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On the significance of the directed acyclic word graph in cryptology

  • Section 8 Theory
  • Conference paper
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Advances in Cryptology — AUSCRYPT '90 (AUSCRYPT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 453))

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Abstract

Blumer's algorithm can be used to build a Directed Acyclic Word Graph (DAWG) in linear time and memory from a given sequence of characters. In this paper we introduce the DAWG and show that Blumer's algorithm can be used very effectively to determine the maximum order (or nonlinear) complexity profile of a given sequence. We also show that this algorithm can be used to determine the period of a periodic sequence in linear time and memory. It also appears that the DAWG is an even more efficient means of generating the sequence, given a number of characters, than e.g. the nonlinear feedback shift register equivalent of that sequence, as it always needs the least amount of characters to generate the remainder of the sequence.

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References

  1. A. Blumer, J. Blumer, A. Ehrenfeucht, D. Haussler and R. McConnell. “Linear Size Finite Automata for the Set of all Subwords of a Word: An Outline of Results”, Bul. Eur. Assoc. Theor. Comp. Sci., no. 21, pp. 12–20, 1983.

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  2. A. Blumer. “A Generalization of Run-Length Coding”, IEEE Intern. Symp. on Info. Theory 1985, Brighton, England, June 24–28, 1985.

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  3. N. G. de Bruijn. “A Combinatorial Problem”, Nederl. Akad. Wetensch. Proc., vol. 49, pp. 758–754, 1946.

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  4. C. J. A. Jansen. Investigations On Nonlinear Streamcipher Systems: Construction and Evaluation Methods, PhD. Thesis, Technical University of Delft, Delft, april 1989.

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  5. R. A. Rueppel. New Approaches to Stream Ciphers, PhD. Thesis, Swiss Federal Institute of Technology, Zurich, 1984.

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Author information

Authors and Affiliations

  1. Philips USFA B.V., P.O. Box 218, 5600 MD, Eindhoven, The Netherlands

    Cees J. A. Jansen

  2. Technical University of Delft, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Dick E. Boekee

Authors
  1. Cees J. A. Jansen
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  2. Dick E. Boekee
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Editor information

Jennifer Seberry Josef Pieprzyk

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© 1990 Springer-Verlag Berlin Heidelberg

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Jansen, C.J.A., Boekee, D.E. (1990). On the significance of the directed acyclic word graph in cryptology. In: Seberry, J., Pieprzyk, J. (eds) Advances in Cryptology — AUSCRYPT '90. AUSCRYPT 1990. Lecture Notes in Computer Science, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030372

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  • DOI: https://doi.org/10.1007/BFb0030372

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53000-8

  • Online ISBN: 978-3-540-46297-2

  • eBook Packages: Springer Book Archive

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