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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

   
 

 

Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm


Authors: Kevin Atighehchi, Stéphane Ballet, Alexis Bonnecaze and Robert Rolland
Journal: Math. Comp.
MSC (2010): Primary 12Y05, 14Q05, 14Q20
DOI: https://doi.org/10.1090/mcom/3230
Published electronically: March 29, 2017
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Abstract: Thanks to a new construction of the so-called Chudnovsky-
Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field $ \mathbb{F}_{16^{13}}$.


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Additional Information

Kevin Atighehchi
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, LIF, Marseille, France
Email: Kevin.Atighehchi@univ-amu.fr

Stéphane Ballet
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email: Stephane.Ballet@univ-amu.fr

Alexis Bonnecaze
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email: Alexis.Bonnecaze@univ-amu.fr

Robert Rolland
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email: Robert.Rolland@univ-amu.fr

DOI: https://doi.org/10.1090/mcom/3230
Received by editor(s): October 7, 2015
Received by editor(s) in revised form: June 13, 2016
Published electronically: March 29, 2017
Article copyright: © Copyright 2017 by the authors