Chapter

Recent Developments in Applied Probability and Statistics

pp 103-125

On the Inversive Pseudorandom Number Generator

  • Wilfried MeidlAffiliated withMDBF, Sabancı University Email author 
  • , Alev TopuzoğluAffiliated withMDBF, Sabancı University

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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 \(\mathbb{F}_{p}\).