Abstract
A cellular automata-based linear model that computes all the solutions of linear binary difference equations has been developed. Such a model is based on successive concatenations of a basic linear automaton. Different sequential solutions are obtained from different automaton initial states. Many of these solutions are binary sequences of cryptographic utility. In this way, a linear structure based on cellular automata realizes not only difference equation solutions but also generates sequences currently used in cryptography. The model is simple, linear and can be applied in a range of practical cryptographic applications.
This work has been developed in the frame of the project HESPERIA ( http://www. proyecto-hesperia.org ) under programme CENIT and supported by Centro para el Desarrollo Tecnológico Industrial (CDTI) as well as by the companies: Soluziona, Unión Fenosa, Tecnobit, Visual-Tools, BrainStorm, SAC and TechnoSafe.
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.
References
Beth, T., Piper, F.: The Stop-and-Go Generator. In: EUROCRYPT 1984. LNCS, vol. 228. Springer, Heidelberg (1985)
Bluetooth, Specifications of the Bluetooth system, http://www.bluetooth.com/
Cattell., K., et al.: 2-by-n Hybrid Cellular Automata with Regular Configuration: Theory and Application. IEEE Trans. Computers 48(3), 285–295 (1999)
Coppersmith, D., Krawczyk, H., Mansour, Y.: The Shrinking Generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)
Fúster-Sabater, A., de la Guía-Martínez, D.: Linealization of Stream Ciphers. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 612–622. Springer, Heidelberg (2004)
Fúster-Sabater, A., Caballero-Gil, P.: Cellular Automata in Cryptanalysis of Stream Ciphers. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 611–616. Springer, Heidelberg (2006)
Gollmann, D., Chambers, W.G.: Clock-Controlled Shift Register. IEEE J. Selected Areas Commun. 7(4), 525–533 (1987)
Gong, G.: Theory and Applications of q-ary Interleaved Sequences. IEEE Trans. Information Theory 41(2), 400–411 (1995)
GSM, Global Systems for Mobile Communications, http://cryptome.org/gsm-a512.htm
Jennings, S.M.: Multiplexed Sequences: Some Properties. In: EUROCRYPT 1982. LNCS, vol. 149. Springer, Heidelberg (1983)
Kari, J.: Theory of cellular automata: A survey. Theoretical Computer Science 334, 3–33 (2005)
Key, E.L.: An Analysis of the Structure and Complexity of Nonlinear Binary Sequence Generators. IEEE Trans. Informat. Theory 22(6), 732–736 (1976)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1986)
Wolfram, S.: Random Sequence Generation by Cellular Automata. Adv. in Appl. Math. 7, 127–169 (1986)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fúster-Sabater, A., Caballero-Gil, P., Delgado, O. (2008). Cellular Automata-Based Structures to Compute the Solutions of Linear Difference Equations. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-79992-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
eBook Packages: Computer ScienceComputer Science (R0)