Abstract:We modify the approach of H. Niederreiter and I. E. Shparlinski and improve one of their results on the distribution of inversive congruential pseudorandom numbers over a finite field for almost all initial values. However the main application of the new method is a similar result for pseudorandom numbers generated by iterations of a nonlinear permutation polynomial over a finite field, to which the original approach of H. Niederreiter and I. E. Shparlinski does not apply.
- Igor E. Shparlinski
- Affiliation: Department of Computing, Macquarie University, NSW 2109, Australia
- MR Author ID: 192194
- Email: firstname.lastname@example.org
- Received by editor(s): July 9, 2009
- Received by editor(s) in revised form: December 21, 2009
- Published electronically: August 31, 2010
- Additional Notes: The author was supported in part by ARC Grant DP0881473
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Math. Comp. 80 (2011), 1053-1061
- MSC (2010): Primary 11K45, 11T23, 65C10
- DOI: https://doi.org/10.1090/S0025-5718-2010-02408-1
- MathSciNet review: 2772110