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Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332341
Description: 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. ... More
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Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/339382
Description: D. Gómez-Pérez, A. Ostafe, A.P. Nicol-Las and D. Sadornil have recently shown that for almost all polynomials f ∈ Fq[X] over the finite field of q elements, where q is an odd prime power, their iterat ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/195847
Description: We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well ... More
Reviewed: Reviewed
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/178175
Description: 13 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173573
Description: We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a prime ... More
Reviewed: Reviewed
Authors: Ostafe, Alina
Date: 2012
Language: eng
Resource Type: conference paper abstract
Identifier: http://hdl.handle.net/1959.14/217475
Description: The goal of this talk is to present the state-of-the-art construction of pseudorandom number generators (PRNGs) using multivariate polynomials or rational functions. We recall that all previously know ... More
Reviewed: Reviewed
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/176439
Description: We recall that a polynomial f(X)= K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) = ℤ[X] are stable over ℚ. We ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/205033
Description: For a polynomial f∈Fp[X] , we obtain upper bounds on the number of points (x, f (x)) modulo a prime p which belong to an arbitrary square with the side length H. Our results in particular are based on ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/177143
Description: We obtain a new estimate on the discrepancy of the power generator over a part of the period that improves several previous results. We also introduce a multidimensional analogue and show that the cor ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/214862
Description: We extend recent results of Gomez and Winterhof, and Ostafe and Shparlinski on the Waring problem with univariate Dickson polynomials in a finite field to the multivariate case. We give some sufficien ... More
Reviewed: Reviewed
Authors: Ostafe, Alina
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/195232
Description: In this paper we study the period of vector sequences generated by triangular polynomial systems and we characterize the case when their orbits are of maximal period. Moreover, we estimate multiplicat ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/151252
Description: We estimate multiplicative character sums along the orbits of a class of nonlinear recurrence vector sequences. In the one-dimensional case, only much weaker estimates are known and our results have n ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/159883
Description: 16 page(s)
Reviewed: Reviewed
Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146978
Description: We improve recent results of D. Gomez and A. Winterhof on the Waring problem with Dickson polynomials in finite fields. Our approach is based on recent advances in arithmetic combinatorics in arbitrar ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146993
Description: We obtain some theoretical and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Ferm ... More
Reviewed: Reviewed