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On the Inversive Pseudorandom Number Generator

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Recent Developments in Applied Probability and Statistics

Abstract

The inversive generator was introduced by J. Eichenauer and J. Lehn in 1986. A large number of papers on this generator have appeared in the last three decades, some investigating its properties, some generalizing it. It has been shown that the generated sequence and its variants behave very favorably with respect to most measures of randomness.

In this survey article we present a comprehensive overview of results on the inversive generator, its generalizations and variants. As regards to recent work, our emphasis is on a particular generalization, focusing on the underlying permutation P(x)=ax p−2+b of \(\mathbb{F}_{p}\).

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Authors and Affiliations

  1. MDBF, Sabancı University, Orhanlı, 34956, Tuzla, İstanbul, Turkey

    Wilfried Meidl & Alev Topuzoğlu

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  1. Wilfried Meidl
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  2. Alev Topuzoğlu
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Correspondence to Wilfried Meidl .

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Editors and Affiliations

  1. , School of Computer Science, McGill University, University St., Montreal, H9X 3V9, Canada

    Luc Devroye

  2. , Mathematics & Institute of Applied Mathe, Middle East Technical University, Inonu Bulvari, Ankara, 06531, Turkey

    Bülent Karasözen

  3. FB Mathematik, TU Darmstadt, Schloßgartenstr. 7, Darmstadt, 64289, Germany

    Michael Kohler

  4. , Mathematics, University of Kaiserslautern, E.-Schrödinger-Str., Kaiserslautern, 67663, Germany

    Ralf Korn

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Meidl, W., Topuzoğlu, A. (2010). On the Inversive Pseudorandom Number Generator. In: Devroye, L., Karasözen, B., Kohler, M., Korn, R. (eds) Recent Developments in Applied Probability and Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2598-5_5

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