Skip to main content

Ultra-Fast Physical Generation of Random Numbers Using Hybrid Boolean Networks

  • Chapter
  • First Online:
Dynamics of Complex Autonomous Boolean Networks

Part of the book series: Springer Theses ((Springer Theses))

Abstract

I discuss in this chapter how chaotic dynamics in autonomous Boolean networks can be used for high-speed physical random number generation. I start this chapter in Sect. 5.1 with an introduction to random number generation (Results of this chapter are published in reference Rosin et al. Phys Rev E 87: 040902(R), 2013.). In Sect. 5.2, I develop a hybrid Boolean network that consists of both autonomous and synchronous Boolean nodes. In Sect. 5.3, the Boolean network is utilized for random number generation. The main contribution of this chapter are:

  • introducing a network-based approach to random number generation, which allows for post-processing schemes that do not reduce the rate or increase the size of the system;

  • realizing a physical random number generator based on a chaotic Boolean system with a compact circuit that is inexpensive and can be integrated with other components as a system on a chip (SoC);

  • realizing an ultra-high bit rate of \(12.8\,\mathrm {GHz}\).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The letters RSA are the initials of the inventors Ron Rivest, Adi Shamir, and Leonard Adleman.

References

  1. D.P. Rosin, D. Rontani, D.J. Gauthier, Ultrafast physical generation of random numbers using hybrid Boolean networks. Phys. Rev. E 87, 040902(R) (2013)

    Article  ADS  Google Scholar 

  2. S. Asmussen, P.W. Glynn, Stochastic Simulation: Algorithms and Analysis (Springer, Berlin, 2007)

    Google Scholar 

  3. B. Jun, P. Kocher, The Intel random number generator. White paper prepared for Intel Corporation (1999), http://decuslib.com/decus/vmslt99a/sec/intelrng.pdf

  4. S. Nakamoto, Bitcoin: a peer-to-peer electronic cash system (2008), http://s.kwma.kr/pdf/Bitcoin/bitcoin.pdf

  5. K. Binder, D.W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, New York, 2010)

    Book  Google Scholar 

  6. N. Metropolis, S. Ulam, The Monte Carlo method. J. Am. Statist. Assoc. 44, 335 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  7. C.Z. Mooney, Monte Carlo Simulation (Sage, Thousand Oaks, 1997)

    Book  MATH  Google Scholar 

  8. V. Vedral, J. Friedman, Introduction to Quantum Information Science, vol. 1 (Oxford University Press, Oxford, 2006)

    Book  MATH  Google Scholar 

  9. S. Singh, The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography (Random House LLC, New York, 2011)

    Google Scholar 

  10. J. Katz, Y. Lindell, Introduction to Modern Cryptography: Principles and Protocols (CRC Press, Boca Raton, 2007)

    Google Scholar 

  11. S. Robinson, Still guarding secrets after years of attacks, RSA earns accolades for its founders. SIAM News 36, 1 (2003)

    Google Scholar 

  12. L.M. Adleman, R.L. Rivest, A. Shamir, Cryptographic communications system and method, US Patent 4,405,829, 1983

    Google Scholar 

  13. N. Perlroth, Experts find a door ajar in an Internet security method thought safe. New York Times (2014), http://bits.blogs.nytimes.com/2014/04/08/flaw-found-in-key-method-for-protecting-data-on-the-internet/. Accessed 8 April 2014

  14. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, S. Vo, A statistical tests suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800–22 (2001)

    Google Scholar 

  15. I. Goldberg, D. Wagner, Randomness and the Netscape Browser. Dr. Dobb’s J. 21, 66 (1996)

    Google Scholar 

  16. M.A. Wayne, P.G. Kwiat, Low-bias high-speed quantum random number generator via shaped optical pulses. Opt. Express 18, 9351 (2010)

    Article  ADS  Google Scholar 

  17. T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K.I. Arai, A. Uchida, P. Davis, Theory of fast nondeterministic physical random-bit generation with chaotic lasers. Phys. Rev. E 85, 046215 (2012)

    Article  ADS  Google Scholar 

  18. I. Reidler, Y. Aviad, M. Rosenbluh, I. Kanter, Ultrahigh-speed random number generation based on a chaotic semiconductor laser. Phys. Rev. Lett. 103, 024102 (2009)

    Article  ADS  Google Scholar 

  19. T. Stojanovski, J. Pihl, L. Kocarev, Chaos-based random number generators. Part II: practical realization. IEEE Trans. Circuits Syst. I 48, 382 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, Fast physical random bit generation with chaotic semiconductor lasers. Nat. Photonics 2, 728 (2008)

    Article  ADS  Google Scholar 

  21. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, M. Rosenbluh, An optical ultrafast random bit generator. Nat. Photonics 4, 58 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, Fast nondeterministic random-bit generation using on-chip chaos lasers. Phys. Rev. A 83, 031803(R) (2011)

    Article  ADS  Google Scholar 

  24. W. Li, I. Reidler, Y. Aviad, Y. Huang, H. Song, Y. Zhang, M. Rosenbluh, I. Kanter, Fast physical random-number generation based on room-temperature chaotic oscillations in weakly coupled superlattices. Phys. Rev. Lett. 111, 044102 (2013)

    Article  ADS  Google Scholar 

  25. T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)

    Book  MATH  Google Scholar 

  26. N.N. Taleb, The Black Swan: The Impact of the Highly Improbable Fragility (Random House LLC, New York, 2010)

    Google Scholar 

  27. P. Horowitz, W. Hill, T.C. Hayes, The Art of Electronics, vol. 2 (Cambridge University Press, Cambridge, 1989)

    Google Scholar 

  28. B. Sunar, W.J. Martin, D.R. Stinson, A provably secure true random number generator with built-in tolerance to active attacks. IEEE Trans. Comput. 56, 109 (2007)

    Article  MathSciNet  Google Scholar 

  29. K. Wold, C.H. Tan, Analysis and enhancement of random number generator in FPGA based on oscillator rings. Int. J. Reconf. Comput. 2009, 501672 (2009)

    Google Scholar 

  30. M. Dichtl, J. Golić, High-Speed True Random Number Generation with Logic Gates Only, in Cryptographic Hardware and Embedded Systems—CHES 2007, ed. by P. Paillier, I. Verbauwhede (Springer, New York, 2007), pp. 45–62

    Chapter  Google Scholar 

  31. C. Baetoniu, Method and apparatus for true random number generation, U.S. Patent 7,389,316, 2008

    Google Scholar 

  32. A. Hajimiri, T.H. Lee, A general theory of phase noise in electrical oscillators. IEEE J. Solid-St. Circ. 33, 179 (1998)

    Article  Google Scholar 

  33. S. Ihara, Information Theory for Continuous Systems, vol. 2 (World Scientific, Singapore, 1993)

    Book  MATH  Google Scholar 

  34. L. Glass, C. Hill, Ordered and disordered dynamics in random networks. Europhys. Lett. 41, 599 (1998)

    Article  ADS  Google Scholar 

  35. T. Mestl, C. Lemay, L. Glass, Chaos in high-dimensional neural and gene networks. Phys. D 98, 33 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  36. M. Khellah, S. Brown, Z. Vranesic, Minimizing interconnection delays in array-based FPGAs, in Proceedings of the IEEE Custom Integrated Circuits Conference (IEEE, 1994), pp. 181–184

    Google Scholar 

  37. C. Maxfield, FPGAs World Class Designs (Newnes, Burlington, 2009)

    Google Scholar 

  38. R. Zhang, H.L.D.S. de Cavalcante, Z. Gao, D.J. Gauthier, J.E.S. Socolar, M.M. Adams, D.P. Lathrop, Boolean chaos. Phys. Rev. E 80, 045202 (2009)

    Article  ADS  Google Scholar 

  39. J.S. White, A t-test for the serial correlation coefficient. Ann. Math. Stat. 28, 1046 (1957)

    Article  MATH  Google Scholar 

  40. Z. Gao, H.L.D.S. de Cavalcante, S.D. Cohen, R. Zhang, J.E.S. Socolar, D.J. Gauthier, Using synchronization of chaos to identify multiple delay times in Boolean-delay systems. Poster Presentation, 2009

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David P. Rosin .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Rosin, D.P. (2015). Ultra-Fast Physical Generation of Random Numbers Using Hybrid Boolean Networks. In: Dynamics of Complex Autonomous Boolean Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-13578-6_5

Download citation

Publish with us

Policies and ethics