On the structure of digital explicit nonlinear and inversive pseudorandom number generators |
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Authors: | Gottlieb Pirsic Arne Winterhof |
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Affiliation: | Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria |
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Abstract: | We analyze the lattice structure and distribution of the digital explicit inversive pseudorandom number generator introduced by Niederreiter and Winterhof as well as of a general digital explicit nonlinear generator. In particular, we extend a lattice test designed for this class of pseudorandom number generators to parts of the period and arbitrary lags and prove that these generators pass this test up to very high dimensions. We also analyze the behavior of digital explicit inversive and nonlinear generators under another very strong lattice test which in its easiest form can be traced back to Marsaglia and provides a complexity measure essentially equivalent to linear complexity. |
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Keywords: | Nonlinear pseudorandom number generator Lattice test Inversive method Complexity measure for sequences |
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