Abstract
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Yi, X.: Hash function based on chaotic tent maps. IEEE Transactions on Circuits and Systems II: Express Briefs 52(6), 354–357 (2005)
Dawei, Z., Guanrong, C., Wenbo, L.: A chaos-based robust wavelet-domain watermarking algorithm. Chaos, Solitons and Fractals 22, 47–54 (2004)
Stojanovski, T., Kocarev, L.: Chaos-based random number generators-part I: analysis [cryptography]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48(3), 281–288 (2001)
Devaney, R.L.: An Introduction to Chaotic Dynamical Systems, 2nd edn. Addison-Wesley, Redwood City (1989)
Bahi, J.M., Guyeux, C.: Topological chaos and chaotic iterations, application to hash functions. In: WCCI 2010 IEEE World Congress on Computational Intelligence, Barcelona, Spain, pp. 1–7 (2010)
Banks, J., Brooks, J., Cairns, G., Stacey, P.: On devaney’s definition of chaos. Amer. Math. Monthly 99, 332–334 (1992)
Tarjan, R.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)
Bahi, J., Guyeux, C., Wang, Q.: A novel pseudo-random generator based on discrete chaotic iterations. In: INTERNET 2009 1-st Int. Conf. on Evolving Internet, Cannes, France, pp. 71–76 (2009)
Marsaglia, G.: Xorshift rngs. Journal of Statistical Software 8(14), 1–6 (2003)
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. National Institute of Standards and Technology (2010), http://csrc.nist.gov/groups/ST/toolkit/rng/documents/SP800-22rev1a.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bahi, J.M., Couchot, JF., Guyeux, C., Richard, A. (2011). On the Link between Strongly Connected Iteration Graphs and Chaotic Boolean Discrete-Time Dynamical Systems. In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-22953-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22952-7
Online ISBN: 978-3-642-22953-4
eBook Packages: Computer ScienceComputer Science (R0)