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

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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https://hal.archives-ouvertes.fr/hal-01491790
Contributor : Aigle I2m <>
Submitted on : Friday, March 17, 2017 - 1:26:00 PM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

### Citation

Kevin Atighehchi, Stéphane Ballet, Alexis Bonnecaze, Robert Rolland. Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm. Mathematics of Computation, American Mathematical Society, 2017, 86 (308), pp.2975 - 3000. ⟨10.1090/mcom/3230⟩. ⟨hal-01491790⟩

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