On the significance of the directed acyclic word graph in cryptology

  • Cees J. A. Jansen
  • Dick E. Boekee
Section 8 Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 453)


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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  1. [Blum 83]
    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.Google Scholar
  2. [Blum 85]
    A. Blumer. “A Generalization of Run-Length Coding”, IEEE Intern. Symp. on Info. Theory 1985, Brighton, England, June 24–28, 1985.Google Scholar
  3. [Debr 46]
    N. G. de Bruijn. “A Combinatorial Problem”, Nederl. Akad. Wetensch. Proc., vol. 49, pp. 758–754, 1946.Google Scholar
  4. [Jans 89]
    C. J. A. Jansen. Investigations On Nonlinear Streamcipher Systems: Construction and Evaluation Methods, PhD. Thesis, Technical University of Delft, Delft, april 1989.Google Scholar
  5. [Ruep 84]
    R. A. Rueppel. New Approaches to Stream Ciphers, PhD. Thesis, Swiss Federal Institute of Technology, Zurich, 1984.Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Cees J. A. Jansen
    • 1
  • Dick E. Boekee
    • 2
  1. 1.Philips USFA B.V.EindhovenThe Netherlands
  2. 2.Technical University of DelftDelftThe Netherlands

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