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Cunningham numbers in modular arithmetic

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Abstract

The paper considers methods for modular arithmetic acceleration, based on a specific moduli selection method. Special attention is paid to the moduli of the form 2n − 1 and 2n + 1. Different schemes of choice of these types of moduli and algorithms for conversion of arbitrary precision integers into the modular representation and back are considered. Results of experimental implementation of the described algorithms in the GMP system are discussed.

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Authors and Affiliations

  1. Physics and Computer Science Department, Wilfrid Laurier University, 75 University Avenue West, N2L 3C5, Waterloo, Ontario, Canada

    E. V. Zima

  2. Symbolic Computation Group, University of Waterloo, 200 University Avenue West, N2L 3G1, Waterloo, Ontario, Canada

    A. M. Stewart

Authors
  1. E. V. Zima
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  2. A. M. Stewart
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Original Russian Text © E.V. Zima, A.M. Stewart, 2007, published in Programmirovanie, 2007, Vol. 33, No. 2.

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Zima, E.V., Stewart, A.M. Cunningham numbers in modular arithmetic. Program Comput Soft 33, 80–86 (2007). https://doi.org/10.1134/S0361768807020053

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  • DOI: https://doi.org/10.1134/S0361768807020053

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