The Shortest Feedback Shift Register That Can Generate A Given Sequence

  • Cees J. A. Jansen
  • Dick E. Boekee
Conference paper

DOI: 10.1007/0-387-34805-0_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 435)
Cite this paper as:
Jansen C.J.A., Boekee D.E. (1990) The Shortest Feedback Shift Register That Can Generate A Given Sequence. In: Brassard G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY


In this paper the problem of finding the absolutely shortest (possibly nonlin- ear) feedback shift register, which can generate a given sequence with characters from some arbitrary finite alphabet, is considered. To this end, a new complex- ity measure is defined, called the maximum order complexity. A new theory of the nonlinear feedback shift register is developed, concerning elementary complexity properties of transposed and reciprocal sequences, and feedback functions of the maximum order feedback shift register equivalent. Moreover, Blumer’s algorithm is identified as a powerful tool for determining the maxi- mum order complexity profile of sequences, as well as their period, in linear time and memory. The typical behaviour of the maximum order complexity profile is shown and the consequences for the analysis of given sequences and the synthesis of feedback shift registers are discussed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 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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