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On the average distribution of pseudorandom numbers generated by nonlinear permutations


Author: Igor E. Shparlinski
Journal: Math. Comp. 80 (2011), 1053-1061
MSC (2010): Primary 11K45, 11T23, 65C10
DOI: https://doi.org/10.1090/S0025-5718-2010-02408-1
Published electronically: August 31, 2010
MathSciNet review: 2772110
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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.


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Additional Information

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, NSW 2109, Australia
Email: igor.shparlinski@mq.edu.au

DOI: https://doi.org/10.1090/S0025-5718-2010-02408-1
Keywords: Pseudorandom numbers, inversive congruential generator, permutation polynomial
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.