Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Quenet, B., Horn, D.: The dynamic neural filter: a binary model of spatiotemporal coding. Neural Comput. 15, 309–329 (2003)
Hertz, J., Krogh, A., Palmer, R.G.: Introduction to the Theory of Neural Computation. Addison-Wesley Longman Publishing, Amsterdam (1991)
Peretto, P.: An Introduction to the Modeling of Neural Networks. Cambridge University Press, Cambridge (1992)
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)
Bastolla, U., Parisi, G.: Attractors in Fully Asymmetric Neural Networks. J. Phys. A: Math. Gen. 30, 5613–5631 (1997)
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)
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)
Yao, A.C.: Theory and applications of trapdoor functions. In: Proc. 23th FOCS, pp. 464–479 (1982)
Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13, 850–864 (1984)
Massey, J.L.: An introduction to contemporary cryptology. Proc. of the IEEE 76, 533–549 (1988)
Goldreich, O.: Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)
Goldreich, O., Levin, L.: Hard-core predicates for any one-way function. In: Proc. of the 21st ACM STOC, pp. 25–32 (1989)
Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. John Wiley and Sons, Chichester (1988)
Johnson, E., Nemhauser, G., Savelsbergh, M.: Progress in linear programming based branch-and-bound algorithms: An exposition. INFORMS J. Comp. 12, 2–23 (2000)
Makhorin, A.: Gnu linear programming kit version 4.4. Free Software Foundation (2004)
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), http://csrc.nist.gov/rng/SP800–22b.pdf
Soto, J.: Statistical testing of random number generators. In: Proc. 22nd NISSC (1999)
Driver, P.M., Humphries, N.: Protean Behavior: The Biology of Unpredictability. Oxford University Press, Oxford (1988)
Rapoport, A., Budescu, D.V.: Generation of random series in two-person strictly competitive games. J. Exp. Psych.: Gen. 121, 352–363 (1992)
Neuringer, A.: Can people behave ”randoml”? the role of feedback. J. Exp Psych: Gen. 115, 62–75 (1986)
Neuringer, A., Voss, C.: Approximating chaotic behavior. Psych. Sci. 4, 113–119 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Elyada, Y.M., Horn, D. (2005). Can Dynamic Neural Filters Produce Pseudo-Random Sequences?. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Biological Inspirations – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550822_34
Download citation
DOI: https://doi.org/10.1007/11550822_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28752-0
Online ISBN: 978-3-540-28754-4
eBook Packages: Computer ScienceComputer Science (R0)