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On the Inversive Pseudorandom Number Generator

In: Recent Developments in Applied Probability and Statistics

Author

Listed:
  • Wilfried Meidl

    (Sabancı University, MDBF)

  • Alev Topuzoğlu

    (Sabancı University, MDBF)

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 $\mathbb{F}_{p}$ .

Suggested Citation

  • Wilfried Meidl & Alev Topuzoğlu, 2010. "On the Inversive Pseudorandom Number Generator," Springer Books, in: Luc Devroye & Bülent Karasözen & Michael Kohler & Ralf Korn (ed.), Recent Developments in Applied Probability and Statistics, pages 103-125, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2598-5_5
    DOI: 10.1007/978-3-7908-2598-5_5
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