Can Dynamic Neural Filters Produce Pseudo-Random Sequences?

  • Yishai M. Elyada
  • David Horn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3696)


Dynamic neural filters (DNFs) are recurrent networks of binary neurons. Under proper conditions of their synaptic matrix they are known to generate exponentially large cycles. We show that choosing the synaptic matrix to be a random orthogonal one, the average cycle length becomes close to that of a random map. We then proceed to investigate the inversion problem and argue that such a DNF could be used to construct a pseudo-random generator. Subjecting this generator’s output to a battery of tests we demonstrate that the sequences it generates may indeed be regarded as pseudo-random.


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  1. 1.
    Quenet, B., Horn, D.: The dynamic neural filter: a binary model of spatiotemporal coding. Neural Comput. 15, 309–329 (2003)zbMATHCrossRefGoogle Scholar
  2. 2.
    Hertz, J., Krogh, A., Palmer, R.G.: Introduction to the Theory of Neural Computation. Addison-Wesley Longman Publishing, Amsterdam (1991)Google Scholar
  3. 3.
    Peretto, P.: An Introduction to the Modeling of Neural Networks. Cambridge University Press, Cambridge (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Gutfreund, H., Reger, D.J., Young, A.P.: The nature of attractors in an asymmetric spin glass with deterministic dynamics. J. Phys. A: Math. Gen. 21, 2775–2797 (1988)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bastolla, U., Parisi, G.: Attractors in Fully Asymmetric Neural Networks. J. Phys. A: Math. Gen. 30, 5613–5631 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Karrasa, D.A., Zorkadis, V.: On neural network techniques in the secure management of communication systems through improving and quality assessing pseudorandom stream generators. Neural Networks 16, 899–905 (2003)CrossRefGoogle Scholar
  7. 7.
    Crounse, K., Yang, T., Chua, L.O.: Pseudo-random sequence generation using the cnn universal machine with applications to cryptography. In: Proc. IVth IEEE International Workshop on Cellular Neural Networks and Their Applications, pp. 433–438 (1996)Google Scholar
  8. 8.
    Yao, A.C.: Theory and applications of trapdoor functions. In: Proc. 23th FOCS, pp. 464–479 (1982)Google Scholar
  9. 9.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13, 850–864 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Massey, J.L.: An introduction to contemporary cryptology. Proc. of the IEEE 76, 533–549 (1988)CrossRefGoogle Scholar
  11. 11.
    Goldreich, O.: Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Goldreich, O., Levin, L.: Hard-core predicates for any one-way function. In: Proc. of the 21st ACM STOC, pp. 25–32 (1989)Google Scholar
  13. 13.
    Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. John Wiley and Sons, Chichester (1988)zbMATHGoogle Scholar
  14. 14.
    Johnson, E., Nemhauser, G., Savelsbergh, M.: Progress in linear programming based branch-and-bound algorithms: An exposition. INFORMS J. Comp. 12, 2–23 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Makhorin, A.: Gnu linear programming kit version 4.4. Free Software Foundation (2004)Google Scholar
  16. 16.
    Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J., Vo, S.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. In: NIST (2001),–22b.pdf
  17. 17.
    Soto, J.: Statistical testing of random number generators. In: Proc. 22nd NISSC (1999)Google Scholar
  18. 18.
    Driver, P.M., Humphries, N.: Protean Behavior: The Biology of Unpredictability. Oxford University Press, Oxford (1988)Google Scholar
  19. 19.
    Rapoport, A., Budescu, D.V.: Generation of random series in two-person strictly competitive games. J. Exp. Psych.: Gen. 121, 352–363 (1992)CrossRefGoogle Scholar
  20. 20.
    Neuringer, A.: Can people behave ”randoml”? the role of feedback. J. Exp Psych: Gen. 115, 62–75 (1986)CrossRefGoogle Scholar
  21. 21.
    Neuringer, A., Voss, C.: Approximating chaotic behavior. Psych. Sci. 4, 113–119 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yishai M. Elyada
    • 1
  • David Horn
    • 2
  1. 1.Max-Planck Institute of NeurobiologyDepartment of Systems and Computational NeurobiologyMartinsriedGermany
  2. 2.School of Physics and Astronomy, Raymond & Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael

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