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Lattice Structure of Nonlinear Pseudorandom Number Generators in Parts of the Period

In: Monte Carlo and Quasi-Monte Carlo Methods 2002

Author

Listed:
  • Gerhard Dorfer

    (Vienna University of Technology, Department of Algebra and Computational Mathematics)

  • Arne Winterhof

    (National University of Singapore, Temasek Laboratories)

Abstract

Summary Recently, we showed that an extension of Marsaglia’s lattice test for segments of sequences over arbitrary fields and the linear complexity profile provide essentially equivalent quality measures for the intrinsic structure of pseudorandom number sequences. More precisely, the knowledge of the linear complexity profile yields a value S such that the largest dimension for passing the above lattice test is either S or S — 1. In the present paper for periodic sequences over finite fields and sufficiently long parts of the period we determine the exact value S or S —1. As an application we deduce from recently obtained lower bounds on the linear complexity profile of certain nonlinear pseudorandom number generators new results on their lattice structure.

Suggested Citation

  • Gerhard Dorfer & Arne Winterhof, 2004. "Lattice Structure of Nonlinear Pseudorandom Number Generators in Parts of the Period," Springer Books, in: Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 199-211, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18743-8_11
    DOI: 10.1007/978-3-642-18743-8_11
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