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On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Hassan Aly

  2. Johann Radon Institute of Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria

    Arne Winterhof

Authors
  1. Hassan Aly
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  2. Arne Winterhof
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Correspondence to Hassan Aly.

Additional information

Communicated by: G. Mullen

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Aly, H., Winterhof, A. On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials. Des Codes Crypt 39, 155–162 (2006). https://doi.org/10.1007/s10623-005-3190-x

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  • DOI: https://doi.org/10.1007/s10623-005-3190-x

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