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Pseudorandom numbers and hash functions from iterations of multivariate polynomials

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Abstract

Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather stronger bounds on the discrepancy for pseudorandom vectors generated by these iterations. Here we add new arguments to our original approach and also extend some of our recent constructions and results to more general orbits of polynomial iterations which may involve distinct polynomials as well. Using this construction we design a new class of hash functions from iterations of polynomials and use our estimates to motivate their “mixing” properties.

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Acknowledgements

The authors are grateful to the Fields Institute for its support and stimulating atmosphere which led to the initiation of this work at the “Fields Cryptography Retrospective Meeting” Toronto, 2009.

During the preparation of this paper, A. O. was supported in part by the Swiss National Science Foundation Grant 121874 and I. S. by the Australian Research Council Grant DP0556431.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Alina Ostafe

  2. Department of Computing, Macquarie University, Sydney, New South Wales, 2109, Australia

    Igor E. Shparlinski

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  1. Alina Ostafe
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  2. Igor E. Shparlinski
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Correspondence to Igor E. Shparlinski.

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Ostafe, A., Shparlinski, I.E. Pseudorandom numbers and hash functions from iterations of multivariate polynomials. Cryptogr. Commun. 2, 49–67 (2010). https://doi.org/10.1007/s12095-009-0016-0

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