On the correlation of pseudorandom numbers generated by inversive methods

We introduce two new types of inversive generators for pseudorandom numbers. These new methods offer several advantages over the conventional inversive generator. For instance, we establish good correlation properties of our generators that cannot be obtained for the conventional inversive generator with current methods. A new bound on character sums for finite fields is the essential technical tool for this work. Authors’ addresses: Harald Niederreiter, Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore; Jo?l Rivat, Institut de Mathématiques de Luminy, Université de la Méditerranée, CNRS-UMR 6206, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France