On the inversive pseudorandom number generator
Meidl, Wilfried and Topuzoğlu, Alev (2010) On the inversive pseudorandom number generator. In: Devroye, Luc and Karasözen, Bülent and Kohler, Michael and Korn, Ralf, (eds.) Recent Developments in Applied Probability and Statistics. Springer-Verlag, Berlin Heidelberg, Germany, pp. 103-125. ISBN 978-3-7908-2598-5 ; 978-3-7908-2597-8
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Official URL: http://dx.doi.org/10.1007/978-3-7908-2598-5_5
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 F-p.
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