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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators


Authors: Domingo Gómez-Pérez, Alina Ostafe and Igor Shparlinski
Journal: Math. Comp. 83 (2014), 1535-1550
MSC (2010): Primary 11K45, 37A45; Secondary 11T71, 65C10, 94A60
Published electronically: September 30, 2013
MathSciNet review: 3167471
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Abstract: We present several general results that show how algebraic dynamical systems with a slow degree growth and also rational automorphisms can be used to construct stronger pseudorandom number generators. We then give several concrete constructions that illustrate the applicability of these general results.


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Additional Information

Domingo Gómez-Pérez
Affiliation: Department of Mathematics, University of Cantabria, Santander 39005, Spain
Email: domingo.gomez@unican.es

Alina Ostafe
Affiliation: Department of Computing, Macquarie University, Sydney NSW 2109, Australia
Email: alina.ostafe@mq.edu.au

Igor Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney NSW 2109, Australia
Address at time of publication: Department of Pure Mathematics, University of New South Wales, Sydney, \indent NSW 2052, Australia
Email: igor.shparlinski@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02780-9
Keywords: Pseudorandom numbers, polynomial iterations
Received by editor(s): May 19, 2012
Received by editor(s) in revised form: October 2, 2012, and November 16, 2012
Published electronically: September 30, 2013
Article copyright: © Copyright 2013 American Mathematical Society