On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials |
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Authors: | Hassan Aly Arne Winterhof |
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Institution: | (1) Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt;(2) Johann Radon Institute of Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria |
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Abstract: | Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography
and Monte-Carlo methods.
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom
number generation.
Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator
was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected.
Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number
generators with Dickson polynomials. |
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Keywords: | linear complexity profile nonlinear congruential generator Dickson polynomials cryptography |
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