New modular multiplication and division algorithms based on continued fraction expansion

Mourad Gouicem 1
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are based on the Euclidean algorithm and are of quadratic complexity.
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https://hal.archives-ouvertes.fr/hal-00800497
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Submitted on : Wednesday, March 13, 2013 - 5:25:37 PM
Last modification on : Thursday, March 21, 2019 - 1:21:00 PM
Long-term archiving on : Friday, June 14, 2013 - 7:25:06 AM

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  • HAL Id : hal-00800497, version 1
  • ARXIV : 1303.3445

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Mourad Gouicem. New modular multiplication and division algorithms based on continued fraction expansion. 2013. ⟨hal-00800497⟩

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