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Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

 It is shown that a q-periodic sequence over the finite field F q passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large. The consequences of this result for nonlinear and inversive pseudorandom number generators are worked out.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore (e-mail: nied@math.nus.edu.sg), , , , , , SG

    Harald Niederreiter

  2. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010 Vienna, Austria (e-mail: arne.winterhof@oeaw.ac.at), , , , , , AT

    Arne Winterhof

Authors
  1. Harald Niederreiter
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  2. Arne Winterhof
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Received: October 2, 2001

Keywords: Pseudorandom number generator, Nonlinear method, Inversive method, Linear complexity, Marsaglia's lattice test.

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Niederreiter, H., Winterhof, A. Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers. AAECC 13, 319–326 (2002). https://doi.org/10.1007/s002000200105

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  • DOI: https://doi.org/10.1007/s002000200105

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