randomness and ‘chaos’. Science 243, 182–187 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  19. Wolfram, S. Random sequence generation by cellular automaton. Adv. Appl. Math. 7, 123–169 (1986).

    Article  MathSciNet  Google Scholar 

  20. Stojanovski, T. & Kocarev, L. Chaos-based random number generators-part I: analysis [cryptography]. IEEE Trans. Circ. Syst. I: Fund. Theory Appl. 48, 281–288 (2001).

    Article  Google Scholar 

  21. Pappu, R., Recht, B., Taylor, J. & Gershenfeld, N. Physical one-way functions. Science 297, 2026–2030 (2002).

    Article  ADS  Google Scholar 

  22. Gleeson, J. T. Truly random number generator based on turbulent electroconvection. Appl. Phys. Lett. 81, 1949–1951 (2002).

    Article  ADS  Google Scholar 

  23. Callegari, S., Rovatti, R. & Setti, G. Embeddable ADC-based true random number generator for cryptographic applications using nonlinear signal processing and chaos. IEEE Trans. Signal Process. 53, 793–805 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  24. VanWiggeren, G. D. & Roy, R. Communication with chaotic lasers. Science 279, 1198–1200 (1998).

    Article  ADS  Google Scholar 

  25. Argyris, A. et al. Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438, 343–346 (2005).

    Article  ADS  Google Scholar 

  26. Liu, J. M., Chen, H. F. & Tang, S. Synchronized chaotic optical communications at high bit rates. IEEE J. Quant. Electron. 38, 1184–1196 (2002).

    Article  ADS  Google Scholar 

  27. Lang, R. & Kobayashi, K. External optical feedback effects on semiconductor injection laser properties. IEEE J. Quant. Electron. 16, 347–355 (1980).

    Article  ADS  Google Scholar 

  28. Uchida, A., Liu, Y. & Davis, P. Characteristics of chaotic masking in synchronized semiconductor lasers. IEEE J. Quant. Electron. 39, 963–970 (2003).

    Article  ADS  Google Scholar 

  29. Bracikowski, C., Fox, R. F. & Roy, R. Amplification of intrinsic noise in a chaotic multimode laser system. Phys. Rev. A 45, 403–408 (1992).

    Article  ADS  Google Scholar 

  30. Uchida, A., Heil, T., Liu, Y., Davis, P. & Aida, T. High-frequency broad-band signal generation using a semiconductor laser with a chaotic optical injection. IEEE J. Quant. Electron. 39, 1462–1467 (2003).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors thank Y. Tonomura, N. Ueda, S. Makino, K. Nakazawa, M. Miyoshi and J. Muramatsu of NTT Communication Science Laboratories and S. Katagiri of Doshisha University for their support and encouragement. A.U. acknowledges support from NTT Corporation, Support Centre for Advanced Telecommunications Technology Research, and Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science. We thank K. Umeno, S.-J. Kim and H. Terai for advice on the statistical evaluation of random numbers. We are grateful to I. Fischer, L. Larger, C. R. Mirasso and R. Roy for helpful discussions on laser chaos.

Author information

Authors and Affiliations

  1. Department of Electronics and Computer Systems, Takushoku University, 815-1 Tatemachi, Hachioji, 193-0985, Tokyo, Japan

    Atsushi Uchida, Kazuya Amano, Masaki Inoue, Kunihito Hirano, Sunao Naito, Hiroyuki Someya, Isao Oowada, Takayuki Kurashige, Masaru Shiki & Shigeru Yoshimori

  2. Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama city, 338-8570, Saitama, Japan

    Atsushi Uchida

  3. NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, 619-0237, Kyoto, Japan

    Kazuyuki Yoshimura & Peter Davis

Authors
  1. Atsushi Uchida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazuya Amano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masaki Inoue
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kunihito Hirano
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sunao Naito
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hiroyuki Someya
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Isao Oowada
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Takayuki Kurashige
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Masaru Shiki
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Shigeru Yoshimori
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Kazuyuki Yoshimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Peter Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Atsushi Uchida.

Supplementary information

Supplementary Information

Supplementary Information (PDF 637 kb)

Supplementary Information

Supplementary Information (AVI 6802 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Uchida, A., Amano, K., Inoue, M. et al. Fast physical random bit generation with chaotic semiconductor lasers. Nature Photon 2, 728–732 (2008). https://doi.org/10.1038/nphoton.2008.227

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2008.227

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing